LMFDB - Embedded newform 30.2.e.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,2,Mod(17,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("30.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	30.e (of order $4$, 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:	$0.239551206064$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	30.17
Dual form			30.2.e.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(1.00000 + 2.00000i) q^{10} -1.41421i q^{11} +(0.292893 + 1.70711i) q^{12} -1.41421 q^{14} +(0.585786 - 3.82843i) q^{15} -1.00000 q^{16} +(1.41421 - 1.41421i) q^{17} +(1.29289 - 2.70711i) q^{18} +4.00000i q^{19} +(2.12132 + 0.707107i) q^{20} +(2.00000 + 1.41421i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(2.82843 + 2.82843i) q^{23} +(1.41421 + 1.00000i) q^{24} +(-4.00000 - 3.00000i) q^{25} +(-4.53553 + 2.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} -7.07107 q^{29} +(-2.29289 - 3.12132i) q^{30} -2.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.414214 + 2.41421i) q^{33} -2.00000i q^{34} +(2.82843 - 1.41421i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(6.00000 + 6.00000i) q^{37} +(2.82843 + 2.82843i) q^{38} +(2.00000 - 1.00000i) q^{40} -5.65685i q^{41} +(2.41421 - 0.414214i) q^{42} +(6.00000 - 6.00000i) q^{43} -1.41421 q^{44} +(0.121320 + 6.70711i) q^{45} +4.00000 q^{46} +(1.70711 - 0.292893i) q^{48} -5.00000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(-2.00000 + 2.82843i) q^{51} +(-2.82843 - 2.82843i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} +1.41421i q^{56} +(-1.17157 - 6.82843i) q^{57} +(-5.00000 + 5.00000i) q^{58} +9.89949 q^{59} +(-3.82843 - 0.585786i) q^{60} -6.00000 q^{61} +(-1.41421 + 1.41421i) q^{62} +(-3.82843 - 1.82843i) q^{63} +1.00000i q^{64} +(2.00000 + 1.41421i) q^{66} +(-4.00000 - 4.00000i) q^{67} +(-1.41421 - 1.41421i) q^{68} +(-5.65685 - 4.00000i) q^{69} +(1.00000 - 3.00000i) q^{70} +14.1421i q^{71} +(-2.70711 - 1.29289i) q^{72} +(-5.00000 + 5.00000i) q^{73} +8.48528 q^{74} +(7.70711 + 3.94975i) q^{75} +4.00000 q^{76} +(-1.41421 + 1.41421i) q^{77} +6.00000i q^{79} +(0.707107 - 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(-4.00000 - 4.00000i) q^{82} +(-8.48528 - 8.48528i) q^{83} +(1.41421 - 2.00000i) q^{84} +(2.00000 + 4.00000i) q^{85} -8.48528i q^{86} +(12.0711 - 2.07107i) q^{87} +(-1.00000 + 1.00000i) q^{88} +2.82843 q^{89} +(4.82843 + 4.65685i) q^{90} +(2.82843 - 2.82843i) q^{92} +(3.41421 - 0.585786i) q^{93} +(-8.48528 - 2.82843i) q^{95} +(1.00000 - 1.41421i) q^{96} +(3.00000 + 3.00000i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-1.41421 - 4.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + 4 q^{10} + 4 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{18} + 8 q^{21} - 4 q^{22} - 16 q^{25} - 4 q^{27} - 4 q^{28} - 12 q^{30} - 8 q^{31} - 4 q^{33} - 4 q^{36} + 24 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^6 - 4 * q^7 + 4 * q^10 + 4 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^18 + 8 * q^21 - 4 * q^22 - 16 * q^25 - 4 * q^27 - 4 * q^28 - 12 * q^30 - 8 * q^31 - 4 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 + 4 * q^42 + 24 * q^43 - 8 * q^45 + 16 * q^46 + 4 * q^48 - 8 * q^51 + 12 * q^55 - 16 * q^57 - 20 * q^58 - 4 * q^60 - 24 * q^61 - 4 * q^63 + 8 * q^66 - 16 * q^67 + 4 * q^70 - 8 * q^72 - 20 * q^73 + 28 * q^75 + 16 * q^76 + 28 * q^81 - 16 * q^82 + 8 * q^85 + 20 * q^87 - 4 * q^88 + 8 * q^90 + 8 * q^93 + 4 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	+	2.12132i	−0.316228	+	0.948683i
$5$	−0.707107	+	2.12132i	−0.316228	+	0.948683i
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$	0.292893	+	1.70711i	0.0845510	+	0.492799i
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$	−1.41421			−0.377964
$15$	0.585786	−	3.82843i	0.151249	−	0.988496i
$16$	−1.00000			−0.250000
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	−0.514496	−	0.857493i	$-0.672021\pi$
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	0.857493	+	0.514496i	$0.172021\pi$
$18$	1.29289	−	2.70711i	0.304738	−	0.638071i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	2.12132	+	0.707107i	0.474342	+	0.158114i
$21$	2.00000	+	1.41421i	0.436436	+	0.308607i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	2.82843	+	2.82843i	0.589768	+	0.589768i	0.937568	−	0.347801i	$-0.113071\pi$
$23$	2.82843	+	2.82843i	0.589768	+	0.589768i	−0.347801	+	0.937568i	$0.613071\pi$
$24$	1.41421	+	1.00000i	0.288675	+	0.204124i
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$		0			0
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	−7.07107			−1.31306			−0.656532	−	0.754298i	$-0.727977\pi$
$29$	−7.07107			−1.31306			−0.656532	+	0.754298i	$0.727977\pi$
$30$	−2.29289	−	3.12132i	−0.418623	−	0.569873i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.414214	+	2.41421i	0.0721053	+	0.420261i
$34$		−	2.00000i		−	0.342997i
$35$	2.82843	−	1.41421i	0.478091	−	0.239046i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	0.999909	−	0.0135147i	$-0.00430201\pi$
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	−0.0135147	+	0.999909i	$0.504302\pi$
$38$	2.82843	+	2.82843i	0.458831	+	0.458831i
$39$		0			0
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$	2.41421	−	0.414214i	0.372521	−	0.0639145i
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	−0.0816682	−	0.996660i	$-0.526025\pi$
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	0.996660	+	0.0816682i	$0.0260248\pi$
$44$	−1.41421			−0.213201
$45$	0.121320	+	6.70711i	0.0180854	+	0.999836i
$46$	4.00000			0.589768
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	1.70711	−	0.292893i	0.246400	−	0.0422755i
$49$		−	5.00000i		−	0.714286i
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$	−2.00000	+	2.82843i	−0.280056	+	0.396059i
$52$		0			0
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	0.485643	−	0.874157i	$-0.338586\pi$
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	−0.874157	+	0.485643i	$0.838586\pi$
$54$	−1.41421	+	5.00000i	−0.192450	+	0.680414i
$55$	3.00000	+	1.00000i	0.404520	+	0.134840i
$56$			1.41421i			0.188982i
$57$	−1.17157	−	6.82843i	−0.155179	−	0.904447i
$58$	−5.00000	+	5.00000i	−0.656532	+	0.656532i
$59$	9.89949			1.28880			0.644402	−	0.764687i	$-0.277106\pi$
$59$	9.89949			1.28880			0.644402	+	0.764687i	$0.277106\pi$
$60$	−3.82843	−	0.585786i	−0.494248	−	0.0756247i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	−1.41421	+	1.41421i	−0.179605	+	0.179605i
$63$	−3.82843	−	1.82843i	−0.482336	−	0.230360i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	2.00000	+	1.41421i	0.246183	+	0.174078i
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	0.419211	−	0.907889i	$-0.362307\pi$
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	−0.907889	+	0.419211i	$0.862307\pi$
$68$	−1.41421	−	1.41421i	−0.171499	−	0.171499i
$69$	−5.65685	−	4.00000i	−0.681005	−	0.481543i
$70$	1.00000	−	3.00000i	0.119523	−	0.358569i
$71$			14.1421i			1.67836i	0.543852	+	0.839181i	$0.316965\pi$
$71$			14.1421i			1.67836i	−0.543852	+	0.839181i	$0.683035\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$	8.48528			0.986394
$75$	7.70711	+	3.94975i	0.889940	+	0.456078i
$76$	4.00000			0.458831
$77$	−1.41421	+	1.41421i	−0.161165	+	0.161165i
$78$		0			0
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$	0.707107	−	2.12132i	0.0790569	−	0.237171i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	−4.00000	−	4.00000i	−0.441726	−	0.441726i
$83$	−8.48528	−	8.48528i	−0.931381	−	0.931381i	0.0664117	−	0.997792i	$-0.478845\pi$
$83$	−8.48528	−	8.48528i	−0.931381	−	0.931381i	−0.997792	+	0.0664117i	$0.978845\pi$
$84$	1.41421	−	2.00000i	0.154303	−	0.218218i
$85$	2.00000	+	4.00000i	0.216930	+	0.433861i
$86$		−	8.48528i		−	0.914991i
$87$	12.0711	−	2.07107i	1.29415	−	0.222042i
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	2.82843			0.299813			0.149906	−	0.988700i	$-0.452103\pi$
