LMFDB - Embedded newform 750.2.h.b.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(49,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("750.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			199.2
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.199
Dual form			750.2.h.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.92705 + 2.12663i) q^{11} +(0.587785 - 0.809017i) q^{12} +(-3.80423 + 5.23607i) q^{13} +(2.11803 - 1.53884i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.17557 - 0.381966i) q^{17} +1.00000i q^{18} +(1.76393 + 5.42882i) q^{19} +(-0.809017 + 2.48990i) q^{21} +(-3.44095 - 1.11803i) q^{22} +(-2.62866 - 3.61803i) q^{23} +1.00000 q^{24} -6.47214 q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.48990 + 0.809017i) q^{28} +(-2.61803 + 8.05748i) q^{29} +(2.04508 + 6.29412i) q^{31} -1.00000i q^{32} +(3.44095 - 1.11803i) q^{33} +(1.00000 + 0.726543i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(-4.70228 + 6.47214i) q^{37} +(-3.35520 + 4.61803i) q^{38} +(5.23607 - 3.80423i) q^{39} +(-4.61803 - 3.35520i) q^{41} +(-2.48990 + 0.809017i) q^{42} -7.70820i q^{43} +(-1.11803 - 3.44095i) q^{44} +(1.38197 - 4.25325i) q^{46} +(-1.62460 - 0.527864i) q^{47} +(0.587785 + 0.809017i) q^{48} +0.145898 q^{49} -1.23607 q^{51} +(-3.80423 - 5.23607i) q^{52} +(-1.98787 - 0.645898i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.809017 + 2.48990i) q^{56} -5.70820i q^{57} +(-8.05748 + 2.61803i) q^{58} +(-2.92705 - 2.12663i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(-3.88998 + 5.35410i) q^{62} +(1.53884 - 2.11803i) q^{63} +(0.809017 - 0.587785i) q^{64} +(2.92705 + 2.12663i) q^{66} +(-1.45309 + 0.472136i) q^{67} +1.23607i q^{68} +(1.38197 + 4.25325i) q^{69} +(1.70820 - 5.25731i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-2.07363 - 2.85410i) q^{73} -8.00000 q^{74} -5.70820 q^{76} +(5.56758 + 7.66312i) q^{77} +(6.15537 + 2.00000i) q^{78} +(1.73607 - 5.34307i) q^{79} +(0.309017 + 0.951057i) q^{81} -5.70820i q^{82} +(-2.04087 + 0.663119i) q^{83} +(-2.11803 - 1.53884i) q^{84} +(6.23607 - 4.53077i) q^{86} +(4.97980 - 6.85410i) q^{87} +(2.12663 - 2.92705i) q^{88} +(2.85410 - 2.07363i) q^{89} +(13.7082 + 9.95959i) q^{91} +(4.25325 - 1.38197i) q^{92} -6.61803i q^{93} +(-0.527864 - 1.62460i) q^{94} +(-0.309017 + 0.951057i) q^{96} +(3.21644 + 1.04508i) q^{97} +(0.0857567 + 0.118034i) q^{98} -3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} - 10 q^{11} + 8 q^{14} - 2 q^{16} + 32 q^{19} - 2 q^{21} + 8 q^{24} - 16 q^{26} - 12 q^{29} - 6 q^{31} + 8 q^{34} - 2 q^{36} + 24 q^{39} - 28 q^{41} + 20 q^{46} + 28 q^{49} + 8 q^{51} - 2 q^{54} + 2 q^{56} - 10 q^{59} + 2 q^{64} + 10 q^{66} + 20 q^{69} - 40 q^{71} - 64 q^{74} + 8 q^{76} - 4 q^{79} - 2 q^{81} - 8 q^{84} + 32 q^{86} - 4 q^{89} + 56 q^{91} - 40 q^{94} + 2 q^{96} - 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 - 10 * q^11 + 8 * q^14 - 2 * q^16 + 32 * q^19 - 2 * q^21 + 8 * q^24 - 16 * q^26 - 12 * q^29 - 6 * q^31 + 8 * q^34 - 2 * q^36 + 24 * q^39 - 28 * q^41 + 20 * q^46 + 28 * q^49 + 8 * q^51 - 2 * q^54 + 2 * q^56 - 10 * q^59 + 2 * q^64 + 10 * q^66 + 20 * q^69 - 40 * q^71 - 64 * q^74 + 8 * q^76 - 4 * q^79 - 2 * q^81 - 8 * q^84 + 32 * q^86 - 4 * q^89 + 56 * q^91 - 40 * q^94 + 2 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$		−	2.61803i		−	0.989524i	−0.869029	−	0.494762i	$-0.835255\pi$
