LMFDB - Embedded newform 1050.2.s.i.551.7

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			551.7
Root			$-0.418778 + 1.56290i$ of defining polynomial
Character	$\chi$	$=$	1050.551
Dual form			1050.2.s.i.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.707107 + 1.58114i) q^{6} +(-2.23607 - 1.41421i) q^{7} +1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.707107 + 1.58114i) q^{6} +(-2.23607 - 1.41421i) q^{7} +1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +(-4.05781 + 2.34278i) q^{11} +(-1.40294 + 1.01575i) q^{12} +1.04456i q^{13} +(-1.22938 - 2.34278i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.58114 - 2.73861i) q^{17} +(-2.85008 - 0.936492i) q^{18} +(1.23861 + 0.715113i) q^{19} +(2.03803 - 4.10444i) q^{21} -4.68556 q^{22} +(-3.87739 - 2.23861i) q^{23} +(-1.72286 + 0.178197i) 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} +(-4.75937 - 6.57357i) q^{33} -3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +(1.33146 - 2.30615i) q^{37} +(0.715113 + 1.23861i) q^{38} +(-1.79962 + 0.186137i) q^{39} -1.04456 q^{41} +(3.81721 - 2.53553i) 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} +(4.43649 - 3.21209i) q^{51} +(-0.904612 + 0.522278i) q^{52} +(4.33013 - 2.50000i) q^{53} +(1.10557 - 5.07718i) 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} +(7.43455 + 2.77984i) q^{63} -1.00000 q^{64} +(-0.834952 - 8.07256i) q^{66} +(-7.13505 - 12.3583i) q^{67} +(1.58114 - 2.73861i) q^{68} +(3.16588 - 7.07912i) q^{69} +6.92163i q^{71} +(-0.614017 - 2.93649i) 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} +(8.24597 - 3.60611i) q^{81} +(-0.904612 - 0.522278i) q^{82} -4.06775 q^{83} +(4.57357 - 0.287233i) q^{84} +(5.99430 + 3.46081i) q^{86} +(-11.9250 + 1.23341i) q^{87} +(-2.34278 - 4.05781i) q^{88} +(2.45877 - 4.25871i) q^{89} +(1.47723 - 2.33570i) q^{91} -4.47723i q^{92} +(-6.73076 - 9.29642i) q^{93} +(-9.71584 + 5.60944i) q^{94} +(-1.01575 - 1.40294i) 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}+O(q^{10}) $ 16 * q + 8 * q^4 - 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$4$	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
$9$	−2.93649	+	0.614017i	−0.978831	+	0.204672i
$10$		0			0
$11$	−4.05781	+	2.34278i	−1.22348	+	0.706374i	−0.965657	−	0.259819i	$-0.916337\pi$
$11$	−4.05781	+	2.34278i	−1.22348	+	0.706374i	−0.257819	+	0.966193i	$0.583004\pi$
$12$	−1.40294	+	1.01575i	−0.404994	+	0.293223i
$13$			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	0.608075	−	0.793880i	$-0.291942\pi$
$17$	−1.58114	−	2.73861i	−0.383482	−	0.664211i	−0.991557	+	0.129668i	$0.958609\pi$
$18$	−2.85008	−	0.936492i	−0.671771	−	0.220733i
$19$	1.23861	+	0.715113i	0.284157	+	0.164058i	0.635304	−	0.772262i	$-0.280875\pi$
$19$	1.23861	+	0.715113i	0.284157	+	0.164058i	−0.351147	+	0.936320i	$0.614208\pi$
$20$		0			0
$21$	2.03803	−	4.10444i	0.444735	−	0.895662i
$22$	−4.68556			−0.998964
$23$	−3.87739	−	2.23861i	−0.808492	−	0.466783i	0.0379400	−	0.999280i	$-0.487920\pi$
$23$	−3.87739	−	2.23861i	−0.808492	−	0.466783i	−0.846432	+	0.532497i	$0.821254\pi$
$24$	−1.72286	+	0.178197i	−0.351677	+	0.0363743i
$25$		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	−0.917181	−	0.398471i	$-0.869541\pi$
$31$	−5.73861	+	3.31319i	−1.03069	+	0.595066i	−0.113504	+	0.993537i	$0.536208\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.75937	−	6.57357i	−0.828500	−	1.14431i
$34$		−	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	$-0.763090\pi$
$37$	1.33146	−	2.30615i	0.218890	−	0.379129i	0.954469	+	0.298310i	$0.0964231\pi$
$38$	0.715113	+	1.23861i	0.116007	+	0.200930i
$39$	−1.79962	+	0.186137i	−0.288170	+	0.0298057i
$40$		0			0
$41$	−1.04456			−0.163132			−0.0815661	−	0.996668i	$-0.525992\pi$
$41$	−1.04456			−0.163132			−0.0815661	+	0.996668i	$0.525992\pi$
$42$	3.81721	−	2.53553i	0.589008	−	0.391241i
$43$	6.92163			1.05554			0.527769	−	0.849388i	$-0.323029\pi$
$43$	6.92163			1.05554			0.527769	+	0.849388i	$0.323029\pi$
$44$	−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	0.0887705	+	0.996052i	$0.471706\pi$
$47$	−5.60944	+	9.71584i	−0.818221	+	1.41720i	−0.906992	+	0.421149i	$0.861627\pi$
$48$	−1.58114	−	0.707107i	−0.228218	−	0.102062i
$49$	3.00000	+	6.32456i	0.428571	+	0.903508i
$50$		0			0
$51$	4.43649	−	3.21209i	0.621233	−	0.449783i
$52$	−0.904612	+	0.522278i	−0.125447	+	0.0724269i
$53$	4.33013	−	2.50000i	0.594789	−	0.343401i	−0.172200	−	0.985062i	$-0.555088\pi$
$53$	4.33013	−	2.50000i	0.594789	−	0.343401i	0.766989	+	0.641661i	$0.221754\pi$
$54$	1.10557	−	5.07718i	0.150449	−	0.690916i
$55$		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	0.972376	+	0.233418i	$0.0749911\pi$
$59$	5.28720	+	9.15769i	0.688334	+	1.19223i	−0.284042	+	0.958812i	$0.591676\pi$
$60$		0			0
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	0.679605	−	0.733578i	$-0.262151\pi$
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	−0.295495	+	0.955344i	$0.595484\pi$
$62$	−6.62638			−0.841551
$63$	7.43455	+	2.77984i	0.936665	+	0.350227i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.834952	−	8.07256i	−0.102776	−	0.993663i
$67$	−7.13505	−	12.3583i	−0.871685	−	1.50980i	−0.860253	−	0.509868i	$-0.829694\pi$
$67$	−7.13505	−	12.3583i	−0.871685	−	1.50980i	−0.0114319	−	0.999935i	$-0.503639\pi$
$68$	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	$0.865276\pi$
$72$	−0.614017	−	2.93649i	−0.0723626	−	0.346069i
$73$	−3.03397	+	1.75166i	−0.355099	+	0.205017i	−0.666929	−	0.745121i	$-0.732392\pi$
$73$	−3.03397	+	1.75166i	−0.355099	+	0.205017i	0.311830	+	0.950138i	$0.399058\pi$
$74$	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	−0.338508	−	0.940964i	$-0.609922\pi$
$79$	5.73861	−	9.93957i	0.645644	−	1.11829i	0.984152	−	0.177325i	$-0.0567445\pi$
$80$		0			0
$81$	8.24597	−	3.60611i	0.916219	−	0.400679i