$89$	2.82843			0.299813			0.149906	+	0.988700i	$0.452103\pi$
$90$	4.82843	+	4.65685i	0.508961	+	0.490876i
$91$		0			0
$92$	2.82843	−	2.82843i	0.294884	−	0.294884i
$93$	3.41421	−	0.585786i	0.354037	−	0.0607432i
$94$		0			0
$95$	−8.48528	−	2.82843i	−0.870572	−	0.290191i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$	−3.53553	−	3.53553i	−0.357143	−	0.357143i
$99$	−1.41421	−	4.00000i	−0.142134	−	0.402015i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$			9.89949i			0.985037i	0.870302	+	0.492518i	$0.163924\pi$
$101$			9.89949i			0.985037i	−0.870302	+	0.492518i	$0.836076\pi$
$102$	0.585786	+	3.41421i	0.0580015	+	0.338058i
$103$	1.00000	−	1.00000i	0.0985329	−	0.0985329i	−0.656122	−	0.754655i	$-0.727804\pi$
$103$	1.00000	−	1.00000i	0.0985329	−	0.0985329i	0.754655	+	0.656122i	$0.227804\pi$
$104$		0			0
$105$	−4.41421	+	3.24264i	−0.430783	+	0.316449i
$106$	−4.00000			−0.388514
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	−0.830481	−	0.557047i	$-0.811934\pi$
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	0.557047	+	0.830481i	$0.311934\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$	2.82843	−	1.41421i	0.269680	−	0.134840i
$111$	−12.0000	−	8.48528i	−1.13899	−	0.805387i
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	9.89949	+	9.89949i	0.931266	+	0.931266i	0.997785	−	0.0665190i	$-0.0211893\pi$
$113$	9.89949	+	9.89949i	0.931266	+	0.931266i	−0.0665190	+	0.997785i	$0.521189\pi$
$114$	−5.65685	−	4.00000i	−0.529813	−	0.374634i
$115$	−8.00000	+	4.00000i	−0.746004	+	0.373002i
$116$			7.07107i			0.656532i
$117$		0			0
$118$	7.00000	−	7.00000i	0.644402	−	0.644402i
$119$	−2.82843			−0.259281
$120$	−3.12132	+	2.29289i	−0.284936	+	0.209312i
$121$	9.00000			0.818182
$122$	−4.24264	+	4.24264i	−0.384111	+	0.384111i
$123$	1.65685	+	9.65685i	0.149394	+	0.870729i
$124$			2.00000i			0.179605i
$125$	9.19239	−	6.36396i	0.822192	−	0.569210i
$126$	−4.00000	+	1.41421i	−0.356348	+	0.125988i
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	0.324676	−	0.945825i	$-0.394745\pi$
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	−0.945825	+	0.324676i	$0.894745\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.48528	+	12.0000i	−0.747087	+	1.05654i
$130$		0			0
$131$		−	18.3848i		−	1.60629i	−0.595787	−	0.803143i	$-0.703160\pi$
$131$		−	18.3848i		−	1.60629i	0.595787	−	0.803143i	$-0.296840\pi$
$132$	2.41421	−	0.414214i	0.210130	−	0.0360527i
$133$	4.00000	−	4.00000i	0.346844	−	0.346844i
$134$	−5.65685			−0.488678
$135$	−2.17157	−	11.4142i	−0.186899	−	0.982379i
$136$	−2.00000			−0.171499
$137$	−4.24264	+	4.24264i	−0.362473	+	0.362473i	−0.864723	−	0.502249i	$-0.832506\pi$
$137$	−4.24264	+	4.24264i	−0.362473	+	0.362473i	0.502249	+	0.864723i	$0.332506\pi$
$138$	−6.82843	+	1.17157i	−0.581274	+	0.0997309i
$139$			8.00000i			0.678551i	0.940687	+	0.339276i	$0.110182\pi$
$139$			8.00000i			0.678551i	−0.940687	+	0.339276i	$0.889818\pi$
$140$	−1.41421	−	2.82843i	−0.119523	−	0.239046i
$141$		0			0
$142$	10.0000	+	10.0000i	0.839181	+	0.839181i
$143$		0			0
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$	5.00000	−	15.0000i	0.415227	−	1.24568i
$146$			7.07107i			0.585206i
$147$	1.46447	+	8.53553i	0.120787	+	0.703999i
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	12.7279			1.04271			0.521356	−	0.853339i	$-0.325426\pi$
$149$	12.7279			1.04271			0.521356	+	0.853339i	$0.325426\pi$
$150$	8.24264	−	2.65685i	0.673009	−	0.216931i
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	2.82843	−	2.82843i	0.229416	−	0.229416i
$153$	2.58579	−	5.41421i	0.209048	−	0.437713i
$154$			2.00000i			0.161165i
$155$	1.41421	−	4.24264i	0.113592	−	0.340777i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	4.24264	+	4.24264i	0.337526	+	0.337526i
$159$	5.65685	+	4.00000i	0.448618	+	0.317221i
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$		−	5.65685i		−	0.445823i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$	−5.65685			−0.441726
$165$	−5.41421	−	0.828427i	−0.421496	−	0.0644930i
$166$	−12.0000			−0.931381
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	−0.891251	−	0.453510i	$-0.850171\pi$
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	0.453510	+	0.891251i	$0.350171\pi$
$168$	−0.414214	−	2.41421i	−0.0319573	−	0.186261i
$169$			13.0000i			1.00000i
$170$	4.24264	+	1.41421i	0.325396	+	0.108465i
$171$	4.00000	+	11.3137i	0.305888	+	0.865181i
$172$	−6.00000	−	6.00000i	−0.457496	−	0.457496i
$173$	−1.41421	−	1.41421i	−0.107521	−	0.107521i	0.651300	−	0.758820i	$-0.274224\pi$
$173$	−1.41421	−	1.41421i	−0.107521	−	0.107521i	−0.758820	+	0.651300i	$0.774224\pi$
$174$	7.07107	−	10.0000i	0.536056	−	0.758098i
$175$	1.00000	+	7.00000i	0.0755929	+	0.529150i
$176$			1.41421i			0.106600i
$177$	−16.8995	+	2.89949i	−1.27024	+	0.217939i
$178$	2.00000	−	2.00000i	0.149906	−	0.149906i
$179$	−18.3848			−1.37414			−0.687071	−	0.726590i	$-0.741104\pi$
$179$	−18.3848			−1.37414			−0.687071	+	0.726590i	$0.741104\pi$
$180$	6.70711	−	0.121320i	0.499918	−	0.00904268i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	10.2426	−	1.75736i	0.757158	−	0.129908i
$184$		−	4.00000i		−	0.294884i
$185$	−16.9706	+	8.48528i	−1.24770	+	0.623850i
$186$	2.00000	−	2.82843i	0.146647	−	0.207390i
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$		0			0
$189$	7.07107	+	2.00000i	0.514344	+	0.145479i
$190$	−8.00000	+	4.00000i	−0.580381	+	0.290191i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$	−0.292893	−	1.70711i	−0.0211377	−	0.123200i
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$	4.24264			0.304604
$195$		0			0
$196$	−5.00000			−0.357143
$197$	16.9706	−	16.9706i	1.20910	−	1.20910i	0.237785	−	0.971318i	$-0.423579\pi$
$197$	16.9706	−	16.9706i	1.20910	−	1.20910i	0.971318	−	0.237785i	$-0.0764212\pi$
$198$	−3.82843	−	1.82843i	−0.272074	−	0.129941i
$199$		−	24.0000i		−	1.70131i	−0.525720	−	0.850657i	$-0.676204\pi$
$199$		−	24.0000i		−	1.70131i	0.525720	−	0.850657i	$-0.323796\pi$
$200$	0.707107	+	4.94975i	0.0500000	+	0.350000i
$201$	8.00000	+	5.65685i	0.564276	+	0.399004i
$202$	7.00000	+	7.00000i	0.492518	+	0.492518i
$203$	7.07107	+	7.07107i	0.496292	+	0.496292i
$204$	2.82843	+	2.00000i	0.198030	+	0.140028i
$205$	12.0000	+	4.00000i	0.838116	+	0.279372i
$206$		−	1.41421i		−	0.0985329i
$207$	10.8284	+	5.17157i	0.752628	+	0.359449i
$208$		0			0
$209$	5.65685			0.391293
$210$	−0.828427	+	5.41421i	−0.0571669	+	0.373616i
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	−2.82843	+	2.82843i	−0.194257	+	0.194257i
$213$	−4.14214	−	24.1421i	−0.283814	−	1.65419i
$214$			4.00000i			0.273434i
$215$	8.48528	+	16.9706i	0.578691	+	1.15738i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	2.00000	+	2.00000i	0.135769	+	0.135769i
$218$	−7.07107	−	7.07107i	−0.478913	−	0.478913i
$219$	7.07107	−	10.0000i	0.477818	−	0.675737i
$220$	1.00000	−	3.00000i	0.0674200	−	0.202260i
$221$		0			0
$222$	−14.4853	+	2.48528i	−0.972188	+	0.166801i
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	−0.941024	−	0.338340i	$-0.890135\pi$
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	0.338340	+	0.941024i	$0.390135\pi$
$224$	1.41421			0.0944911
$225$	−14.3137	−	4.48528i	−0.954247	−	0.299019i
$226$	14.0000			0.931266
$227$	15.5563	−	15.5563i	1.03251	−	1.03251i	0.0330577	−	0.999453i	$-0.489475\pi$
$227$	15.5563	−	15.5563i	1.03251	−	1.03251i	0.999453	−	0.0330577i	$-0.0105245\pi$
$228$	−6.82843	+	1.17157i	−0.452224	+	0.0775893i
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$	−2.82843	+	8.48528i	−0.186501	+	0.559503i
$231$	2.00000	−	2.82843i	0.131590	−	0.186097i
$232$	5.00000	+	5.00000i	0.328266	+	0.328266i
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	0.154205	−	0.988039i	$-0.450718\pi$
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	−0.988039	+	0.154205i	$0.950718\pi$
$234$		0			0
$235$		0			0
$236$		−	9.89949i		−	0.644402i
$237$	−1.75736	−	10.2426i	−0.114153	−	0.665331i