$7$		−	2.61803i		−	0.989524i	0.869029	−	0.494762i	$-0.164745\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	−2.92705	+	2.12663i	−0.882539	+	0.641202i	−0.933922	−	0.357477i	$-0.883637\pi$
$11$	−2.92705	+	2.12663i	−0.882539	+	0.641202i	0.0513829	+	0.998679i	$0.483637\pi$
$12$	0.587785	−	0.809017i	0.169679	−	0.233543i
$13$	−3.80423	+	5.23607i	−1.05510	+	1.45222i	−0.170802	+	0.985305i	$0.554636\pi$
$13$	−3.80423	+	5.23607i	−1.05510	+	1.45222i	−0.884300	+	0.466919i	$0.845364\pi$
$14$	2.11803	−	1.53884i	0.566068	−	0.411273i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.17557	−	0.381966i	0.285118	−	0.0926404i	−0.162967	−	0.986632i	$-0.552106\pi$
$17$	1.17557	−	0.381966i	0.285118	−	0.0926404i	0.448085	+	0.893991i	$0.352106\pi$
$18$			1.00000i			0.235702i
$19$	1.76393	+	5.42882i	0.404674	+	1.24546i	0.921167	+	0.389167i	$0.127237\pi$
$19$	1.76393	+	5.42882i	0.404674	+	1.24546i	−0.516494	+	0.856291i	$0.672763\pi$
$20$		0			0
$21$	−0.809017	+	2.48990i	−0.176542	+	0.543340i
$22$	−3.44095	−	1.11803i	−0.733614	−	0.238366i
$23$	−2.62866	−	3.61803i	−0.548113	−	0.754412i	0.441642	−	0.897191i	$-0.354396\pi$
$23$	−2.62866	−	3.61803i	−0.548113	−	0.754412i	−0.989755	+	0.142779i	$0.954396\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	−6.47214			−1.26929
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	2.48990	+	0.809017i	0.470547	+	0.152890i
$29$	−2.61803	+	8.05748i	−0.486157	+	1.49624i	0.344142	+	0.938918i	$0.388170\pi$
$29$	−2.61803	+	8.05748i	−0.486157	+	1.49624i	−0.830299	+	0.557319i	$0.811830\pi$
$30$		0			0
$31$	2.04508	+	6.29412i	0.367308	+	1.13046i	0.948523	+	0.316708i	$0.102578\pi$
$31$	2.04508	+	6.29412i	0.367308	+	1.13046i	−0.581215	+	0.813750i	$0.697422\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.44095	−	1.11803i	0.598993	−	0.194625i
$34$	1.00000	+	0.726543i	0.171499	+	0.124601i
$35$		0			0
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−4.70228	+	6.47214i	−0.773050	+	1.06401i	0.222965	+	0.974827i	$0.428427\pi$
$37$	−4.70228	+	6.47214i	−0.773050	+	1.06401i	−0.996015	+	0.0891861i	$0.971573\pi$
$38$	−3.35520	+	4.61803i	−0.544285	+	0.749144i
$39$	5.23607	−	3.80423i	0.838442	−	0.609164i
$40$		0			0
$41$	−4.61803	−	3.35520i	−0.721216	−	0.523994i	0.165557	−	0.986200i	$-0.447058\pi$
$41$	−4.61803	−	3.35520i	−0.721216	−	0.523994i	−0.886772	+	0.462206i	$0.847058\pi$
$42$	−2.48990	+	0.809017i	−0.384200	+	0.124834i
$43$		−	7.70820i		−	1.17549i	−0.809046	−	0.587745i	$-0.800016\pi$
$43$		−	7.70820i		−	1.17549i	0.809046	−	0.587745i	$-0.199984\pi$
$44$	−1.11803	−	3.44095i	−0.168550	−	0.518743i
$45$		0			0
$46$	1.38197	−	4.25325i	0.203760	−	0.627108i
$47$	−1.62460	−	0.527864i	−0.236972	−	0.0769969i	0.188123	−	0.982145i	$-0.439759\pi$
$47$	−1.62460	−	0.527864i	−0.236972	−	0.0769969i	−0.425096	+	0.905149i	$0.639759\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	0.145898			0.0208426
$50$		0			0
$51$	−1.23607			−0.173084
$52$	−3.80423	−	5.23607i	−0.527551	−	0.726112i
$53$	−1.98787	−	0.645898i	−0.273055	−	0.0887209i	0.169289	−	0.985566i	$-0.445853\pi$
$53$	−1.98787	−	0.645898i	−0.273055	−	0.0887209i	−0.442344	+	0.896846i	$0.645853\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$		0			0
$56$	0.809017	+	2.48990i	0.108109	+	0.332727i
$57$		−	5.70820i		−	0.756070i
$58$	−8.05748	+	2.61803i	−1.05800	+	0.343765i
$59$	−2.92705	−	2.12663i	−0.381070	−	0.276863i	0.380717	−	0.924692i	$-0.375677\pi$
$59$	−2.92705	−	2.12663i	−0.381070	−	0.276863i	−0.761786	+	0.647829i	$0.775677\pi$
$60$		0			0
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	−0.721660	−	0.692247i	$-0.756621\pi$