$82$	−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	$0.571666\pi$
$84$	4.57357	−	0.287233i	0.499017	−	0.0313397i
$85$		0			0
$86$	5.99430	+	3.46081i	0.646382	+	0.373189i
$87$	−11.9250	+	1.23341i	−1.27849	+	0.132236i
$88$	−2.34278	−	4.05781i	−0.249741	−	0.432564i
$89$	2.45877	−	4.25871i	0.260629	−	0.451423i	−0.705780	−	0.708431i	$-0.749403\pi$
$89$	2.45877	−	4.25871i	0.260629	−	0.451423i	0.966409	+	0.257008i	$0.0827367\pi$
$90$		0			0
$91$	1.47723	−	2.33570i	0.154855	−	0.244848i
$92$		−	4.47723i		−	0.466783i
$93$	−6.73076	−	9.29642i	−0.697948	−	0.963994i
$94$	−9.71584	+	5.60944i	−1.00211	+	0.578570i
$95$		0			0
$96$	−1.01575	−	1.40294i	−0.103670	−	0.143187i
$97$			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	0.997244	+	0.0741967i	$0.0236393\pi$
$101$	5.65685	+	9.79796i	0.562878	+	0.974933i	−0.434366	+	0.900737i	$0.643027\pi$
$102$	5.44816	−	0.563508i	0.539448	−	0.0557956i
$103$	−4.25871	−	2.45877i	−0.419624	−	0.242270i	0.275293	−	0.961360i	$-0.411225\pi$
$103$	−4.25871	−	2.45877i	−0.419624	−	0.242270i	−0.694916	+	0.719091i	$0.744559\pi$
$104$	−1.04456			−0.102427
$105$		0			0
$106$	5.00000			0.485643
$107$	−4.74342	−	2.73861i	−0.458563	−	0.264752i	0.252877	−	0.967499i	$-0.418623\pi$
$107$	−4.74342	−	2.73861i	−0.458563	−	0.264752i	−0.711440	+	0.702747i	$0.751957\pi$
$108$	3.49604	−	3.84418i	0.336406	−	0.369906i
$109$	−10.2158	−	17.6944i	−0.978500	−	1.69481i	−0.667866	−	0.744282i	$-0.732792\pi$
$109$	−10.2158	−	17.6944i	−0.978500	−	1.69481i	−0.310634	−	0.950529i	$-0.600541\pi$
$110$		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	$0.307175\pi$
$113$			17.4772i			1.64412i	−0.569402	+	0.822060i	$0.692825\pi$
$114$	−2.00653	+	1.45276i	−0.187928	+	0.136063i
$115$		0			0
$116$	−5.99430	+	3.46081i	−0.556557	+	0.321328i
$117$	−0.641375	−	3.06733i	−0.0592951	−	0.283575i
$118$			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
$123$	−0.186137	−	1.79962i	−0.0167834	−	0.162267i
$124$	−5.73861	−	3.31319i	−0.515343	−	0.297533i
$125$		0			0
$126$	5.04858	+	6.12469i	0.449764	+	0.545631i
$127$	8.73085			0.774738			0.387369	−	0.921925i	$-0.373384\pi$
$127$	8.73085			0.774738			0.387369	+	0.921925i	$0.373384\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.23341	+	11.9250i	0.108596	+	1.04994i
$130$		0			0
$131$	−6.88624	+	11.9273i	−0.601654	+	1.04209i	0.390917	+	0.920426i	$0.372158\pi$
$131$	−6.88624	+	11.9273i	−0.601654	+	1.04209i	−0.992571	+	0.121669i	$0.961175\pi$
$132$	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	−0.365814	−	0.930688i	$-0.619209\pi$
$137$	3.01137	−	1.73861i	0.257278	−	0.148540i	0.623092	+	0.782148i	$0.285876\pi$
$138$	6.28129	−	4.54776i	0.534699	−	0.387131i
$139$			20.1810i			1.71173i	0.517202	+	0.855863i	$0.326974\pi$
$139$			20.1810i			1.71173i	−0.517202	+	0.855863i	$0.673026\pi$
$140$		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
$144$	0.936492	−	2.85008i	0.0780410	−	0.237507i
$145$		0			0
$146$	−3.50333			−0.289937
$147$	−10.3617	+	6.29560i	−0.854621	+	0.519252i
$148$	2.66291			0.218890
$149$	2.12132	+	1.22474i	0.173785	+	0.100335i	0.584370	−	0.811488i	$-0.301342\pi$
$149$	2.12132	+	1.22474i	0.173785	+	0.100335i	−0.410584	+	0.911823i	$0.634675\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−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
$156$	−1.06101	−	1.46545i	−0.0849489	−	0.117330i
$157$	12.5118	−	7.22369i	0.998550	−	0.576513i	0.0907311	−	0.995875i	$-0.471080\pi$
$157$	12.5118	−	7.22369i	0.998550	−	0.576513i	0.907819	+	0.419362i	$0.137746\pi$
$158$	9.93957	−	5.73861i	0.790750	−	0.456540i
$159$	5.07877	+	7.01471i	0.402772	+	0.556303i
$160$		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	0.420402	+	0.907338i	$0.361889\pi$
$163$	−7.34847	+	12.7279i	−0.575577	+	0.996928i	−0.995979	+	0.0895899i	$0.971444\pi$
$164$	−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	$0.446911\pi$
$168$	4.10444	+	2.03803i	0.316664	+	0.157238i
$169$	11.9089			0.916069
$170$		0			0
$171$	−4.07627	−	1.33940i	−0.311720	−	0.102426i
$172$	3.46081	+	5.99430i	0.263885	+	0.457061i
$173$	−0.564201	+	0.977226i	−0.0428954	+	0.0742971i	−0.886676	−	0.462391i	$-0.846992\pi$
$173$	−0.564201	+	0.977226i	−0.0428954	+	0.0742971i	0.843781	+	0.536688i	$0.180325\pi$
$174$	−10.9441	−	4.89433i	−0.829666	−	0.371038i
$175$		0			0
$176$		−	4.68556i		−	0.353187i
$177$	−14.8353	+	10.7410i	−1.11509	+	0.807341i
$178$	4.25871	−	2.45877i	0.319204	−	0.184293i
$179$	−16.7857	+	9.69125i	−1.25462	+	0.724358i	−0.972024	−	0.234880i	$-0.924530\pi$
$179$	−16.7857	+	9.69125i	−1.25462	+	0.724358i	−0.282600	+	0.959238i	$0.591197\pi$
$180$		0			0
$181$		−	3.16228i		−	0.235050i	−0.993070	−	0.117525i	$-0.962504\pi$
$181$		−	3.16228i		−	0.235050i	0.993070	−	0.117525i	$-0.0374961\pi$
$182$	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
$186$	−1.18080	−	11.4163i	−0.0865805	−	0.837085i
$187$	12.8319	+	7.40852i	0.938364	+	0.541764i
$188$	−11.2189			−0.818221
$189$	−3.46447	+	13.3040i	−0.252003	+	0.967726i
$190$		0			0
$191$	−14.1099	−	8.14637i	−1.02096	−	0.589451i	−0.106577	−	0.994304i	$-0.533989\pi$
$191$	−14.1099	−	8.14637i	−1.02096	−	0.589451i	−0.914381	+	0.404854i	$0.867322\pi$
$192$	−0.178197	−	1.72286i	−0.0128603	−	0.124337i
$193$	3.67423	+	6.36396i	0.264477	+	0.458088i	0.967427	−	0.253152i	$-0.0814673\pi$
$193$	3.67423	+	6.36396i	0.264477	+	0.458088i	−0.702949	+	0.711240i	$0.748134\pi$
$194$	−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	$-0.896112\pi$
$197$		−	9.00000i		−	0.641223i	0.947211	−	0.320612i	$-0.103888\pi$
$198$	13.7591	−	2.87701i	0.977817	−	0.204460i
$199$	−13.4317	+	7.75478i	−0.952146	+	0.549722i	−0.893747	−	0.448571i	$-0.851933\pi$
$199$	−13.4317	+	7.75478i	−0.952146	+	0.549722i	−0.0583993	+	0.998293i	$0.518600\pi$
$200$		0			0
$201$	20.0201	−	14.4949i	1.41211	−	1.02239i