$238$	−2.00000	+	2.00000i	−0.129641	+	0.129641i
$239$	−8.48528			−0.548867			−0.274434	−	0.961606i	$-0.588490\pi$
$239$	−8.48528			−0.548867			−0.274434	+	0.961606i	$0.588490\pi$
$240$	−0.585786	+	3.82843i	−0.0378124	+	0.247124i
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$	6.36396	−	6.36396i	0.409091	−	0.409091i
$243$	−10.2929	+	11.7071i	−0.660289	+	0.751011i
$244$			6.00000i			0.384111i
$245$	10.6066	+	3.53553i	0.677631	+	0.225877i
$246$	8.00000	+	5.65685i	0.510061	+	0.360668i
$247$		0			0
$248$	1.41421	+	1.41421i	0.0898027	+	0.0898027i
$249$	16.9706	+	12.0000i	1.07547	+	0.760469i
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$			12.7279i			0.803379i	0.915776	+	0.401690i	$0.131577\pi$
$251$			12.7279i			0.803379i	−0.915776	+	0.401690i	$0.868423\pi$
$252$	−1.82843	+	3.82843i	−0.115180	+	0.241168i
$253$	4.00000	−	4.00000i	0.251478	−	0.251478i
$254$	−9.89949			−0.621150
$255$	−4.58579	−	6.24264i	−0.287173	−	0.390929i
$256$	1.00000			0.0625000
$257$	−9.89949	+	9.89949i	−0.617514	+	0.617514i	−0.944893	−	0.327379i	$-0.893834\pi$
$257$	−9.89949	+	9.89949i	−0.617514	+	0.617514i	0.327379	+	0.944893i	$0.393834\pi$
$258$	2.48528	+	14.4853i	0.154727	+	0.901814i
$259$		−	12.0000i		−	0.745644i
$260$		0			0
$261$	−20.0000	+	7.07107i	−1.23797	+	0.437688i
$262$	−13.0000	−	13.0000i	−0.803143	−	0.803143i
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	0.859669	−	0.510852i	$-0.170670\pi$
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	−0.510852	+	0.859669i	$0.670670\pi$
$264$	1.41421	−	2.00000i	0.0870388	−	0.123091i
$265$	8.00000	−	4.00000i	0.491436	−	0.245718i
$266$		−	5.65685i		−	0.346844i
$267$	−4.82843	+	0.828427i	−0.295495	+	0.0506989i
$268$	−4.00000	+	4.00000i	−0.244339	+	0.244339i
$269$	−15.5563			−0.948487			−0.474244	−	0.880394i	$-0.657278\pi$
$269$	−15.5563			−0.948487			−0.474244	+	0.880394i	$0.657278\pi$
$270$	−9.60660	−	6.53553i	−0.584639	−	0.397740i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	−1.41421	+	1.41421i	−0.0857493	+	0.0857493i
$273$		0			0
$274$			6.00000i			0.362473i
$275$	−4.24264	+	5.65685i	−0.255841	+	0.341121i
$276$	−4.00000	+	5.65685i	−0.240772	+	0.340503i
$277$	−6.00000	−	6.00000i	−0.360505	−	0.360505i	0.503494	−	0.863999i	$-0.332048\pi$
$277$	−6.00000	−	6.00000i	−0.360505	−	0.360505i	−0.863999	+	0.503494i	$0.832048\pi$
$278$	5.65685	+	5.65685i	0.339276	+	0.339276i
$279$	−5.65685	+	2.00000i	−0.338667	+	0.119737i
$280$	−3.00000	−	1.00000i	−0.179284	−	0.0597614i
$281$			8.48528i			0.506189i	0.967442	+	0.253095i	$0.0814484\pi$
$281$			8.48528i			0.506189i	−0.967442	+	0.253095i	$0.918552\pi$
$282$		0			0
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.211498	−	0.977378i	$-0.432166\pi$
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.977378	−	0.211498i	$-0.0678343\pi$
$284$	14.1421			0.839181
$285$	15.3137	+	2.34315i	0.907106	+	0.138796i
$286$		0			0
$287$	−5.65685	+	5.65685i	−0.333914	+	0.333914i
$288$	−1.29289	+	2.70711i	−0.0761845	+	0.159518i
$289$			13.0000i			0.764706i
$290$	−7.07107	−	14.1421i	−0.415227	−	0.830455i
$291$	−6.00000	−	4.24264i	−0.351726	−	0.248708i
$292$	5.00000	+	5.00000i	0.292603	+	0.292603i
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	7.07107	+	5.00000i	0.412393	+	0.291606i
$295$	−7.00000	+	21.0000i	−0.407556	+	1.22267i
$296$		−	8.48528i		−	0.493197i
$297$	3.58579	+	6.41421i	0.208068	+	0.372190i
$298$	9.00000	−	9.00000i	0.521356	−	0.521356i
$299$		0			0
$300$	3.94975	−	7.70711i	0.228039	−	0.444970i
$301$	−12.0000			−0.691669
$302$	11.3137	−	11.3137i	0.651031	−	0.651031i
$303$	−2.89949	−	16.8995i	−0.166572	−	0.970851i
$304$		−	4.00000i		−	0.229416i
$305$	4.24264	−	12.7279i	0.242933	−	0.728799i
$306$	−2.00000	−	5.65685i	−0.114332	−	0.323381i
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.999616	+	0.0276979i	$0.00881765\pi$
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.0276979	+	0.999616i	$0.491182\pi$
$308$	1.41421	+	1.41421i	0.0805823	+	0.0805823i
$309$	−1.41421	+	2.00000i	−0.0804518	+	0.113776i
$310$	−2.00000	−	4.00000i	−0.113592	−	0.227185i
$311$		−	19.7990i		−	1.12270i	−0.827579	−	0.561349i	$-0.810283\pi$
$311$		−	19.7990i		−	1.12270i	0.827579	−	0.561349i	$-0.189717\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$		0			0
$315$	6.58579	−	6.82843i	0.371067	−	0.384738i
$316$	6.00000			0.337526
$317$	−12.7279	+	12.7279i	−0.714871	+	0.714871i	−0.967550	−	0.252679i	$-0.918688\pi$
$317$	−12.7279	+	12.7279i	−0.714871	+	0.714871i	0.252679	+	0.967550i	$0.418688\pi$
$318$	6.82843	−	1.17157i	0.382919	−	0.0656985i
$319$			10.0000i			0.559893i
$320$	−2.12132	−	0.707107i	−0.118585	−	0.0395285i
$321$	4.00000	−	5.65685i	0.223258	−	0.315735i
$322$	−4.00000	−	4.00000i	−0.222911	−	0.222911i
$323$	5.65685	+	5.65685i	0.314756	+	0.314756i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$		0			0
$326$			5.65685i			0.313304i
$327$	2.92893	+	17.0711i	0.161970	+	0.944032i
$328$	−4.00000	+	4.00000i	−0.220863	+	0.220863i
$329$		0			0
$330$	−4.41421	+	3.24264i	−0.242994	+	0.178501i
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	−8.48528	+	8.48528i	−0.465690	+	0.465690i
$333$	22.9706	+	10.9706i	1.25878	+	0.601183i
$334$			8.00000i			0.437741i
$335$	11.3137	−	5.65685i	0.618134	−	0.309067i
$336$	−2.00000	−	1.41421i	−0.109109	−	0.0771517i
$337$	−9.00000	−	9.00000i	−0.490261	−	0.490261i	0.418127	−	0.908388i	$-0.362687\pi$
$337$	−9.00000	−	9.00000i	−0.490261	−	0.490261i	−0.908388	+	0.418127i	$0.862687\pi$
$338$	9.19239	+	9.19239i	0.500000	+	0.500000i
$339$	−19.7990	−	14.0000i	−1.07533	−	0.760376i
$340$	4.00000	−	2.00000i	0.216930	−	0.108465i
$341$			2.82843i			0.153168i
$342$	10.8284	+	5.17157i	0.585534	+	0.279647i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−8.48528			−0.457496
$345$	12.4853	−	9.17157i	0.672185	−	0.493781i
$346$	−2.00000			−0.107521
$347$	9.89949	−	9.89949i	0.531433	−	0.531433i	−0.389566	−	0.920999i	$-0.627375\pi$
$347$	9.89949	−	9.89949i	0.531433	−	0.531433i	0.920999	+	0.389566i	$0.127375\pi$
$348$	−2.07107	−	12.0711i	−0.111021	−	0.647077i
$349$		−	2.00000i		−	0.107058i	−0.998566	−	0.0535288i	$-0.982953\pi$
$349$		−	2.00000i		−	0.107058i	0.998566	−	0.0535288i	$-0.0170469\pi$
$350$	5.65685	+	4.24264i	0.302372	+	0.226779i
$351$		0			0
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	12.7279	+	12.7279i	0.677439	+	0.677439i	0.959420	−	0.281981i	$-0.0909915\pi$
$353$	12.7279	+	12.7279i	0.677439	+	0.677439i	−0.281981	+	0.959420i	$0.590992\pi$
$354$	−9.89949	+	14.0000i	−0.526152	+	0.744092i
$355$	−30.0000	−	10.0000i	−1.59223	−	0.530745i
$356$		−	2.82843i		−	0.149906i
$357$	4.82843	−	0.828427i	0.255547	−	0.0438450i
$358$	−13.0000	+	13.0000i	−0.687071	+	0.687071i
$359$	11.3137			0.597115			0.298557	−	0.954392i	$-0.403495\pi$
$359$	11.3137			0.597115			0.298557	+	0.954392i	$0.403495\pi$
$360$	4.65685	−	4.82843i	0.245438	−	0.254480i
$361$	3.00000			0.157895
$362$	−15.5563	+	15.5563i	−0.817624	+	0.817624i
$363$	−15.3640	+	2.63604i	−0.806399	+	0.138356i
$364$		0			0
$365$	−7.07107	−	14.1421i	−0.370117	−	0.740233i
$366$	6.00000	−	8.48528i	0.313625	−	0.443533i
$367$	−19.0000	−	19.0000i	−0.991792	−	0.991792i	0.00817466	−	0.999967i	$-0.497398\pi$
$367$	−19.0000	−	19.0000i	−0.991792	−	0.991792i	−0.999967	+	0.00817466i	$0.997398\pi$
$368$	−2.82843	−	2.82843i	−0.147442	−	0.147442i
$369$	−5.65685	−	16.0000i	−0.294484	−	0.832927i
$370$	−6.00000	+	18.0000i	−0.311925	+	0.935775i
$371$			5.65685i			0.293689i
$372$	−0.585786	−	3.41421i	−0.0303716	−	0.177019i
$373$	4.00000	−	4.00000i	0.207112	−	0.207112i	−0.595927	−	0.803039i	$-0.703215\pi$
$373$	4.00000	−	4.00000i	0.207112	−	0.207112i	0.803039	+	0.595927i	$0.203215\pi$
$374$	−2.82843			−0.146254
$375$	−13.8284	+	13.5563i	−0.714097	+	0.700047i
$376$		0			0
$377$		0			0
$378$	6.41421	−	3.58579i	0.329912	−	0.184433i
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$	−2.82843	+	8.48528i	−0.145095	+	0.435286i
$381$	14.0000	+	9.89949i	0.717242	+	0.507166i
$382$	−2.00000	−	2.00000i	−0.102329	−	0.102329i
$383$	−16.9706	−	16.9706i	−0.867155	−	0.867155i	0.125001	−	0.992157i	$-0.460106\pi$
$383$	−16.9706	−	16.9706i	−0.867155	−	0.867155i	−0.992157	+	0.125001i	$0.960106\pi$
$384$	−1.41421	−	1.00000i	−0.0721688	−	0.0510310i
$385$	−2.00000	−	4.00000i	−0.101929	−	0.203859i
$386$			21.2132i			1.07972i
$387$	10.9706	−	22.9706i	0.557665	−	1.16766i
$388$	3.00000	−	3.00000i	0.152302	−	0.152302i
$389$	4.24264			0.215110			0.107555	−	0.994199i	$-0.465698\pi$
$389$	4.24264			0.215110			0.107555	+	0.994199i	$0.465698\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$	−3.53553	+	3.53553i	−0.178571	+	0.178571i
$393$	5.38478	+	31.3848i	0.271626	+	1.58315i
$394$		−	24.0000i		−	1.20910i
$395$	−12.7279	−	4.24264i	−0.640411	−	0.213470i
$396$	−4.00000	+	1.41421i	−0.201008	+	0.0710669i
$397$	22.0000	+	22.0000i	1.10415	+	1.10415i	0.993905	+	0.110244i	$0.0351632\pi$
$397$	22.0000	+	22.0000i	1.10415	+	1.10415i	0.110244	+	0.993905i	$0.464837\pi$
$398$	−16.9706	−	16.9706i	−0.850657	−	0.850657i
$399$	−5.65685	+	8.00000i	−0.283197	+	0.400501i
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$		−	8.48528i		−	0.423735i	−0.977298	−	0.211867i	$-0.932046\pi$
$401$		−	8.48528i		−	0.423735i	0.977298	−	0.211867i	$-0.0679545\pi$
$402$	9.65685	−	1.65685i	0.481640	−	0.0826364i
$403$		0			0
$404$	9.89949			0.492518
$405$	7.05025	+	18.8492i	0.350330	+	0.936626i
$406$	10.0000			0.496292
$407$	8.48528	−	8.48528i	0.420600	−	0.420600i
$408$	3.41421	−	0.585786i	0.169029	−	0.0290008i
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$	11.3137	−	5.65685i	0.558744	−	0.279372i
$411$	6.00000	−	8.48528i	0.295958	−	0.418548i
$412$	−1.00000	−	1.00000i	−0.0492665	−	0.0492665i
$413$	−9.89949	−	9.89949i	−0.487122	−	0.487122i
$414$	11.3137	−	4.00000i	0.556038	−	0.196589i
$415$	24.0000	−	12.0000i	1.17811	−	0.589057i
$416$		0			0
$417$	−2.34315	−	13.6569i	−0.114744	−	0.668779i
$418$	4.00000	−	4.00000i	0.195646	−	0.195646i
$419$	21.2132			1.03633			0.518166	−	0.855280i	$-0.326615\pi$
$419$	21.2132			1.03633			0.518166	+	0.855280i	$0.326615\pi$
$420$	3.24264	+	4.41421i	0.158225	+	0.215392i
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	5.65685	−	5.65685i	0.275371	−	0.275371i
$423$		0			0
$424$			4.00000i			0.194257i
$425$	−9.89949	+	1.41421i	−0.480196	+	0.0685994i
$426$	−20.0000	−	14.1421i	−0.969003	−	0.685189i
$427$	6.00000	+	6.00000i	0.290360	+	0.290360i
$428$	2.82843	+	2.82843i	0.136717	+	0.136717i
$429$		0			0
$430$	18.0000	+	6.00000i	0.868037	+	0.289346i
$431$			11.3137i			0.544962i	0.962161	+	0.272481i	$0.0878442\pi$
$431$			11.3137i			0.544962i	−0.962161	+	0.272481i	$0.912156\pi$
$432$	4.53553	−	2.53553i	0.218216	−	0.121991i
$433$	−1.00000	+	1.00000i	−0.0480569	+	0.0480569i	−0.730727	−	0.682670i	$-0.760819\pi$
$433$	−1.00000	+	1.00000i	−0.0480569	+	0.0480569i	0.682670	+	0.730727i	$0.260819\pi$
$434$	2.82843			0.135769
$435$	−4.14214	+	27.0711i	−0.198600	+	1.29796i
$436$	−10.0000			−0.478913
$437$	−11.3137	+	11.3137i	−0.541208	+	0.541208i
$438$	−2.07107	−	12.0711i	−0.0989594	−	0.576778i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	−1.41421	−	2.82843i	−0.0674200	−	0.134840i
$441$	−5.00000	−	14.1421i	−0.238095	−	0.673435i
$442$		0			0
$443$	−4.24264	−	4.24264i	−0.201574	−	0.201574i	0.599100	−	0.800674i	$-0.295525\pi$
$443$	−4.24264	−	4.24264i	−0.201574	−	0.201574i	−0.800674	+	0.599100i	$0.795525\pi$
$444$	−8.48528	+	12.0000i	−0.402694	+	0.569495i
$445$	−2.00000	+	6.00000i	−0.0948091	+	0.284427i
$446$			12.7279i			0.602685i
$447$	−21.7279	+	3.72792i	−1.02770	+	0.176325i
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	14.1421			0.667409			0.333704	−	0.942678i	$-0.391701\pi$
$449$	14.1421			0.667409			0.333704	+	0.942678i	$0.391701\pi$
$450$	−13.2929	+	6.94975i	−0.626633	+	0.327614i
$451$	−8.00000			−0.376705
$452$	9.89949	−	9.89949i	0.465633	−	0.465633i
$453$	−27.3137	+	4.68629i	−1.28331	+	0.220181i
$454$		−	22.0000i		−	1.03251i
$455$		0			0
$456$	−4.00000	+	5.65685i	−0.187317	+	0.264906i
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	0.263099	−	0.964769i	$-0.415256\pi$
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	−0.964769	+	0.263099i	$0.915256\pi$
$458$	−4.24264	−	4.24264i	−0.198246	−	0.198246i
$459$	−2.82843	+	10.0000i	−0.132020	+	0.466760i
$460$	4.00000	+	8.00000i	0.186501	+	0.373002i
$461$			7.07107i			0.329332i	0.986349	+	0.164666i	$0.0526547\pi$
$461$			7.07107i			0.329332i	−0.986349	+	0.164666i	$0.947345\pi$
$462$	−0.585786	−	3.41421i	−0.0272533	−	0.158844i
$463$	5.00000	−	5.00000i	0.232370	−	0.232370i	−0.581311	−	0.813681i	$-0.697460\pi$
$463$	5.00000	−	5.00000i	0.232370	−	0.232370i	0.813681	+	0.581311i	$0.197460\pi$
$464$	7.07107			0.328266
$465$	−1.17157	+	7.65685i	−0.0543304	+	0.355078i
$466$	−18.0000			−0.833834
$467$	−19.7990	+	19.7990i	−0.916188	+	0.916188i	−0.996750	−	0.0805616i	$-0.974329\pi$
$467$	−19.7990	+	19.7990i	−0.916188	+	0.916188i	0.0805616	+	0.996750i	$0.474329\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$		0			0
$471$		0			0
$472$	−7.00000	−	7.00000i	−0.322201	−	0.322201i
$473$	−8.48528	−	8.48528i	−0.390154	−	0.390154i
$474$	−8.48528	−	6.00000i	−0.389742	−	0.275589i
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$			2.82843i			0.129641i
$477$	−10.8284	−	5.17157i	−0.495800	−	0.236790i
$478$	−6.00000	+	6.00000i	−0.274434	+	0.274434i
$479$	31.1127			1.42158			0.710788	−	0.703407i	$-0.248339\pi$
$479$	31.1127			1.42158			0.710788	+	0.703407i	$0.248339\pi$
$480$	2.29289	+	3.12132i	0.104656	+	0.142468i
$481$		0			0
$482$	2.82843	−	2.82843i	0.128831	−	0.128831i
$483$	1.65685	+	9.65685i	0.0753895	+	0.439402i
$484$		−	9.00000i		−	0.409091i
$485$	−8.48528	+	4.24264i	−0.385297	+	0.192648i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	9.00000	+	9.00000i	0.407829	+	0.407829i	0.880981	−	0.473152i	$-0.156884\pi$
$487$	9.00000	+	9.00000i	0.407829	+	0.407829i	−0.473152	+	0.880981i	$0.656884\pi$
$488$	4.24264	+	4.24264i	0.192055	+	0.192055i
$489$	5.65685	−	8.00000i	0.255812	−	0.361773i
$490$	10.0000	−	5.00000i	0.451754	−	0.225877i
$491$			26.8701i			1.21263i	0.795225	+	0.606314i	$0.207353\pi$
$491$			26.8701i			1.21263i	−0.795225	+	0.606314i	$0.792647\pi$
$492$	9.65685	−	1.65685i	0.435365	−	0.0746968i
$493$	−10.0000	+	10.0000i	−0.450377	+	0.450377i
$494$		0			0
$495$	9.48528	−	0.171573i	0.426332	−	0.00771163i
$496$	2.00000			0.0898027
$497$	14.1421	−	14.1421i	0.634361	−	0.634361i
$498$	20.4853	−	3.51472i	0.917967	−	0.157498i
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$	−6.36396	−	9.19239i	−0.284605	−	0.411096i
$501$	8.00000	−	11.3137i	0.357414	−	0.505459i
$502$	9.00000	+	9.00000i	0.401690	+	0.401690i
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	0.870503	−	0.492163i	$-0.163794\pi$
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	−0.492163	+	0.870503i	$0.663794\pi$
$504$	1.41421	+	4.00000i	0.0629941	+	0.178174i
$505$	−21.0000	−	7.00000i	−0.934488	−	0.311496i
$506$		−	5.65685i		−	0.251478i
$507$	−3.80761	−	22.1924i	−0.169102	−	0.985599i
$508$	−7.00000	+	7.00000i	−0.310575	+	0.310575i
$509$	−24.0416			−1.06563			−0.532813	−	0.846233i	$-0.678865\pi$
$509$	−24.0416			−1.06563			−0.532813	+	0.846233i	$0.678865\pi$
$510$	−7.65685	−	1.17157i	−0.339051	−	0.0518781i
$511$	10.0000			0.442374
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−10.1421	−	18.1421i	−0.447786	−	0.800995i
$514$			14.0000i			0.617514i
$515$	1.41421	+	2.82843i	0.0623177	+	0.124635i
$516$	12.0000	+	8.48528i	0.528271	+	0.373544i
$517$		0			0
$518$	−8.48528	−	8.48528i	−0.372822	−	0.372822i
$519$	2.82843	+	2.00000i	0.124154	+	0.0877903i
$520$		0			0
$521$		−	25.4558i		−	1.11524i	−0.830096	−	0.557620i	$-0.811714\pi$
$521$		−	25.4558i		−	1.11524i	0.830096	−	0.557620i	$-0.188286\pi$