$202$			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
$207$	12.7605	+	4.19288i	0.886914	+	0.291426i
$208$	−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
$213$	−11.9250	+	1.23341i	−0.817087	+	0.0845121i
$214$	−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
$219$	−3.55851	−	4.91496i	−0.240462	−	0.332122i
$220$		0			0
$221$	2.86064	−	1.65159i	0.192427	−	0.111098i
$222$	2.70486	+	3.73591i	0.181538	+	0.250738i
$223$		−	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	0.640451	−	0.767999i	$-0.278747\pi$
$227$	−5.19615	−	9.00000i	−0.344881	−	0.597351i	−0.985332	+	0.170648i	$0.945414\pi$
$228$	−2.46408	+	0.254862i	−0.163188	+	0.0168787i
$229$	11.7386	+	6.77729i	0.775709	+	0.447856i	0.834908	−	0.550390i	$-0.185521\pi$
$229$	11.7386	+	6.77729i	0.775709	+	0.447856i	−0.0591982	+	0.998246i	$0.518854\pi$
$230$		0			0
$231$	1.34585	+	21.4297i	0.0885503	+	1.40997i
$232$	−6.92163			−0.454427
$233$	3.46410	+	2.00000i	0.226941	+	0.131024i	0.609160	−	0.793047i	$-0.291507\pi$
$233$	3.46410	+	2.00000i	0.226941	+	0.131024i	−0.382219	+	0.924072i	$0.624840\pi$
$234$	0.978218	−	2.97707i	0.0639481	−	0.194617i
$235$		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	−0.958024	−	0.286689i	$-0.907445\pi$
$241$	−18.4545	+	10.6547i	−1.18876	+	0.686328i	−0.230732	+	0.973017i	$0.574112\pi$
$242$	9.48683	−	5.47723i	0.609837	−	0.352089i
$243$	7.68223	+	13.5640i	0.492815	+	0.870134i
$244$			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
$249$	−0.724861	−	7.00816i	−0.0459362	−	0.444124i
$250$		0			0
$251$	−8.85494			−0.558919			−0.279459	−	0.960158i	$-0.590155\pi$
$251$	−8.85494			−0.558919			−0.279459	+	0.960158i	$0.590155\pi$
$252$	1.30986	+	7.82843i	0.0825133	+	0.493145i
$253$	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	−0.984980	−	0.172669i	$-0.944761\pi$
$257$	−5.49798	+	9.52277i	−0.342954	+	0.594014i	0.642026	+	0.766683i	$0.278094\pi$
$258$	−4.89433	+	10.9441i	−0.304708	+	0.681347i
$259$	−6.23861	+	3.27374i	−0.387649	+	0.203421i
$260$		0			0
$261$	−4.24999	−	20.3253i	−0.263068	−	1.25810i
$262$	−11.9273	+	6.88624i	−0.736872	+	0.425433i
$263$	−1.73205	+	1.00000i	−0.106803	+	0.0616626i	−0.552450	−	0.833546i	$-0.686307\pi$
$263$	−1.73205	+	1.00000i	−0.106803	+	0.0616626i	0.445647	+	0.895209i	$0.352974\pi$
$264$	6.57357	−	4.75937i	0.404575	−	0.292919i
$265$		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	−0.999116	−	0.0420423i	$-0.986614\pi$
$269$	−8.79052	−	15.2256i	−0.535968	−	0.928323i	0.463148	−	0.886281i	$-0.346720\pi$
$270$		0			0
$271$	−5.47723	−	3.16228i	−0.332718	−	0.192095i	0.324329	−	0.945944i	$-0.394861\pi$
$271$	−5.47723	−	3.16228i	−0.332718	−	0.192095i	−0.657047	+	0.753850i	$0.728195\pi$
$272$	3.16228			0.191741
$273$	4.28732	+	2.12884i	0.259480	+	0.128843i
$274$	3.47723			0.210067
$275$		0			0
$276$	7.71363	−	0.797828i	0.464306	−	0.0480236i
$277$	4.89898	+	8.48528i	0.294351	+	0.509831i	0.974834	−	0.222933i	$-0.0715631\pi$
$277$	4.89898	+	8.48528i	0.294351	+	0.509831i	−0.680483	+	0.732764i	$0.738230\pi$
$278$	−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	$0.982814\pi$
$282$	−11.3956	−	15.7394i	−0.678599	−	0.937270i
$283$	−7.98873	+	4.61230i	−0.474881	+	0.274173i	−0.718281	−	0.695753i	$-0.755071\pi$
$283$	−7.98873	+	4.61230i	−0.474881	+	0.274173i	0.243400	+	0.969926i	$0.421737\pi$
$284$	−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
$291$	−20.6547	+	2.13633i	−1.21080	+	0.125234i
$292$	−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	$0.424381\pi$
$294$	−12.1213	+	0.271281i	−0.706930	+	0.0158214i
$295$		0			0
$296$	2.30615	+	1.33146i	0.134042	+	0.0773893i
$297$	18.0121	+	16.3809i	1.04517	+	0.950515i
$298$	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
$303$	−15.8725	+	11.4919i	−0.911850	+	0.660194i
$304$	−1.23861	+	0.715113i	−0.0710393	+	0.0410146i
$305$		0			0
$306$	1.94169	+	9.28600i	0.110999	+	0.530845i
$307$		−	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	$-0.000563970\pi$
$311$	8.79052	+	15.2256i	0.498465	+	0.863366i	−0.501534	+	0.865138i	$0.667231\pi$
$312$	−0.186137	−	1.79962i	−0.0105379	−	0.101884i
$313$	20.1246	+	11.6190i	1.13751	+	0.656742i	0.945813	−	0.324712i	$-0.105267\pi$
$313$	20.1246	+	11.6190i	1.13751	+	0.656742i	0.191697	+	0.981454i	$0.438601\pi$
$314$	14.4474			0.815313
$315$		0			0
$316$	11.4772			0.645644
$317$	−8.58136	−	4.95445i	−0.481977	−	0.278270i	0.239263	−	0.970955i	$-0.423094\pi$
$317$	−8.58136	−	4.95445i	−0.481977	−	0.278270i	−0.721240	+	0.692685i	$0.756428\pi$
$318$	0.890985	+	8.61430i	0.0499640	+	0.483066i
$319$	−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
$324$	7.24597	+	5.33816i	0.402554	+	0.296565i
$325$		0			0
$326$	−12.7279	+	7.34847i	−0.704934	+	0.406994i
$327$	28.6645	−	20.7535i	1.58515	−	1.14767i
$328$		−	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	0.405369	+	0.914153i	$0.367143\pi$
$331$	−10.7158	+	18.5604i	−0.588996	+	1.02017i	−0.994364	+	0.106017i	$0.966190\pi$
$332$	−2.03387	−	3.52277i	−0.111623	−	0.193337i
$333$	−2.49379	+	7.58952i	−0.136659	+	0.415903i
$334$	3.71584	+	2.14534i	0.203322	+	0.117388i
$335$		0			0
$336$	2.53553	+	3.81721i	0.138325	+	0.208246i
$337$	−17.1464			−0.934025			−0.467013	−	0.884251i	$-0.654670\pi$
$337$	−17.1464			−0.934025			−0.467013	+	0.884251i	$0.654670\pi$
$338$	10.3134	+	5.95445i	0.560976	+	0.323879i
$339$	−30.1108	+	3.11439i	−1.63539	+	0.169150i
$340$		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	−0.0353049	−	0.999377i	$-0.511240\pi$
$347$	15.1357	−	8.73861i	0.812528	−	0.469113i	0.847833	+	0.530263i	$0.177907\pi$
$348$	−7.03066	−	9.71064i	−0.376883	−	0.520545i
$349$		−	11.7436i		−	0.628623i	−0.949320	−	0.314311i	$-0.898226\pi$
$349$		−	11.7436i		−	0.628623i	0.949320	−	0.314311i	$-0.101774\pi$
$350$		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	0.873946	−	0.486023i	$-0.161553\pi$