$522$	−9.14214	+	19.1421i	−0.400140	+	0.837829i
$523$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$523$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$524$	−18.3848			−0.803143
$525$	−3.75736	−	11.6569i	−0.163985	−	0.508747i
$526$	8.00000			0.348817
$527$	−2.82843	+	2.82843i	−0.123208	+	0.123208i
$528$	−0.414214	−	2.41421i	−0.0180263	−	0.105065i
$529$		−	7.00000i		−	0.304348i
$530$	2.82843	−	8.48528i	0.122859	−	0.368577i
$531$	28.0000	−	9.89949i	1.21510	−	0.429601i
$532$	−4.00000	−	4.00000i	−0.173422	−	0.173422i
$533$		0			0
$534$	−2.82843	+	4.00000i	−0.122398	+	0.173097i
$535$	−4.00000	−	8.00000i	−0.172935	−	0.345870i
$536$			5.65685i			0.244339i
$537$	31.3848	−	5.38478i	1.35435	−	0.232370i
$538$	−11.0000	+	11.0000i	−0.474244	+	0.474244i
$539$	−7.07107			−0.304572
$540$	−11.4142	+	2.17157i	−0.491190	+	0.0934496i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		0			0
$543$	37.5563	−	6.44365i	1.61170	−	0.276524i
$544$			2.00000i			0.0857493i
$545$	21.2132	+	7.07107i	0.908674	+	0.302891i
$546$		0			0
$547$	6.00000	+	6.00000i	0.256541	+	0.256541i	0.823646	−	0.567104i	$-0.191936\pi$
$547$	6.00000	+	6.00000i	0.256541	+	0.256541i	−0.567104	+	0.823646i	$0.691936\pi$
$548$	4.24264	+	4.24264i	0.181237	+	0.181237i
$549$	−16.9706	+	6.00000i	−0.724286	+	0.256074i
$550$	1.00000	+	7.00000i	0.0426401	+	0.298481i
$551$		−	28.2843i		−	1.20495i
$552$	1.17157	+	6.82843i	0.0498655	+	0.290637i
$553$	6.00000	−	6.00000i	0.255146	−	0.255146i
$554$	−8.48528			−0.360505
$555$	26.4853	−	19.4558i	1.12424	−	0.825855i
$556$	8.00000			0.339276
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$	−2.58579	+	5.41421i	−0.109465	+	0.229202i
$559$		0			0
$560$	−2.82843	+	1.41421i	−0.119523	+	0.0597614i
$561$	4.00000	+	2.82843i	0.168880	+	0.119416i
$562$	6.00000	+	6.00000i	0.253095	+	0.253095i
$563$	21.2132	+	21.2132i	0.894030	+	0.894030i	0.994900	−	0.100870i	$-0.0321625\pi$
$563$	21.2132	+	21.2132i	0.894030	+	0.894030i	−0.100870	+	0.994900i	$0.532163\pi$
$564$		0			0
$565$	−28.0000	+	14.0000i	−1.17797	+	0.588984i
$566$		−	28.2843i		−	1.18888i
$567$	−12.6569	−	1.34315i	−0.531538	−	0.0564068i
$568$	10.0000	−	10.0000i	0.419591	−	0.419591i
$569$	−14.1421			−0.592869			−0.296435	−	0.955053i	$-0.595798\pi$
$569$	−14.1421			−0.592869			−0.296435	+	0.955053i	$0.595798\pi$
$570$	12.4853	−	9.17157i	0.522951	−	0.384155i
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		0			0
$573$	0.828427	+	4.82843i	0.0346080	+	0.201710i
$574$			8.00000i			0.333914i
$575$	−2.82843	−	19.7990i	−0.117954	−	0.825675i
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	13.0000	+	13.0000i	0.541197	+	0.541197i	0.923880	−	0.382683i	$-0.125000\pi$
$577$	13.0000	+	13.0000i	0.541197	+	0.541197i	−0.382683	+	0.923880i	$0.625000\pi$
$578$	9.19239	+	9.19239i	0.382353	+	0.382353i
$579$	21.2132	−	30.0000i	0.881591	−	1.24676i
$580$	−15.0000	−	5.00000i	−0.622841	−	0.207614i
$581$			16.9706i			0.704058i
$582$	−7.24264	+	1.24264i	−0.300217	+	0.0515091i
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	7.07107			0.292603
$585$		0			0
$586$		0			0
$587$	−25.4558	+	25.4558i	−1.05068	+	1.05068i	−0.0520296	+	0.998646i	$0.516569\pi$
$587$	−25.4558	+	25.4558i	−1.05068	+	1.05068i	−0.998646	+	0.0520296i	$0.983431\pi$
$588$	8.53553	−	1.46447i	0.351999	−	0.0603936i
$589$		−	8.00000i		−	0.329634i
$590$	9.89949	+	19.7990i	0.407556	+	0.815112i
$591$	−24.0000	+	33.9411i	−0.987228	+	1.39615i
$592$	−6.00000	−	6.00000i	−0.246598	−	0.246598i
$593$	15.5563	+	15.5563i	0.638823	+	0.638823i	0.950265	−	0.311442i	$-0.100812\pi$
$593$	15.5563	+	15.5563i	0.638823	+	0.638823i	−0.311442	+	0.950265i	$0.600812\pi$
$594$	7.07107	+	2.00000i	0.290129	+	0.0820610i
$595$	2.00000	−	6.00000i	0.0819920	−	0.245976i
$596$		−	12.7279i		−	0.521356i
$597$	7.02944	+	40.9706i	0.287696	+	1.67681i
$598$		0			0
$599$	−45.2548			−1.84906			−0.924531	−	0.381106i	$-0.875543\pi$
$599$	−45.2548			−1.84906			−0.924531	+	0.381106i	$0.875543\pi$
$600$	−2.65685	−	8.24264i	−0.108466	−	0.336504i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	−8.48528	+	8.48528i	−0.345834	+	0.345834i
$603$	−15.3137	−	7.31371i	−0.623622	−	0.297837i
$604$		−	16.0000i		−	0.651031i
$605$	−6.36396	+	19.0919i	−0.258732	+	0.776195i
$606$	−14.0000	−	9.89949i	−0.568711	−	0.402139i
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	0.765364	−	0.643598i	$-0.222559\pi$
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	−0.643598	+	0.765364i	$0.722559\pi$
$608$	−2.82843	−	2.82843i	−0.114708	−	0.114708i
$609$	−14.1421	−	10.0000i	−0.573068	−	0.405220i
$610$	−6.00000	−	12.0000i	−0.242933	−	0.485866i
$611$		0			0
$612$	−5.41421	−	2.58579i	−0.218857	−	0.104524i
$613$	18.0000	−	18.0000i	0.727013	−	0.727013i	−0.243011	−	0.970024i	$-0.578135\pi$
$613$	18.0000	−	18.0000i	0.727013	−	0.727013i	0.970024	+	0.243011i	$0.0781350\pi$
$614$	25.4558			1.02731
$615$	−21.6569	−	3.31371i	−0.873289	−	0.133622i
$616$	2.00000			0.0805823
$617$	21.2132	−	21.2132i	0.854011	−	0.854011i	−0.136613	−	0.990624i	$-0.543622\pi$
$617$	21.2132	−	21.2132i	0.854011	−	0.854011i	0.990624	+	0.136613i	$0.0436217\pi$
$618$	0.414214	+	2.41421i	0.0166621	+	0.0971139i
$619$			24.0000i			0.964641i	0.875995	+	0.482321i	$0.160206\pi$
$619$			24.0000i			0.964641i	−0.875995	+	0.482321i	$0.839794\pi$
$620$	−4.24264	−	1.41421i	−0.170389	−	0.0567962i
$621$	−20.0000	−	5.65685i	−0.802572	−	0.227002i
$622$	−14.0000	−	14.0000i	−0.561349	−	0.561349i
$623$	−2.82843	−	2.82843i	−0.113319	−	0.113319i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		−	12.7279i		−	0.508710i
$627$	−9.65685	+	1.65685i	−0.385658	+	0.0661684i
$628$		0			0
$629$	16.9706			0.676661
$630$	−0.171573	−	9.48528i	−0.00683563	−	0.377903i
$631$	−14.0000			−0.557331			−0.278666	−	0.960388i	$-0.589892\pi$
$631$	−14.0000			−0.557331			−0.278666	+	0.960388i	$0.589892\pi$
$632$	4.24264	−	4.24264i	0.168763	−	0.168763i
$633$	−13.6569	+	2.34315i	−0.542811	+	0.0931317i
$634$			18.0000i			0.714871i
$635$	19.7990	−	9.89949i	0.785699	−	0.392849i
$636$	4.00000	−	5.65685i	0.158610	−	0.224309i
$637$		0			0
$638$	7.07107	+	7.07107i	0.279946	+	0.279946i
$639$	14.1421	+	40.0000i	0.559454	+	1.58238i
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$			5.65685i			0.223432i	0.993740	+	0.111716i	$0.0356347\pi$
$641$			5.65685i			0.223432i	−0.993740	+	0.111716i	$0.964365\pi$
$642$	−1.17157	−	6.82843i	−0.0462383	−	0.269497i
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	−0.0521706	−	0.998638i	$-0.516614\pi$
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	0.998638	+	0.0521706i	$0.0166140\pi$
$644$	−5.65685			−0.222911
$645$	−19.4558	−	26.4853i	−0.766073	−	1.04286i
$646$	8.00000			0.314756
$647$	19.7990	−	19.7990i	0.778379	−	0.778379i	−0.201176	−	0.979555i	$-0.564476\pi$
$647$	19.7990	−	19.7990i	0.778379	−	0.778379i	0.979555	+	0.201176i	$0.0644765\pi$
$648$	−8.94975	−	0.949747i	−0.351579	−	0.0373096i
$649$		−	14.0000i		−	0.549548i
$650$		0			0
$651$	−4.00000	−	2.82843i	−0.156772	−	0.110855i
$652$	4.00000	+	4.00000i	0.156652	+	0.156652i
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	0.785231	−	0.619203i	$-0.212544\pi$
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	−0.619203	+	0.785231i	$0.712544\pi$
$654$	14.1421	+	10.0000i	0.553001	+	0.391031i
$655$	39.0000	+	13.0000i	1.52386	+	0.507952i
$656$			5.65685i			0.220863i
$657$	−9.14214	+	19.1421i	−0.356669	+	0.746806i
$658$		0			0
$659$	−35.3553			−1.37725			−0.688624	−	0.725118i	$-0.741785\pi$
$659$	−35.3553			−1.37725			−0.688624	+	0.725118i	$0.741785\pi$
$660$	−0.828427	+	5.41421i	−0.0322465	+	0.210748i
$661$	50.0000			1.94477			0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000			1.94477			0.972387	+	0.233373i	$0.0749763\pi$
$662$	−5.65685	+	5.65685i	−0.219860	+	0.219860i
$663$		0			0
$664$			12.0000i			0.465690i
$665$	5.65685	+	11.3137i	0.219363	+	0.438727i
$666$	24.0000	−	8.48528i	0.929981	−	0.328798i