$353$	0.301824	+	0.522774i	0.0160645	+	0.0278245i	−0.857881	+	0.513848i	$0.828220\pi$
$354$	−18.2182	+	1.88433i	−0.968286	+	0.100151i
$355$		0			0
$356$	4.91754			0.260629
$357$	−14.4629	+	0.908312i	−0.765457	+	0.0480730i
$358$	−19.3825			−1.02440
$359$	−9.86729	−	5.69688i	−0.520775	−	0.300670i	0.216476	−	0.976288i	$-0.430544\pi$
$359$	−9.86729	−	5.69688i	−0.520775	−	0.300670i	−0.737252	+	0.675618i	$0.763877\pi$
$360$		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
$366$	−4.85993	+	3.51867i	−0.254033	+	0.183924i
$367$	0.320133	−	0.184829i	0.0167108	−	0.00964798i	−0.491621	−	0.870809i	$-0.663596\pi$
$367$	0.320133	−	0.184829i	0.0167108	−	0.00964798i	0.508332	+	0.861161i	$0.330262\pi$
$368$	3.87739	−	2.23861i	0.202123	−	0.116696i
$369$	3.06733	−	0.641375i	0.159679	−	0.0333887i
$370$		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	−0.391673	−	0.920104i	$-0.628104\pi$
$373$	11.6072	−	20.1042i	0.600997	−	1.04096i	0.992670	−	0.120853i	$-0.0385630\pi$
$374$	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
$378$	−9.65234	+	9.78940i	−0.496463	+	0.503513i
$379$	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
$381$	1.55581	+	15.0420i	0.0797066	+	0.770627i
$382$	−8.14637	−	14.1099i	−0.416805	−	0.721927i
$383$	−9.07354	+	15.7158i	−0.463636	+	0.803042i	−0.999139	−	0.0414919i	$-0.986789\pi$
$383$	−9.07354	+	15.7158i	−0.463636	+	0.803042i	0.535502	+	0.844534i	$0.320122\pi$
$384$	0.707107	−	1.58114i	0.0360844	−	0.0806872i
$385$		0			0
$386$			7.34847i			0.374027i
$387$	−20.3253	+	4.24999i	−1.03319	+	0.216039i
$388$	−10.3824	+	5.99430i	−0.527088	+	0.304315i
$389$	−6.36396	+	3.67423i	−0.322666	+	0.186291i	−0.652580	−	0.757720i	$-0.726313\pi$
$389$	−6.36396	+	3.67423i	−0.322666	+	0.186291i	0.329914	+	0.944011i	$0.392980\pi$
$390$		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
$396$	13.3542	+	4.38799i	0.671076	+	0.220505i
$397$	−12.8877	−	7.44073i	−0.646816	−	0.373439i	0.140419	−	0.990092i	$-0.455155\pi$
$397$	−12.8877	−	7.44073i	−0.646816	−	0.373439i	−0.787235	+	0.616653i	$0.788488\pi$
$398$	−15.5096			−0.777424
$399$	5.45947	−	3.62639i	0.273315	−	0.181547i
$400$		0			0
$401$	−0.827520	−	0.477769i	−0.0413244	−	0.0238586i	0.479195	−	0.877708i	$-0.340928\pi$
$401$	−0.827520	−	0.477769i	−0.0413244	−	0.0238586i	−0.520520	+	0.853850i	$0.674262\pi$
$402$	24.5854	−	2.54289i	1.22621	−	0.126828i
$403$	−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
$408$	3.21209	+	4.43649i	0.159022	+	0.219639i
$409$	−13.4317	+	7.75478i	−0.664154	+	0.383449i	−0.793858	−	0.608103i	$-0.791931\pi$
$409$	−13.4317	+	7.75478i	−0.664154	+	0.383449i	0.129704	+	0.991553i	$0.458597\pi$
$410$		0			0
$411$	3.53200	+	4.87835i	0.174221	+	0.240631i
$412$		−	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
$417$	−34.7690	+	3.59619i	−1.70264	+	0.176106i
$418$	−5.80359	−	3.35071i	−0.283863	−	0.163888i
$419$	−8.85494			−0.432592			−0.216296	−	0.976328i	$-0.569398\pi$
$419$	−8.85494			−0.432592			−0.216296	+	0.976328i	$0.569398\pi$
$420$		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
$423$	10.5064	−	31.9748i	0.510838	−	1.55467i
$424$	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
$429$	6.86646	−	4.97143i	0.331516	−	0.240023i
$430$		0			0
$431$	6.63699	−	3.83187i	0.319693	−	0.184575i	−0.331563	−	0.943433i	$-0.607576\pi$
$431$	6.63699	−	3.83187i	0.319693	−	0.184575i	0.651256	+	0.758858i	$0.274243\pi$
$432$	5.07718	+	1.10557i	0.244276	+	0.0531916i
$433$		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
$438$	−0.624282	−	6.03574i	−0.0298294	−	0.288399i
$439$	7.69306	+	4.44159i	0.367170	+	0.211986i	0.672221	−	0.740350i	$-0.265340\pi$
$439$	7.69306	+	4.44159i	0.367170	+	0.211986i	−0.305051	+	0.952336i	$0.598674\pi$
$440$		0			0
$441$	−12.6929	−	16.7300i	−0.604422	−	0.796664i
$442$	3.30318			0.157116
$443$	13.0298	+	7.52277i	0.619066	+	0.357418i	0.776505	−	0.630111i	$-0.216991\pi$
$443$	13.0298	+	7.52277i	0.619066	+	0.357418i	−0.157439	+	0.987529i	$0.550324\pi$
$444$	0.474523	+	4.58782i	0.0225199	+	0.217728i
$445$		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
$453$	−2.80588	+	2.03151i	−0.131832	+	0.0954485i
$454$		−	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	$-0.749902\pi$
$457$	5.53924	−	9.59425i	0.259115	−	0.448800i	0.966005	+	0.258523i	$0.0832358\pi$
$458$	6.77729	+	11.7386i	0.316682	+	0.548509i
$459$	−11.0554	+	12.1564i	−0.516024	+	0.567411i
$460$		0			0
$461$	31.7876			1.48050			0.740248	−	0.672334i	$-0.234708\pi$
$461$	31.7876			1.48050			0.740248	+	0.672334i	$0.234708\pi$
$462$	−9.54931	+	19.2316i	−0.444274	+	0.894735i
$463$	−22.5741			−1.04911			−0.524554	−	0.851377i	$-0.675768\pi$
$463$	−22.5741			−1.04911			−0.524554	+	0.851377i	$0.675768\pi$
$464$	−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	0.335375	+	0.942085i	$0.391137\pi$
$467$	−14.0073	+	24.2614i	−0.648181	+	1.12268i	−0.983557	+	0.180599i	$0.942197\pi$
$468$	2.33570	−	2.08911i	0.107968	−	0.0965693i
$469$	−1.52277	+	37.7244i	−0.0703152	+	1.74195i
$470$		0			0
$471$	14.6750	+	20.2688i	0.676187	+	0.933938i
$472$	−9.15769	+	5.28720i	−0.421517	+	0.243363i
$473$	−28.0867	+	16.2158i	−1.29143	+	0.745605i
$474$	11.6580	+	16.1019i	0.535471	+	0.739584i
$475$		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	0.701940	+	0.712236i	$0.252317\pi$
$479$	21.1810	+	36.6866i	0.967784	+	1.67625i	0.265844	+	0.964016i	$0.414349\pi$
$480$		0			0
$481$	2.40890	+	1.39078i	0.109836	+	0.0634141i
$482$	−21.3094			−0.970615
$483$	−17.0905	+	11.3522i	−0.777644	+	0.516541i
$484$	10.9545			0.497930
$485$		0			0
$486$	−0.129018	+	15.5879i	−0.00585235	+	0.707083i
$487$	8.51743	+	14.7526i	0.385962	+	0.668505i	0.991902	−	0.127005i	$-0.0405364\pi$
$487$	8.51743	+	14.7526i	0.385962	+	0.668505i	−0.605941	+	0.795510i	$0.707203\pi$