$667$	−20.0000	−	20.0000i	−0.774403	−	0.774403i
$668$	5.65685	+	5.65685i	0.218870	+	0.218870i
$669$	12.7279	−	18.0000i	0.492090	−	0.695920i
$670$	4.00000	−	12.0000i	0.154533	−	0.463600i
$671$			8.48528i			0.327571i
$672$	−2.41421	+	0.414214i	−0.0931303	+	0.0159786i
$673$	13.0000	−	13.0000i	0.501113	−	0.501113i	−0.410671	−	0.911784i	$-0.634705\pi$
$673$	13.0000	−	13.0000i	0.501113	−	0.501113i	0.911784	+	0.410671i	$0.134705\pi$
$674$	−12.7279			−0.490261
$675$	25.7487	+	3.46447i	0.991069	+	0.133347i
$676$	13.0000			0.500000
$677$	18.3848	−	18.3848i	0.706584	−	0.706584i	−0.259231	−	0.965815i	$-0.583469\pi$
$677$	18.3848	−	18.3848i	0.706584	−	0.706584i	0.965815	+	0.259231i	$0.0834691\pi$
$678$	−23.8995	+	4.10051i	−0.917855	+	0.157479i
$679$		−	6.00000i		−	0.230259i
$680$	1.41421	−	4.24264i	0.0542326	−	0.162698i
$681$	−22.0000	+	31.1127i	−0.843042	+	1.19224i
$682$	2.00000	+	2.00000i	0.0765840	+	0.0765840i
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	0.0256307	−	0.999671i	$-0.491841\pi$
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	−0.999671	+	0.0256307i	$0.991841\pi$
$684$	11.3137	−	4.00000i	0.432590	−	0.152944i
$685$	−6.00000	−	12.0000i	−0.229248	−	0.458496i
$686$			16.9706i			0.647939i
$687$	1.75736	+	10.2426i	0.0670474	+	0.390781i
$688$	−6.00000	+	6.00000i	−0.228748	+	0.228748i
$689$		0			0
$690$	2.34315	−	15.3137i	0.0892020	−	0.582983i
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	−1.41421	+	1.41421i	−0.0537603	+	0.0537603i
$693$	−2.58579	+	5.41421i	−0.0982259	+	0.205669i
$694$		−	14.0000i		−	0.531433i
$695$	−16.9706	−	5.65685i	−0.643730	−	0.214577i
$696$	−10.0000	−	7.07107i	−0.379049	−	0.268028i
$697$	−8.00000	−	8.00000i	−0.303022	−	0.303022i
$698$	−1.41421	−	1.41421i	−0.0535288	−	0.0535288i
$699$	25.4558	+	18.0000i	0.962828	+	0.680823i
$700$	7.00000	−	1.00000i	0.264575	−	0.0377964i
$701$		−	26.8701i		−	1.01487i	−0.861691	−	0.507434i	$-0.830594\pi$
$701$		−	26.8701i		−	1.01487i	0.861691	−	0.507434i	$-0.169406\pi$
$702$		0			0
$703$	−24.0000	+	24.0000i	−0.905177	+	0.905177i
$704$	1.41421			0.0533002
$705$		0			0
$706$	18.0000			0.677439
$707$	9.89949	−	9.89949i	0.372309	−	0.372309i
$708$	2.89949	+	16.8995i	0.108970	+	0.635122i
$709$			10.0000i			0.375558i	0.982211	+	0.187779i	$0.0601289\pi$
$709$			10.0000i			0.375558i	−0.982211	+	0.187779i	$0.939871\pi$
$710$	−28.2843	+	14.1421i	−1.06149	+	0.530745i
$711$	6.00000	+	16.9706i	0.225018	+	0.636446i
$712$	−2.00000	−	2.00000i	−0.0749532	−	0.0749532i
$713$	−5.65685	−	5.65685i	−0.211851	−	0.211851i
$714$	2.82843	−	4.00000i	0.105851	−	0.149696i
$715$		0			0
$716$			18.3848i			0.687071i
$717$	14.4853	−	2.48528i	0.540963	−	0.0928145i
$718$	8.00000	−	8.00000i	0.298557	−	0.298557i
$719$	22.6274			0.843860			0.421930	−	0.906628i	$-0.361353\pi$
$719$	22.6274			0.843860			0.421930	+	0.906628i	$0.361353\pi$
$720$	−0.121320	−	6.70711i	−0.00452134	−	0.249959i
$721$	−2.00000			−0.0744839
$722$	2.12132	−	2.12132i	0.0789474	−	0.0789474i
$723$	−6.82843	+	1.17157i	−0.253952	+	0.0435713i
$724$			22.0000i			0.817624i
$725$	28.2843	+	21.2132i	1.05045	+	0.787839i
$726$	−9.00000	+	12.7279i	−0.334021	+	0.472377i
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	0.649283	−	0.760547i	$-0.275069\pi$
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	−0.760547	+	0.649283i	$0.775069\pi$
$728$		0			0
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	−15.0000	−	5.00000i	−0.555175	−	0.185058i
$731$		−	16.9706i		−	0.627679i
$732$	−1.75736	−	10.2426i	−0.0649539	−	0.378579i
$733$	−26.0000	+	26.0000i	−0.960332	+	0.960332i	−0.999243	−	0.0389108i	$-0.987611\pi$
$733$	−26.0000	+	26.0000i	−0.960332	+	0.960332i	0.0389108	+	0.999243i	$0.487611\pi$
$734$	−26.8701			−0.991792
$735$	−19.1421	−	2.92893i	−0.706068	−	0.108035i
$736$	−4.00000			−0.147442
$737$	−5.65685	+	5.65685i	−0.208373	+	0.208373i
$738$	−15.3137	−	7.31371i	−0.563705	−	0.269221i
$739$		−	40.0000i		−	1.47142i	−0.677295	−	0.735712i	$-0.736848\pi$
$739$		−	40.0000i		−	1.47142i	0.677295	−	0.735712i	$-0.263152\pi$
$740$	8.48528	+	16.9706i	0.311925	+	0.623850i
$741$		0			0
$742$	4.00000	+	4.00000i	0.146845	+	0.146845i
$743$	−36.7696	−	36.7696i	−1.34894	−	1.34894i	−0.886810	−	0.462134i	$-0.847084\pi$
$743$	−36.7696	−	36.7696i	−1.34894	−	1.34894i	−0.462134	−	0.886810i	$-0.652916\pi$
$744$	−2.82843	−	2.00000i	−0.103695	−	0.0733236i
$745$	−9.00000	+	27.0000i	−0.329734	+	0.989203i
$746$		−	5.65685i		−	0.207112i
$747$	−32.4853	−	15.5147i	−1.18857	−	0.567654i
$748$	−2.00000	+	2.00000i	−0.0731272	+	0.0731272i
$749$	5.65685			0.206697
$750$	−0.192388	+	19.3640i	−0.00702502	+	0.707072i
$751$	−30.0000			−1.09472			−0.547358	−	0.836899i	$-0.684366\pi$
$751$	−30.0000			−1.09472			−0.547358	+	0.836899i	$0.684366\pi$
$752$		0			0
$753$	−3.72792	−	21.7279i	−0.135853	−	0.791809i
$754$		0			0
$755$	−11.3137	+	33.9411i	−0.411748	+	1.23524i
$756$	2.00000	−	7.07107i	0.0727393	−	0.257172i
$757$	−30.0000	−	30.0000i	−1.09037	−	1.09037i	−0.995489	−	0.0948798i	$-0.969753\pi$
$757$	−30.0000	−	30.0000i	−1.09037	−	1.09037i	−0.0948798	−	0.995489i	$-0.530247\pi$
$758$	11.3137	+	11.3137i	0.410932	+	0.410932i
$759$	−5.65685	+	8.00000i	−0.205331	+	0.290382i
$760$	4.00000	+	8.00000i	0.145095	+	0.290191i
$761$			36.7696i			1.33290i	0.745552	+	0.666448i	$0.232186\pi$
$761$			36.7696i			1.33290i	−0.745552	+	0.666448i	$0.767814\pi$
$762$	16.8995	−	2.89949i	0.612204	−	0.105038i
$763$	−10.0000	+	10.0000i	−0.362024	+	0.362024i
$764$	−2.82843			−0.102329
$765$	9.65685	+	9.31371i	0.349144	+	0.336738i
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−1.70711	+	0.292893i	−0.0615999	+	0.0105689i
$769$		−	22.0000i		−	0.793340i	−0.917961	−	0.396670i	$-0.870166\pi$
$769$		−	22.0000i		−	0.793340i	0.917961	−	0.396670i	$-0.129834\pi$
$770$	−4.24264	−	1.41421i	−0.152894	−	0.0509647i
$771$	14.0000	−	19.7990i	0.504198	−	0.713043i
$772$	15.0000	+	15.0000i	0.539862	+	0.539862i
$773$	29.6985	+	29.6985i	1.06818	+	1.06818i	0.997499	+	0.0706813i	$0.0225173\pi$
$773$	29.6985	+	29.6985i	1.06818	+	1.06818i	0.0706813	+	0.997499i	$0.477483\pi$
$774$	−8.48528	−	24.0000i	−0.304997	−	0.862662i
$775$	8.00000	+	6.00000i	0.287368	+	0.215526i
$776$		−	4.24264i		−	0.152302i
$777$	3.51472	+	20.4853i	0.126090	+	0.734905i
$778$	3.00000	−	3.00000i	0.107555	−	0.107555i
$779$	22.6274			0.810711
$780$		0			0
$781$	20.0000			0.715656
$782$	5.65685	−	5.65685i	0.202289	−	0.202289i
$783$	32.0711	−	17.9289i	1.14613	−	0.640728i
$784$			5.00000i			0.178571i
$785$		0			0
$786$	26.0000	+	18.3848i	0.927389	+	0.655763i
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	0.999998	−	0.00190598i	$-0.000606691\pi$
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	−0.00190598	+	0.999998i	$0.500607\pi$
$788$	−16.9706	−	16.9706i	−0.604551	−	0.604551i
$789$	−11.3137	−	8.00000i	−0.402779	−	0.284808i
$790$	−12.0000	+	6.00000i	−0.426941	+	0.213470i
$791$		−	19.7990i		−	0.703971i
$792$	−1.82843	+	3.82843i	−0.0649703	+	0.136037i
$793$		0			0
$794$	31.1127			1.10415
$795$	−12.4853	+	9.17157i	−0.442807	+	0.325282i
$796$	−24.0000			−0.850657
$797$	12.7279	−	12.7279i	0.450846	−	0.450846i	−0.444789	−	0.895635i	$-0.646721\pi$
$797$	12.7279	−	12.7279i	0.450846	−	0.450846i	0.895635	+	0.444789i	$0.146721\pi$
$798$	1.65685	+	9.65685i	0.0586520	+	0.341849i
$799$		0			0
$800$	4.94975	−	0.707107i	0.175000	−	0.0250000i
$801$	8.00000	−	2.82843i	0.282666	−	0.0999376i
$802$	−6.00000	−	6.00000i	−0.211867	−	0.211867i
$803$	7.07107	+	7.07107i	0.249533	+	0.249533i
$804$	5.65685	−	8.00000i	0.199502	−	0.282138i
$805$	12.0000	+	4.00000i	0.422944	+	0.140981i
$806$		0			0
$807$	26.5563	−	4.55635i	0.934828	−	0.160391i
$808$	7.00000	−	7.00000i	0.246259	−	0.246259i
$809$	−22.6274			−0.795538			−0.397769	−	0.917486i	$-0.630215\pi$
$809$	−22.6274			−0.795538			−0.397769	+	0.917486i	$0.630215\pi$