$488$	−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	$-0.101122\pi$
$492$	1.46545	−	1.06101i	0.0660677	−	0.0478341i
$493$	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	−0.843871	−	0.536546i	$-0.819729\pi$
$499$	0.954451	−	1.65316i	0.0427271	−	0.0740055i	0.886598	+	0.462541i	$0.153062\pi$
$500$		0			0
$501$	0.764586	+	7.39224i	0.0341592	+	0.330261i
$502$	−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	$0.387618\pi$
$504$	−2.77984	+	7.43455i	−0.123824	+	0.331161i
$505$		0			0
$506$	18.1677	+	10.4891i	0.807655	+	0.466300i
$507$	2.12213	+	20.5174i	0.0942471	+	0.911208i
$508$	4.36543	+	7.56114i	0.193684	+	0.335471i
$509$	12.3583	−	21.4051i	0.547770	−	0.948766i	−0.450656	−	0.892697i	$-0.648810\pi$
$509$	12.3583	−	21.4051i	0.547770	−	0.948766i	0.998427	−	0.0560688i	$-0.0178566\pi$
$510$		0			0
$511$	9.26139	+	0.373843i	0.409700	+	0.0165378i
$512$		−	1.00000i		−	0.0441942i
$513$	1.58121	−	7.26151i	0.0698122	−	0.320604i
$514$	−9.52277	+	5.49798i	−0.420032	+	0.242505i
$515$		0			0
$516$	−9.71064	+	7.03066i	−0.427487	+	0.309508i
$517$		−	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	−0.932087	−	0.362235i	$-0.882014\pi$
$521$	−17.7981	−	30.8272i	−0.779748	−	1.35056i	0.152339	−	0.988328i	$-0.451320\pi$
$522$	6.48204	−	19.7272i	0.283711	−	0.863437i
$523$	−14.6412	−	8.45307i	−0.640213	−	0.369627i	0.144484	−	0.989507i	$-0.453848\pi$
$523$	−14.6412	−	8.45307i	−0.640213	−	0.369627i	−0.784697	+	0.619880i	$0.787181\pi$
$524$	−13.7725			−0.601654
$525$		0			0
$526$	−2.00000			−0.0872041
$527$	18.1471	+	10.4772i	0.790500	+	0.456395i
$528$	8.07256	−	0.834952i	0.351313	−	0.0363366i
$529$	−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
$534$	4.99501	+	6.89902i	0.216155	+	0.298550i
$535$		0			0
$536$	12.3583	−	7.13505i	0.533796	−	0.308187i
$537$	−19.6878	−	27.1925i	−0.849593	−	1.17344i
$538$		−	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	−0.942972	−	0.332871i	$-0.891983\pi$
$541$	−4.26139	+	7.38094i	−0.183211	+	0.317331i	0.759761	+	0.650202i	$0.225316\pi$
$542$	−3.16228	−	5.47723i	−0.135831	−	0.235267i
$543$	5.44816	−	0.563508i	0.233803	−	0.0241825i
$544$	2.73861	+	1.58114i	0.117417	+	0.0677908i
$545$		0			0
$546$	2.64851	+	3.98729i	0.113346	+	0.170640i
$547$	−3.61845			−0.154714			−0.0773569	−	0.997003i	$-0.524648\pi$
$547$	−3.61845			−0.154714			−0.0773569	+	0.997003i	$0.524648\pi$
$548$	3.01137	+	1.73861i	0.128639	+	0.0742699i
$549$	−9.87298	−	3.24410i	−0.421369	−	0.138455i
$550$		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	−0.914809	−	0.403887i	$-0.867659\pi$
$557$	−24.1304	+	13.9317i	−1.02244	+	0.590304i	−0.107628	+	0.994191i	$0.534326\pi$
$558$	19.4583	−	4.06871i	0.823736	−	0.172242i
$559$			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	0.954500	−	0.298211i	$-0.0963899\pi$
$563$	5.19615	+	9.00000i	0.218992	+	0.379305i	−0.735508	+	0.677516i	$0.763057\pi$
$564$	−1.99917	−	19.3286i	−0.0841803	−	0.813879i
$565$		0			0
$566$	−9.22460			−0.387739
$567$	−23.5384	−	3.59805i	−0.988518	−	0.151104i
$568$	−6.92163			−0.290425
$569$	6.54879	+	3.78095i	0.274540	+	0.158505i	0.630949	−	0.775824i	$-0.282666\pi$
$569$	6.54879	+	3.78095i	0.274540	+	0.158505i	−0.356409	+	0.934330i	$0.615999\pi$
$570$		0			0
$571$	−7.47723	−	12.9509i	−0.312912	−	0.541980i	0.666079	−	0.745881i	$-0.267971\pi$
$571$	−7.47723	−	12.9509i	−0.312912	−	0.541980i	−0.978991	+	0.203901i	$0.934638\pi$
$572$	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
$576$	2.93649	−	0.614017i	0.122354	−	0.0255840i
$577$	−0.584480	+	0.337449i	−0.0243322	+	0.0140482i	−0.512117	−	0.858916i	$-0.671138\pi$
$577$	−0.584480	+	0.337449i	−0.0243322	+	0.0140482i	0.487785	+	0.872964i	$0.337805\pi$
$578$	6.06218	−	3.50000i	0.252153	−	0.145581i
$579$	−10.3095	+	7.46423i	−0.428447	+	0.310203i
$580$		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	$0.356690\pi$
$588$	−10.6330	−	5.82572i	−0.438498	−	0.240249i
$589$	−9.47723			−0.390502
$590$		0			0
$591$	15.5057	−	1.60377i	0.637821	−	0.0659704i
$592$	1.33146	+	2.30615i	0.0547225	+	0.0947821i
$593$	0.826579	−	1.43168i	0.0339435	−	0.0587919i	−0.848555	−	0.529108i	$-0.822527\pi$
$593$	0.826579	−	1.43168i	0.0339435	−	0.0587919i	0.882498	+	0.470316i	$0.155860\pi$
$594$	7.40852	+	23.1923i	0.303975	+	0.951593i
$595$		0			0
$596$			2.44949i			0.100335i
$597$	−15.7539	−	21.7590i	−0.644764	−	0.890537i
$598$	4.05015	−	2.33836i	0.165623	−	0.0956225i
$599$	20.4739	−	11.8206i	0.836540	−	0.482977i	−0.0195464	−	0.999809i	$-0.506222\pi$
$599$	20.4739	−	11.8206i	0.836540	−	0.482977i	0.856087	+	0.516832i	$0.172889\pi$
$600$		0			0
$601$			4.06775i			0.165927i	0.996553	+	0.0829635i	$0.0264385\pi$
$601$			4.06775i			0.165927i	−0.996553	+	0.0829635i	$0.973562\pi$
$602$	−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
$606$	−19.4919	+	2.01607i	−0.791806	+	0.0818972i
$607$	−10.6468	−	6.14692i	−0.432140	−	0.249496i	0.268118	−	0.963386i	$-0.413598\pi$
$607$	−10.6468	−	6.14692i	−0.432140	−	0.249496i	−0.700258	+	0.713890i	$0.746932\pi$
$608$	−1.43023			−0.0580034
$609$	28.4094	+	14.1065i	1.15121	+	0.571624i
$610$		0			0
$611$	−10.1487	−	5.85938i	−0.410574	−	0.237045i
$612$	−2.96145	+	9.01276i	−0.119709	+	0.364319i
$613$	2.92726	+	5.07016i	0.118231	+	0.204782i	0.919067	−	0.394102i	$-0.128944\pi$
$613$	2.92726	+	5.07016i	0.118231	+	0.204782i	−0.800836	+	0.598884i	$0.795611\pi$
$614$	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	$-0.905569\pi$
$617$		−	14.5228i		−	0.584665i	0.956317	−	0.292332i	$-0.0944314\pi$
$618$	6.89902	−	4.99501i	0.277519	−	0.200929i
$619$	−26.1475	+	15.0963i	−1.05096	+	0.606771i	−0.922917	−	0.384998i	$-0.874202\pi$
$619$	−26.1475	+	15.0963i	−1.05096	+	0.606771i	−0.128040	+	0.991769i	$0.540869\pi$
$620$		0			0
$621$	−4.94987	+	22.7317i	−0.198632	+	0.912190i
$622$			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
$627$	−1.19417	−	11.5456i	−0.0476906	−	0.461086i
$628$	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
$633$	4.36177	+	42.1708i	0.173365	+	1.67614i
$634$	−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
$639$	−4.24999	−	20.3253i	−0.168127	−	0.804056i
$640$		0			0
$641$	13.9251	−	8.03966i	0.550008	−	0.317547i	−0.199117	−	0.979976i	$-0.563807\pi$
$641$	13.9251	−	8.03966i	0.550008	−	0.317547i	0.749125	+	0.662428i	$0.230474\pi$
$642$	7.68423	−	5.56351i	0.303272	−	0.219574i
$643$		−	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	0.592777	−	0.805367i	$-0.298032\pi$
$647$	−10.2019	−	17.6703i	−0.401080	−	0.694691i	−0.993857	+	0.110676i	$0.964698\pi$
$648$	3.60611	+	8.24597i	0.141661	+	0.323932i
$649$	−42.9089	−	24.7735i	−1.68432	−	0.972444i
$650$		0			0
$651$	1.90332	+	30.3062i	0.0745969	+	1.18779i
$652$	−14.6969			−0.575577
$653$	−34.5227	−	19.9317i	−1.35098	−	0.779987i	−0.362590	−	0.931949i	$-0.618108\pi$
$653$	−34.5227	−	19.9317i	−1.35098	−	0.779987i	−0.988386	+	0.151962i	$0.951441\pi$
$654$	35.2009	−	3.64086i	1.37646	−	0.142369i
$655$		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	−0.489799	−	0.871836i	$-0.662930\pi$
$661$	0.522774	−	0.301824i	0.0203336	−	0.0117396i	0.510132	+	0.860096i	$0.329596\pi$
$662$	−18.5604	+	10.7158i	−0.721370	+	0.416483i
$663$	3.35521	+	4.63416i	0.130306	+	0.179976i
$664$		−	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
$669$	37.7101	−	3.90039i	1.45796	−	0.150798i
$670$		0			0
$671$	−16.2312			−0.626600
$672$	0.287233	+	4.57357i	0.0110803	+	0.176429i
$673$	−14.1585			−0.545771			−0.272885	−	0.962047i	$-0.587978\pi$
$673$	−14.1585			−0.545771			−0.272885	+	0.962047i	$0.587978\pi$
$674$	−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	0.354663	+	0.934994i	$0.384596\pi$
$677$	−16.4545	+	28.5000i	−0.632397	+	1.09534i	−0.987060	+	0.160350i	$0.948738\pi$
$678$	−27.6339	−	12.3583i	−1.06127	−	0.474616i
$679$	16.9545	−	26.8073i	0.650652	−	1.02877i
$680$		0			0
$681$	14.5798	−	10.5560i	0.558699	−	0.404507i
$682$	26.8886	−	15.5241i	1.02962	−	0.594450i
$683$	−16.4150	+	9.47723i	−0.628104	+	0.362636i	−0.780017	−	0.625758i	$-0.784790\pi$
$683$	−16.4150	+	9.47723i	−0.628104	+	0.362636i	0.151913	+	0.988394i	$0.451456\pi$
$684$	−0.878183	−	4.19985i	−0.0335782	−	0.160585i
$685$		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	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$	−1.12840			−0.0428954
$693$	−36.6805	+	6.13742i	−1.39338	+	0.233141i
$694$	17.4772			0.663426
$695$		0			0
$696$	−1.23341	−	11.9250i	−0.0467524	−	0.452016i
$697$	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	$-0.432155\pi$
$702$	5.30340	+	1.15483i	0.200164	+	0.0435861i
$703$	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	−0.996059	−	0.0886924i	$-0.971731\pi$
$709$	−11.2158	+	19.4264i	−0.421220	+	0.729574i	0.574839	+	0.818266i	$0.305065\pi$
$710$		0			0
$711$	−10.7483	+	32.7111i	−0.403094	+	1.22676i
$712$	4.25871	+	2.45877i	0.159602	+	0.0921463i
$713$	29.6678			1.11107
$714$	−12.9794	−	6.44482i	−0.485741	−	0.241191i
$715$		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	$-0.838104\pi$
$719$	−0.401865	+	0.696051i	−0.0149870	+	0.0259583i	0.858435	+	0.512923i	$0.171437\pi$
$720$		0			0
$721$	6.04555	+	11.5207i	0.225148	+	0.429054i
$722$		−	16.9545i		−	0.630979i
$723$	−21.6451	−	29.8958i	−0.804988	−	1.11184i
$724$	2.73861	−	1.58114i	0.101780	−	0.0587626i
$725$		0			0
$726$	11.1270	+	15.3685i	0.412962	+	0.570377i
$727$			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
$732$	−5.96816	+	0.617292i	−0.220590	+	0.0228158i
$733$	2.07357	+	1.19718i	0.0765891	+	0.0442187i	0.537805	−	0.843069i	$-0.319253\pi$
$733$	2.07357	+	1.19718i	0.0765891	+	0.0442187i	−0.461216	+	0.887288i	$0.652587\pi$
$734$	0.369657			0.0136443
$735$		0			0
$736$	4.47723			0.165033
$737$	57.9054	+	33.4317i	2.13297	+	1.23147i
$738$	2.97707	+	0.978218i	0.109588	+	0.0360087i
$739$	3.23861	+	5.60944i	0.119134	+	0.206347i	0.919425	−	0.393266i	$-0.128655\pi$
$739$	3.23861	+	5.60944i	0.119134	+	0.206347i	−0.800291	+	0.599612i	$0.795321\pi$
$740$		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	$0.0792412\pi$
$743$			13.4317i			0.492760i	−0.969173	+	0.246380i	$0.920759\pi$
$744$	9.29642	−	6.73076i	0.340823	−	0.246762i
$745$		0			0
$746$	20.1042	−	11.6072i	0.736068	−	0.424969i
$747$	11.9449	−	2.49767i	0.437041	−	0.0913848i
$748$			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	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	−5.60944	−	9.71584i	−0.204555	−	0.354300i
$753$	−1.57792	−	15.2558i	−0.0575027	−	0.555953i
$754$	−6.26139	−	3.61501i	−0.228026	−	0.131651i
$755$		0			0
$756$	−13.2539	+	3.65170i	−0.482039	+	0.132811i
$757$	48.1361			1.74954			0.874768	−	0.484541i	$-0.161014\pi$
$757$	48.1361			1.74954			0.874768	+	0.484541i	$0.161014\pi$
$758$	17.7338	+	10.2386i	0.644121	+	0.371883i
$759$	3.73827	+	36.1427i	0.135691	+	1.31190i
$760$		0			0
$761$	−0.891935	+	1.54488i	−0.0323326	+	0.0560018i	−0.881739	−	0.471738i	$-0.843627\pi$
$761$	−0.891935	+	1.54488i	−0.0323326	+	0.0560018i	0.849406	+	0.527739i	$0.176960\pi$
$762$	−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
$768$	1.40294	−	1.01575i	0.0506243	−	0.0366528i
$769$		−	16.1921i		−	0.583902i	−0.956433	−	0.291951i	$-0.905696\pi$
$769$		−	16.1921i		−	0.583902i	0.956433	−	0.291951i	$-0.0943045\pi$
$770$		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	0.682898	−	0.730514i	$-0.260719\pi$
$773$	−8.09605	−	14.0228i	−0.291195	−	0.504364i	−0.974093	+	0.226150i	$0.927386\pi$
$774$	−19.7272	−	6.48204i	−0.709080	−	0.232992i
$775$		0			0
$776$	−11.9886			−0.430366
$777$	−6.75190	−	10.1649i	−0.242223	−	0.364663i
$778$	−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
$786$	−13.9894	−	19.3220i	−0.498987	−	0.689192i