$810$	18.3137	+	8.34315i	0.643478	+	0.293148i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	7.07107	−	7.07107i	0.248146	−	0.248146i
$813$		0			0
$814$		−	12.0000i		−	0.420600i
$815$	−5.65685	−	11.3137i	−0.198151	−	0.396302i
$816$	2.00000	−	2.82843i	0.0700140	−	0.0990148i
$817$	24.0000	+	24.0000i	0.839654	+	0.839654i
$818$		0			0
$819$		0			0
$820$	4.00000	−	12.0000i	0.139686	−	0.419058i
$821$		−	43.8406i		−	1.53005i	−0.644002	−	0.765024i	$-0.722727\pi$
$821$		−	43.8406i		−	1.53005i	0.644002	−	0.765024i	$-0.277273\pi$
$822$	−1.75736	−	10.2426i	−0.0612949	−	0.357253i
$823$	−25.0000	+	25.0000i	−0.871445	+	0.871445i	−0.992630	−	0.121185i	$-0.961331\pi$
$823$	−25.0000	+	25.0000i	−0.871445	+	0.871445i	0.121185	+	0.992630i	$0.461331\pi$
$824$	−1.41421			−0.0492665
$825$	5.58579	−	10.8995i	0.194472	−	0.379472i
$826$	−14.0000			−0.487122
$827$	−12.7279	+	12.7279i	−0.442593	+	0.442593i	−0.892883	−	0.450289i	$-0.851321\pi$
$827$	−12.7279	+	12.7279i	−0.442593	+	0.442593i	0.450289	+	0.892883i	$0.351321\pi$
$828$	5.17157	−	10.8284i	0.179725	−	0.376314i
$829$			14.0000i			0.486240i	0.969996	+	0.243120i	$0.0781709\pi$
$829$			14.0000i			0.486240i	−0.969996	+	0.243120i	$0.921829\pi$
$830$	8.48528	−	25.4558i	0.294528	−	0.883585i
$831$	12.0000	+	8.48528i	0.416275	+	0.294351i
$832$		0			0
$833$	−7.07107	−	7.07107i	−0.244998	−	0.244998i
$834$	−11.3137	−	8.00000i	−0.391762	−	0.277017i
$835$	−8.00000	−	16.0000i	−0.276851	−	0.553703i
$836$		−	5.65685i		−	0.195646i
$837$	9.07107	−	5.07107i	0.313542	−	0.175282i
$838$	15.0000	−	15.0000i	0.518166	−	0.518166i
$839$	−5.65685			−0.195296			−0.0976481	−	0.995221i	$-0.531132\pi$
$839$	−5.65685			−0.195296			−0.0976481	+	0.995221i	$0.531132\pi$
$840$	5.41421	+	0.828427i	0.186808	+	0.0285835i
$841$	21.0000			0.724138
$842$	9.89949	−	9.89949i	0.341159	−	0.341159i
$843$	−2.48528	−	14.4853i	−0.0855976	−	0.498900i
$844$		−	8.00000i		−	0.275371i
$845$	−27.5772	−	9.19239i	−0.948683	−	0.316228i
$846$		0			0
$847$	−9.00000	−	9.00000i	−0.309244	−	0.309244i
$848$	2.82843	+	2.82843i	0.0971286	+	0.0971286i
$849$	−28.2843	+	40.0000i	−0.970714	+	1.37280i
$850$	−6.00000	+	8.00000i	−0.205798	+	0.274398i
$851$			33.9411i			1.16349i
$852$	−24.1421	+	4.14214i	−0.827096	+	0.141907i
$853$	−2.00000	+	2.00000i	−0.0684787	+	0.0684787i	−0.740517	−	0.672038i	$-0.765419\pi$
$853$	−2.00000	+	2.00000i	−0.0684787	+	0.0684787i	0.672038	+	0.740517i	$0.265419\pi$
$854$	8.48528			0.290360
$855$	−26.8284	+	0.485281i	−0.917513	+	0.0165963i
$856$	4.00000			0.136717
$857$	−38.1838	+	38.1838i	−1.30433	+	1.30433i	−0.378892	+	0.925441i	$0.623695\pi$
$857$	−38.1838	+	38.1838i	−1.30433	+	1.30433i	−0.925441	+	0.378892i	$0.876305\pi$
$858$		0			0
$859$			32.0000i			1.09183i	0.837842	+	0.545913i	$0.183817\pi$
$859$			32.0000i			1.09183i	−0.837842	+	0.545913i	$0.816183\pi$
$860$	16.9706	−	8.48528i	0.578691	−	0.289346i
$861$	8.00000	−	11.3137i	0.272639	−	0.385570i
$862$	8.00000	+	8.00000i	0.272481	+	0.272481i
$863$	36.7696	+	36.7696i	1.25165	+	1.25165i	0.954980	+	0.296670i	$0.0958762\pi$
$863$	36.7696	+	36.7696i	1.25165	+	1.25165i	0.296670	+	0.954980i	$0.404124\pi$
$864$	1.41421	−	5.00000i	0.0481125	−	0.170103i
$865$	4.00000	−	2.00000i	0.136004	−	0.0680020i
$866$			1.41421i			0.0480569i
$867$	−3.80761	−	22.1924i	−0.129313	−	0.753693i
$868$	2.00000	−	2.00000i	0.0678844	−	0.0678844i
$869$	8.48528			0.287843
$870$	16.2132	+	22.0711i	0.549679	+	0.748279i
$871$		0			0
$872$	−7.07107	+	7.07107i	−0.239457	+	0.239457i
$873$	11.4853	+	5.48528i	0.388718	+	0.185649i
$874$			16.0000i			0.541208i
$875$	−15.5563	−	2.82843i	−0.525901	−	0.0956183i
$876$	−10.0000	−	7.07107i	−0.337869	−	0.238909i
$877$	−36.0000	−	36.0000i	−1.21563	−	1.21563i	−0.969146	−	0.246488i	$-0.920724\pi$
$877$	−36.0000	−	36.0000i	−1.21563	−	1.21563i	−0.246488	−	0.969146i	$-0.579276\pi$
$878$	−11.3137	−	11.3137i	−0.381819	−	0.381819i
$879$		0			0
$880$	−3.00000	−	1.00000i	−0.101130	−	0.0337100i
$881$			19.7990i			0.667045i	0.942742	+	0.333522i	$0.108237\pi$
$881$			19.7990i			0.667045i	−0.942742	+	0.333522i	$0.891763\pi$
$882$	−13.5355	−	6.46447i	−0.455765	−	0.217670i
$883$	4.00000	−	4.00000i	0.134611	−	0.134611i	−0.636591	−	0.771202i	$-0.719656\pi$
$883$	4.00000	−	4.00000i	0.134611	−	0.134611i	0.771202	+	0.636591i	$0.219656\pi$
$884$		0			0
$885$	5.79899	−	37.8995i	0.194931	−	1.27398i
$886$	−6.00000			−0.201574
$887$	8.48528	−	8.48528i	0.284908	−	0.284908i	−0.550155	−	0.835063i	$-0.685431\pi$
$887$	8.48528	−	8.48528i	0.284908	−	0.284908i	0.835063	+	0.550155i	$0.185431\pi$
$888$	2.48528	+	14.4853i	0.0834006	+	0.486094i
$889$			14.0000i			0.469545i
$890$	2.82843	+	5.65685i	0.0948091	+	0.189618i
$891$	−8.00000	−	9.89949i	−0.268010	−	0.331646i
$892$	9.00000	+	9.00000i	0.301342	+	0.301342i
$893$		0			0
$894$	−12.7279	+	18.0000i	−0.425685	+	0.602010i
$895$	13.0000	−	39.0000i	0.434542	−	1.30363i
$896$		−	1.41421i		−	0.0472456i
$897$		0			0
$898$	10.0000	−	10.0000i	0.333704	−	0.333704i
$899$	14.1421			0.471667
$900$	−4.48528	+	14.3137i	−0.149509	+	0.477124i
$901$	−8.00000			−0.266519
$902$	−5.65685	+	5.65685i	−0.188353	+	0.188353i
$903$	20.4853	−	3.51472i	0.681707	−	0.116963i
$904$		−	14.0000i		−	0.465633i
$905$	15.5563	−	46.6690i	0.517111	−	1.55133i
$906$	−16.0000	+	22.6274i	−0.531564	+	0.751746i
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	0.970718	−	0.240220i	$-0.0772197\pi$
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	−0.240220	+	0.970718i	$0.577220\pi$
$908$	−15.5563	−	15.5563i	−0.516256	−	0.516256i
$909$	9.89949	+	28.0000i	0.328346	+	0.928701i
$910$		0			0
$911$			39.5980i			1.31194i	0.754787	+	0.655970i	$0.227740\pi$
$911$			39.5980i			1.31194i	−0.754787	+	0.655970i	$0.772260\pi$
$912$	1.17157	+	6.82843i	0.0387947	+	0.226112i
$913$	−12.0000	+	12.0000i	−0.397142	+	0.397142i
$914$	−21.2132			−0.701670
$915$	−3.51472	+	22.9706i	−0.116193	+	0.759383i
$916$	−6.00000			−0.198246
$917$	−18.3848	+	18.3848i	−0.607119	+	0.607119i
$918$	5.07107	+	9.07107i	0.167370	+	0.299390i
$919$		−	34.0000i		−	1.12156i	−0.827966	−	0.560778i	$-0.810502\pi$
$919$		−	34.0000i		−	1.12156i	0.827966	−	0.560778i	$-0.189498\pi$
$920$	8.48528	+	2.82843i	0.279751	+	0.0932505i
$921$	−36.0000	−	25.4558i	−1.18624	−	0.838799i
$922$	5.00000	+	5.00000i	0.164666	+	0.164666i
$923$		0			0
$924$	−2.82843	−	2.00000i	−0.0930484	−	0.0657952i
$925$	−6.00000	−	42.0000i	−0.197279	−	1.38095i
$926$		−	7.07107i		−	0.232370i
$927$	1.82843	−	3.82843i	0.0600534	−	0.125742i
$928$	5.00000	−	5.00000i	0.164133	−	0.164133i
$929$	−2.82843			−0.0927977			−0.0463988	−	0.998923i	$-0.514775\pi$
$929$	−2.82843			−0.0927977			−0.0463988	+	0.998923i	$0.514775\pi$
$930$	4.58579	+	6.24264i	0.150374	+	0.204704i
$931$	20.0000			0.655474
$932$	−12.7279	+	12.7279i	−0.416917	+	0.416917i
$933$	5.79899	+	33.7990i	0.189850	+	1.10653i
$934$			28.0000i			0.916188i
$935$	5.65685	−	2.82843i	0.184999	−	0.0924995i
$936$		0			0
$937$	−5.00000	−	5.00000i	−0.163343	−	0.163343i	0.620703	−	0.784046i	$-0.286847\pi$
$937$	−5.00000	−	5.00000i	−0.163343	−	0.163343i	−0.784046	+	0.620703i	$0.786847\pi$
$938$	5.65685	+	5.65685i	0.184703	+	0.184703i
$939$	−12.7279	+	18.0000i	−0.415360	+	0.587408i
$940$		0			0
$941$		−	12.7279i		−	0.414918i	−0.978244	−	0.207459i	$-0.933481\pi$
$941$		−	12.7279i		−	0.414918i	0.978244	−	0.207459i	$-0.0665194\pi$
$942$		0			0
$943$	16.0000	−	16.0000i	0.521032	−	0.521032i
$944$	−9.89949			−0.322201
$945$	−9.24264	+	13.5858i	−0.300663	+	0.441946i
$946$	−12.0000			−0.390154
$947$	−18.3848	+	18.3848i	−0.597425	+	0.597425i	−0.939627	−	0.342202i	$-0.888827\pi$
$947$	−18.3848	+	18.3848i	−0.597425	+	0.597425i	0.342202	+	0.939627i	$0.388827\pi$
$948$	−10.2426	+	1.75736i	−0.332666	+	0.0570764i
$949$		0			0
$950$	−2.82843	−	19.7990i	−0.0917663	−	0.642364i
$951$	18.0000	−	25.4558i	0.583690	−	0.825462i
$952$	2.00000	+	2.00000i	0.0648204	+	0.0648204i
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	0.635044	−	0.772476i	$-0.280982\pi$