$787$	−43.4506	+	25.0862i	−1.54884	+	0.894226i	−0.550615	+	0.834760i	$0.685607\pi$
$787$	−43.4506	+	25.0862i	−1.54884	+	0.894226i	−0.998230	+	0.0594664i	$0.981060\pi$
$788$	7.79423	−	4.50000i	0.277658	−	0.160306i
$789$	−2.03151	−	2.80588i	−0.0723235	−	0.0998921i
$790$		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	$0.909957\pi$
$798$	6.54124	−	0.410809i	0.231557	−	0.0145425i
$799$	35.4772			1.25509
$800$		0			0
$801$	−4.60523	+	14.0154i	−0.162718	+	0.495210i
$802$	−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
$807$	24.6652	−	17.8580i	0.868256	−	0.628631i
$808$	−9.79796	+	5.65685i	−0.344691	+	0.199007i
$809$	−7.65776	+	4.42121i	−0.269233	+	0.155441i	−0.628539	−	0.777778i	$-0.716347\pi$
$809$	−7.65776	+	4.42121i	−0.269233	+	0.155441i	0.359306	+	0.933220i	$0.383013\pi$
$810$		0			0
$811$			38.3280i			1.34588i	0.739697	+	0.672940i	$0.234969\pi$
$811$			38.3280i			1.34588i	−0.739697	+	0.672940i	$0.765031\pi$
$812$	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
$816$	0.563508	+	5.44816i	0.0197267	+	0.190724i
$817$	8.57321	+	4.94975i	0.299939	+	0.173170i
$818$	−15.5096			−0.542279
$819$	−2.90370	+	7.76580i	−0.101464	+	0.271359i
$820$		0			0
$821$	10.1403	+	5.85452i	0.353900	+	0.204324i	0.666401	−	0.745593i	$-0.267834\pi$
$821$	10.1403	+	5.85452i	0.353900	+	0.204324i	−0.312502	+	0.949917i	$0.601167\pi$
$822$	0.619631	+	5.99077i	0.0216121	+	0.208952i
$823$	−1.59580	−	2.76401i	−0.0556262	−	0.0963474i	0.836871	−	0.547400i	$-0.184382\pi$
$823$	−1.59580	−	2.76401i	−0.0556262	−	0.0963474i	−0.892498	+	0.451052i	$0.851049\pi$
$824$	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	$0.0216500\pi$
$827$			3.90890i			0.135926i	−0.997688	+	0.0679629i	$0.978350\pi$
$828$	2.74909	+	13.1473i	0.0955375	+	0.456901i
$829$	43.6931	−	25.2262i	1.51752	−	0.876142i	0.517735	−	0.855541i	$-0.326775\pi$
$829$	43.6931	−	25.2262i	1.51752	−	0.876142i	0.999788	−	0.0206012i	$-0.00655803\pi$
$830$		0			0
$831$	−13.7460	+	9.95231i	−0.476842	+	0.345242i
$832$		−	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
$837$	25.4730	+	23.1661i	0.880476	+	0.800737i
$838$	−7.66860	−	4.42747i	−0.264907	−	0.152944i
$839$	40.1440			1.38593			0.692963	−	0.720973i	$-0.256305\pi$
$839$	40.1440			1.38593			0.692963	+	0.720973i	$0.256305\pi$
$840$		0			0
$841$	−18.9089			−0.652031
$842$	16.4150	+	9.47723i	0.565700	+	0.326607i
$843$	−3.11704	+	0.322398i	−0.107357	+	0.0111040i
$844$	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
$849$	−9.36991	−	12.9416i	−0.321575	−	0.444154i
$850$		0			0
$851$	−10.3251	+	5.96123i	−0.353942	+	0.204348i
$852$	−7.03066	−	9.71064i	−0.240867	−	0.332681i
$853$			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	0.708230	−	0.705982i	$-0.249494\pi$
$857$	−7.53185	−	13.0455i	−0.257283	−	0.445627i	−0.965513	+	0.260354i	$0.916161\pi$
$858$	8.43224	−	0.872155i	0.287872	−	0.0297749i
$859$	26.4772	+	15.2866i	0.903391	+	0.521573i	0.878299	−	0.478112i	$-0.158679\pi$
$859$	26.4772	+	15.2866i	0.903391	+	0.521573i	0.0250924	+	0.999685i	$0.492012\pi$
$860$		0			0
$861$	−2.12884	+	4.28732i	−0.0725506	+	0.146111i
$862$	7.66374			0.261028
$863$	22.9299	+	13.2386i	0.780545	+	0.450648i	0.836623	−	0.547779i	$-0.184526\pi$
$863$	22.9299	+	13.2386i	0.780545	+	0.450648i	−0.0560787	+	0.998426i	$0.517860\pi$
$864$	3.84418	+	3.49604i	0.130782	+	0.118938i
$865$		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
$873$	−7.36121	−	35.2044i	−0.249139	−	1.19149i
$874$		−	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	−0.175673	+	0.984449i	$0.556210\pi$
$877$	−27.8490	+	48.2359i	−0.940394	+	1.62881i	−0.764721	+	0.644361i	$0.777123\pi$
$878$	4.44159	+	7.69306i	0.149896	+	0.259628i
$879$	1.43566	+	13.8804i	0.0484237	+	0.468174i
$880$		0			0
$881$	−18.7544			−0.631853			−0.315926	−	0.948784i	$-0.602315\pi$
$881$	−18.7544			−0.631853			−0.315926	+	0.948784i	$0.602315\pi$
$882$	−2.62736	−	20.8350i	−0.0884678	−	0.701551i
$883$	24.3833			0.820564			0.410282	−	0.911959i	$-0.365430\pi$
$883$	24.3833			0.820564			0.410282	+	0.911959i	$0.365430\pi$
$884$	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	−0.835481	−	0.549519i	$-0.814811\pi$
$887$	1.73205	−	3.00000i	0.0581566	−	0.100730i	0.893638	+	0.448789i	$0.148144\pi$
$888$	−1.88296	+	4.21043i	−0.0631881	+	0.141293i
$889$	−19.5228	−	12.3473i	−0.654773	−	0.414115i
$890$		0			0
$891$	−25.0123	+	33.9514i	−0.837942	+	1.13741i
$892$	18.9557	−	10.9441i	0.634682	−	0.366434i
$893$	−13.8959	+	8.02277i	−0.465007	+	0.268472i
$894$	−3.43649	+	2.48808i	−0.114933	+	0.0832137i
$895$		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
$903$	14.1065	−	28.4094i	0.469435	−	0.945406i
$904$	−17.4772			−0.581284
$905$		0			0
$906$	−3.44572	+	0.356394i	−0.114476	+	0.0118404i
$907$	4.89898	+	8.48528i	0.162668	+	0.281749i	0.935825	−	0.352466i	$-0.114657\pi$
$907$	4.89898	+	8.48528i	0.162668	+	0.281749i	−0.773157	+	0.634215i	$0.781323\pi$
$908$	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	$0.869460\pi$
$912$	−1.45276	−	2.00653i	−0.0481056	−	0.0664427i
$913$	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	−0.862444	−	0.506153i	$-0.831067\pi$
$919$	0.215838	−	0.373843i	0.00711985	−	0.0123319i	0.869563	+	0.493821i	$0.164400\pi$
$920$		0			0
$921$	20.6547	−	2.13633i	0.680595	−	0.0703946i
$922$	27.5289	+	15.8938i	0.906615	+	0.523434i
$923$	−7.23003			−0.237979
$924$	−17.8857	+	11.8804i	−0.588398	+	0.390836i
$925$		0			0
$926$	−19.5497	−	11.2871i	−0.642444	−	0.370916i
$927$	14.0154	+	4.60523i	0.460326	+	0.151256i
$928$	−3.46081	−	5.99430i	−0.113607	−	0.196773i
$929$	−7.96300	+	13.7923i	−0.261258	+	0.452512i	−0.966576	−	0.256379i	$-0.917471\pi$
$929$	−7.96300	+	13.7923i	−0.261258	+	0.452512i	0.705319	+	0.708890i	$0.250804\pi$
$930$		0			0
$931$	−0.806936	+	9.97902i	−0.0264463	+	0.327049i