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	−0.772476	+	0.635044i	$0.780982\pi$
$954$	−11.3137	+	4.00000i	−0.366295	+	0.129505i
$955$	6.00000	+	2.00000i	0.194155	+	0.0647185i
$956$			8.48528i			0.274434i
$957$	−2.92893	−	17.0711i	−0.0946789	−	0.551829i
$958$	22.0000	−	22.0000i	0.710788	−	0.710788i
$959$	8.48528			0.274004
$960$	3.82843	+	0.585786i	0.123562	+	0.0189062i
$961$	−27.0000			−0.870968
$962$		0			0
$963$	−5.17157	+	10.8284i	−0.166652	+	0.348941i
$964$		−	4.00000i		−	0.128831i
$965$	−21.2132	−	42.4264i	−0.682877	−	1.36575i
$966$	8.00000	+	5.65685i	0.257396	+	0.182006i
$967$	19.0000	+	19.0000i	0.610999	+	0.610999i	0.943206	−	0.332208i	$-0.107793\pi$
$967$	19.0000	+	19.0000i	0.610999	+	0.610999i	−0.332208	+	0.943206i	$0.607793\pi$
$968$	−6.36396	−	6.36396i	−0.204545	−	0.204545i
$969$	−11.3137	−	8.00000i	−0.363449	−	0.256997i
$970$	−3.00000	+	9.00000i	−0.0963242	+	0.288973i
$971$		−	41.0122i		−	1.31614i	−0.752955	−	0.658072i	$-0.771372\pi$
$971$		−	41.0122i		−	1.31614i	0.752955	−	0.658072i	$-0.228628\pi$
$972$	11.7071	+	10.2929i	0.375506	+	0.330145i
$973$	8.00000	−	8.00000i	0.256468	−	0.256468i
$974$	12.7279			0.407829
$975$		0			0
$976$	6.00000			0.192055
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	−0.635975	−	0.771709i	$-0.719402\pi$
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	0.771709	+	0.635975i	$0.219402\pi$
$978$	−1.65685	−	9.65685i	−0.0529804	−	0.308792i
$979$		−	4.00000i		−	0.127841i
$980$	3.53553	−	10.6066i	0.112938	−	0.338815i
$981$	−10.0000	−	28.2843i	−0.319275	−	0.903047i
$982$	19.0000	+	19.0000i	0.606314	+	0.606314i
$983$	14.1421	+	14.1421i	0.451064	+	0.451064i	0.895708	−	0.444644i	$-0.146670\pi$
$983$	14.1421	+	14.1421i	0.451064	+	0.451064i	−0.444644	+	0.895708i	$0.646670\pi$
$984$	5.65685	−	8.00000i	0.180334	−	0.255031i
$985$	24.0000	+	48.0000i	0.764704	+	1.52941i
$986$			14.1421i			0.450377i
$987$		0			0
$988$		0			0
$989$	33.9411			1.07927
$990$	6.58579	−	6.82843i	0.209310	−	0.217022i
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$	1.41421	−	1.41421i	0.0449013	−	0.0449013i
$993$	13.6569	−	2.34315i	0.433387	−	0.0743575i
$994$		−	20.0000i		−	0.634361i
$995$	50.9117	+	16.9706i	1.61401	+	0.538003i
$996$	12.0000	−	16.9706i	0.380235	−	0.537733i
$997$	−8.00000	−	8.00000i	−0.253363	−	0.253363i	0.568985	−	0.822348i	$-0.307336\pi$
$997$	−8.00000	−	8.00000i	−0.253363	−	0.253363i	−0.822348	+	0.568985i	$0.807336\pi$
$998$	14.1421	+	14.1421i	0.447661	+	0.447661i
$999$	−42.4264	−	12.0000i	−1.34231	−	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.2.e.a.17.2	yes	4
3.2	odd	2	inner	30.2.e.a.17.1	✓	4
4.3	odd	2		240.2.v.e.17.2		4
5.2	odd	4		150.2.e.a.143.2		4
5.3	odd	4	inner	30.2.e.a.23.1	yes	4
5.4	even	2		150.2.e.a.107.1		4
8.3	odd	2		960.2.v.c.257.1		4
8.5	even	2		960.2.v.k.257.2		4
9.2	odd	6		810.2.m.f.377.2		8
9.4	even	3		810.2.m.f.107.2		8
9.5	odd	6		810.2.m.f.107.1		8
9.7	even	3		810.2.m.f.377.1		8
12.11	even	2		240.2.v.e.17.1		4
15.2	even	4		150.2.e.a.143.1		4
15.8	even	4	inner	30.2.e.a.23.2	yes	4
15.14	odd	2		150.2.e.a.107.2		4
20.3	even	4		240.2.v.e.113.1		4
20.7	even	4		1200.2.v.b.593.2		4
20.19	odd	2		1200.2.v.b.257.1		4
24.5	odd	2		960.2.v.k.257.1		4
24.11	even	2		960.2.v.c.257.2		4
40.3	even	4		960.2.v.c.833.2		4
40.13	odd	4		960.2.v.k.833.1		4
45.13	odd	12		810.2.m.f.593.2		8
45.23	even	12		810.2.m.f.593.1		8
45.38	even	12		810.2.m.f.53.2		8
45.43	odd	12		810.2.m.f.53.1		8
60.23	odd	4		240.2.v.e.113.2		4
60.47	odd	4		1200.2.v.b.593.1		4
60.59	even	2		1200.2.v.b.257.2		4
120.53	even	4		960.2.v.k.833.2		4
120.83	odd	4		960.2.v.c.833.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.e.a.17.1	✓	4	3.2	odd	2	inner
30.2.e.a.17.2	yes	4	1.1	even	1	trivial
30.2.e.a.23.1	yes	4	5.3	odd	4	inner
30.2.e.a.23.2	yes	4	15.8	even	4	inner
150.2.e.a.107.1		4	5.4	even	2
150.2.e.a.107.2		4	15.14	odd	2
150.2.e.a.143.1		4	15.2	even	4
150.2.e.a.143.2		4	5.2	odd	4
240.2.v.e.17.1		4	12.11	even	2
240.2.v.e.17.2		4	4.3	odd	2
240.2.v.e.113.1		4	20.3	even	4
240.2.v.e.113.2		4	60.23	odd	4
810.2.m.f.53.1		8	45.43	odd	12
810.2.m.f.53.2		8	45.38	even	12
810.2.m.f.107.1		8	9.5	odd	6
810.2.m.f.107.2		8	9.4	even	3
810.2.m.f.377.1		8	9.7	even	3
810.2.m.f.377.2		8	9.2	odd	6
810.2.m.f.593.1		8	45.23	even	12
810.2.m.f.593.2		8	45.13	odd	12
960.2.v.c.257.1		4	8.3	odd	2
960.2.v.c.257.2		4	24.11	even	2
960.2.v.c.833.1		4	120.83	odd	4
960.2.v.c.833.2		4	40.3	even	4
960.2.v.k.257.1		4	24.5	odd	2
960.2.v.k.257.2		4	8.5	even	2
960.2.v.k.833.1		4	40.13	odd	4
960.2.v.k.833.2		4	120.53	even	4
1200.2.v.b.257.1		4	20.19	odd	2
1200.2.v.b.257.2		4	60.59	even	2
1200.2.v.b.593.1		4	60.47	odd	4
1200.2.v.b.593.2		4	20.7	even	4

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(1.00000 + 2.00000i) q^{10} -1.41421i q^{11} +(0.292893 + 1.70711i) q^{12} -1.41421 q^{14} +(0.585786 - 3.82843i) q^{15} -1.00000 q^{16} +(1.41421 - 1.41421i) q^{17} +(1.29289 - 2.70711i) q^{18} +4.00000i q^{19} +(2.12132 + 0.707107i) q^{20} +(2.00000 + 1.41421i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(2.82843 + 2.82843i) q^{23} +(1.41421 + 1.00000i) q^{24} +(-4.00000 - 3.00000i) q^{25} +(-4.53553 + 2.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} -7.07107 q^{29} +(-2.29289 - 3.12132i) q^{30} -2.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.414214 + 2.41421i) q^{33} -2.00000i q^{34} +(2.82843 - 1.41421i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(6.00000 + 6.00000i) q^{37} +(2.82843 + 2.82843i) q^{38} +(2.00000 - 1.00000i) q^{40} -5.65685i q^{41} +(2.41421 - 0.414214i) q^{42} +(6.00000 - 6.00000i) q^{43} -1.41421 q^{44} +(0.121320 + 6.70711i) q^{45} +4.00000 q^{46} +(1.70711 - 0.292893i) q^{48} -5.00000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(-2.00000 + 2.82843i) q^{51} +(-2.82843 - 2.82843i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} +1.41421i q^{56} +(-1.17157 - 6.82843i) q^{57} +(-5.00000 + 5.00000i) q^{58} +9.89949 q^{59} +(-3.82843 - 0.585786i) q^{60} -6.00000 q^{61} +(-1.41421 + 1.41421i) q^{62} +(-3.82843 - 1.82843i) q^{63} +1.00000i q^{64} +(2.00000 + 1.41421i) q^{66} +(-4.00000 - 4.00000i) q^{67} +(-1.41421 - 1.41421i) q^{68} +(-5.65685 - 4.00000i) q^{69} +(1.00000 - 3.00000i) q^{70} +14.1421i q^{71} +(-2.70711 - 1.29289i) q^{72} +(-5.00000 + 5.00000i) q^{73} +8.48528 q^{74} +(7.70711 + 3.94975i) q^{75} +4.00000 q^{76} +(-1.41421 + 1.41421i) q^{77} +6.00000i q^{79} +(0.707107 - 2.12132i) q^{80} +(7.00000 - 5.65685i) q^{81} +(-4.00000 - 4.00000i) q^{82} +(-8.48528 - 8.48528i) q^{83} +(1.41421 - 2.00000i) q^{84} +(2.00000 + 4.00000i) q^{85} -8.48528i q^{86} +(12.0711 - 2.07107i) q^{87} +(-1.00000 + 1.00000i) q^{88} +2.82843 q^{89} +(4.82843 + 4.65685i) q^{90} +(2.82843 - 2.82843i) q^{92} +(3.41421 - 0.585786i) q^{93} +(-8.48528 - 2.82843i) q^{95} +(1.00000 - 1.41421i) q^{96} +(3.00000 + 3.00000i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-1.41421 - 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + 4 q^{10} + 4 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{18} + 8 q^{21} - 4 q^{22} - 16 q^{25} - 4 q^{27} - 4 q^{28} - 12 q^{30} - 8 q^{31} - 4 q^{33} - 4 q^{36} + 24 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^6 - 4 * q^7 + 4 * q^10 + 4 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^18 + 8 * q^21 - 4 * q^22 - 16 * q^25 - 4 * q^27 - 4 * q^28 - 12 * q^30 - 8 * q^31 - 4 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 + 4 * q^42 + 24 * q^43 - 8 * q^45 + 16 * q^46 + 4 * q^48 - 8 * q^51 + 12 * q^55 - 16 * q^57 - 20 * q^58 - 4 * q^60 - 24 * q^61 - 4 * q^63 + 8 * q^66 - 16 * q^67 + 4 * q^70 - 8 * q^72 - 20 * q^73 + 28 * q^75 + 16 * q^76 + 28 * q^81 - 16 * q^82 + 8 * q^85 + 20 * q^87 - 4 * q^88 + 8 * q^90 + 8 * q^93 + 4 * q^96 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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