$932$			4.00000i			0.131024i
$933$	−24.6652	+	17.8580i	−0.807502	+	0.584645i
$934$	−24.2614	+	14.0073i	−0.793857	+	0.458333i
$935$		0			0
$936$	3.06733	−	0.641375i	0.100259	−	0.0209640i
$937$			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	$-0.274969\pi$
$941$	−10.2369	−	17.7309i	−0.333715	−	0.578011i	−0.983237	+	0.182331i	$0.941636\pi$
$942$	2.57448	+	24.8908i	0.0838811	+	0.810986i
$943$	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	0.885177	−	0.465255i	$-0.154037\pi$
$947$	28.4605	+	16.4317i	0.924842	+	0.533958i	0.0396654	+	0.999213i	$0.487371\pi$
$948$	2.04521	+	19.7737i	0.0664252	+	0.642218i
$949$	−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	$0.275047\pi$
$953$			46.9545i			1.52100i	−0.649336	+	0.760502i	$0.724953\pi$
$954$	−14.6825	+	3.07008i	−0.475362	+	0.0993976i
$955$		0			0
$956$		0			0
$957$	45.4998	−	32.9426i	1.47080	−	1.06488i
$958$			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
$963$	15.6106	+	5.12938i	0.503043	+	0.165292i
$964$	−18.4545	−	10.6547i	−0.594378	−	0.343164i
$965$		0			0
$966$	−20.4769	+	1.28601i	−0.658833	+	0.0413766i
$967$	−7.23690			−0.232723			−0.116361	−	0.993207i	$-0.537123\pi$
$967$	−7.23690			−0.232723			−0.116361	+	0.993207i	$0.537123\pi$
$968$	9.48683	+	5.47723i	0.304918	+	0.176045i
$969$	7.79211	−	0.805945i	0.250319	−	0.0258907i
$970$		0			0
$971$	−18.8748	+	32.6922i	−0.605723	+	1.04914i	0.386214	+	0.922409i	$0.373783\pi$
$971$	−18.8748	+	32.6922i	−0.605723	+	1.04914i	−0.991937	+	0.126733i	$0.959551\pi$
$972$	−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	−0.553173	−	0.833067i	$-0.686583\pi$
$977$	−3.38521	+	1.95445i	−0.108302	+	0.0625284i	0.444870	+	0.895595i	$0.353250\pi$
$978$	−14.9285	−	20.6190i	−0.477359	−	0.659321i
$979$			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	−0.888338	−	0.459190i	$-0.848140\pi$
$983$	−26.3941	−	45.7158i	−0.841840	−	1.45811i	0.0464984	−	0.998918i	$-0.485194\pi$
$984$	1.79962	−	0.186137i	0.0573699	−	0.00593382i
$985$		0			0
$986$	21.8881			0.697059
$987$	28.4459	+	42.8248i	0.905442	+	1.36313i
$988$	−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	0.770277	−	0.637709i	$-0.220118\pi$
$991$	−5.26139	−	9.11299i	−0.167133	−	0.289484i	−0.937411	+	0.348225i	$0.886784\pi$
$992$	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
$996$	5.70682	−	4.13183i	0.180827	−	0.130922i
$997$	13.4164	−	7.74597i	0.424902	−	0.245317i	−0.272270	−	0.962221i	$-0.587775\pi$
$997$	13.4164	−	7.74597i	0.424902	−	0.245317i	0.697172	+	0.716904i	$0.254441\pi$
$998$	1.65316	−	0.954451i	0.0523298	−	0.0302126i
$999$	−13.5201	−	2.94403i	−0.427756	−	0.0931449i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.3	✓	8	35.17	even	12
210.2.t.e.59.4	yes	8	105.38	odd	12
210.2.t.e.89.3	yes	8	15.8	even	4
210.2.t.e.89.4	yes	8	5.2	odd	4
210.2.t.f.59.1	yes	8	105.17	odd	12
210.2.t.f.59.2	yes	8	35.3	even	12
210.2.t.f.89.1	yes	8	5.3	odd	4
210.2.t.f.89.2	yes	8	15.2	even	4
1050.2.s.i.101.1		16	7.3	odd	6	inner
1050.2.s.i.101.2		16	105.59	even	6	inner
1050.2.s.i.101.7		16	21.17	even	6	inner
1050.2.s.i.101.8		16	35.24	odd	6	inner
1050.2.s.i.551.1		16	3.2	odd	2	inner
1050.2.s.i.551.2		16	5.4	even	2	inner
1050.2.s.i.551.7		16	1.1	even	1	trivial
1050.2.s.i.551.8		16	15.14	odd	2	inner
1470.2.d.e.1469.2		8	105.2	even	12
1470.2.d.e.1469.3		8	35.33	even	12
1470.2.d.e.1469.6		8	35.23	odd	12
1470.2.d.e.1469.7		8	105.47	odd	12
1470.2.d.f.1469.2		8	105.68	odd	12
1470.2.d.f.1469.3		8	35.2	odd	12
1470.2.d.f.1469.6		8	35.12	even	12
1470.2.d.f.1469.7		8	105.23	even	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.707107 + 1.58114i) q^{6} +(-2.23607 - 1.41421i) q^{7} +1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.707107 + 1.58114i) q^{6} +(-2.23607 - 1.41421i) q^{7} +1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +(-4.05781 + 2.34278i) q^{11} +(-1.40294 + 1.01575i) q^{12} +1.04456i q^{13} +(-1.22938 - 2.34278i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.58114 - 2.73861i) q^{17} +(-2.85008 - 0.936492i) q^{18} +(1.23861 + 0.715113i) q^{19} +(2.03803 - 4.10444i) q^{21} -4.68556 q^{22} +(-3.87739 - 2.23861i) q^{23} +(-1.72286 + 0.178197i) 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} +(-4.75937 - 6.57357i) q^{33} -3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +(1.33146 - 2.30615i) q^{37} +(0.715113 + 1.23861i) q^{38} +(-1.79962 + 0.186137i) q^{39} -1.04456 q^{41} +(3.81721 - 2.53553i) 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} +(4.43649 - 3.21209i) q^{51} +(-0.904612 + 0.522278i) q^{52} +(4.33013 - 2.50000i) q^{53} +(1.10557 - 5.07718i) 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} +(7.43455 + 2.77984i) q^{63} -1.00000 q^{64} +(-0.834952 - 8.07256i) q^{66} +(-7.13505 - 12.3583i) q^{67} +(1.58114 - 2.73861i) q^{68} +(3.16588 - 7.07912i) q^{69} +6.92163i q^{71} +(-0.614017 - 2.93649i) 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} +(8.24597 - 3.60611i) q^{81} +(-0.904612 - 0.522278i) q^{82} -4.06775 q^{83} +(4.57357 - 0.287233i) q^{84} +(5.99430 + 3.46081i) q^{86} +(-11.9250 + 1.23341i) q^{87} +(-2.34278 - 4.05781i) q^{88} +(2.45877 - 4.25871i) q^{89} +(1.47723 - 2.33570i) q^{91} -4.47723i q^{92} +(-6.73076 - 9.29642i) q^{93} +(-9.71584 + 5.60944i) q^{94} +(-1.01575 - 1.40294i) q^{96} +11.9886i q^{97} +(-0.564201 + 6.97723i) q^{98} +(10.4772 - 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 16 * q^9	\( 16 q + 8 q^{4} - 16 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{21} - 48 q^{31} - 32 q^{36} + 16 q^{39} + 8 q^{46} + 48 q^{49} + 40 q^{51} + 48 q^{61} - 16 q^{64} + 24 q^{66} + 48 q^{79} + 8 q^{81} - 8 q^{84} - 64 q^{91} - 24 q^{94} + 80 q^{99}+O(q^{100}) \) 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

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