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	0.435361	+	0.900256i	$0.356621\pi$
$62$	−3.88998	+	5.35410i	−0.494028	+	0.679972i
$63$	1.53884	−	2.11803i	0.193876	−	0.266847i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		0			0
$66$	2.92705	+	2.12663i	0.360295	+	0.261770i
$67$	−1.45309	+	0.472136i	−0.177523	+	0.0576806i	−0.396430	−	0.918065i	$-0.629751\pi$
$67$	−1.45309	+	0.472136i	−0.177523	+	0.0576806i	0.218907	+	0.975746i	$0.429751\pi$
$68$			1.23607i			0.149895i
$69$	1.38197	+	4.25325i	0.166369	+	0.512032i
$70$		0			0
$71$	1.70820	−	5.25731i	0.202727	−	0.623928i	−0.797073	−	0.603884i	$-0.793619\pi$
$71$	1.70820	−	5.25731i	0.202727	−	0.623928i	0.999799	−	0.0200445i	$-0.00638080\pi$
$72$	−0.951057	−	0.309017i	−0.112083	−	0.0364180i
$73$	−2.07363	−	2.85410i	−0.242700	−	0.334047i	0.670238	−	0.742146i	$-0.266192\pi$
$73$	−2.07363	−	2.85410i	−0.242700	−	0.334047i	−0.912938	+	0.408099i	$0.866192\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$	−5.70820			−0.654776
$77$	5.56758	+	7.66312i	0.634485	+	0.873293i
$78$	6.15537	+	2.00000i	0.696958	+	0.226455i
$79$	1.73607	−	5.34307i	0.195323	−	0.601142i	−0.804650	−	0.593750i	$-0.797647\pi$
$79$	1.73607	−	5.34307i	0.195323	−	0.601142i	0.999973	−	0.00739236i	$-0.00235308\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	5.70820i		−	0.630366i
$83$	−2.04087	+	0.663119i	−0.224015	+	0.0727868i	−0.418874	−	0.908044i	$-0.637575\pi$
$83$	−2.04087	+	0.663119i	−0.224015	+	0.0727868i	0.194859	+	0.980831i	$0.437575\pi$
$84$	−2.11803	−	1.53884i	−0.231096	−	0.167901i
$85$		0			0
$86$	6.23607	−	4.53077i	0.672453	−	0.488565i
$87$	4.97980	−	6.85410i	0.533890	−	0.734837i
$88$	2.12663	−	2.92705i	0.226699	−	0.312025i
$89$	2.85410	−	2.07363i	0.302534	−	0.219804i	−0.426152	−	0.904651i	$-0.640131\pi$
$89$	2.85410	−	2.07363i	0.302534	−	0.219804i	0.728686	+	0.684848i	$0.240131\pi$
$90$		0			0
$91$	13.7082	+	9.95959i	1.43701	+	1.04405i
$92$	4.25325	−	1.38197i	0.443432	−	0.144080i
$93$		−	6.61803i		−	0.686258i
$94$	−0.527864	−	1.62460i	−0.0544450	−	0.167565i
$95$		0			0
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	3.21644	+	1.04508i	0.326580	+	0.106112i	0.467718	−	0.883878i	$-0.345076\pi$
$97$	3.21644	+	1.04508i	0.326580	+	0.106112i	−0.141138	+	0.989990i	$0.545076\pi$
$98$	0.0857567	+	0.118034i	0.00866274	+	0.0119232i
$99$	−3.61803			−0.363626
$100$		0			0
$101$	4.38197			0.436022			0.218011	−	0.975946i	$-0.430043\pi$
$101$	4.38197			0.436022			0.218011	+	0.975946i	$0.430043\pi$
$102$	−0.726543	−	1.00000i	−0.0719384	−	0.0990148i
$103$	13.6251	+	4.42705i	1.34252	+	0.436210i	0.890169	−	0.455631i	$-0.150586\pi$
$103$	13.6251	+	4.42705i	1.34252	+	0.436210i	0.452348	+	0.891841i	$0.350586\pi$
$104$	2.00000	−	6.15537i	0.196116	−	0.603583i
$105$		0			0
$106$	−0.645898	−	1.98787i	−0.0627352	−	0.193079i
$107$			11.6180i			1.12316i	0.827423	+	0.561579i	$0.189806\pi$
$107$			11.6180i			1.12316i	−0.827423	+	0.561579i	$0.810194\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	13.9443	+	10.1311i	1.33562	+	0.970384i	0.999593	+	0.0285313i	$0.00908304\pi$
$109$	13.9443	+	10.1311i	1.33562	+	0.970384i	0.336026	+	0.941853i	$0.390917\pi$
$110$		0			0
$111$	6.47214	−	4.70228i	0.614308	−	0.446321i
$112$	−1.53884	+	2.11803i	−0.145407	+	0.200135i
$113$	−11.3067	+	15.5623i	−1.06364	+	1.46398i	−0.187292	+	0.982304i	$0.559971\pi$
$113$	−11.3067	+	15.5623i	−1.06364	+	1.46398i	−0.876350	+	0.481674i	$0.840029\pi$
$114$	4.61803	−	3.35520i	0.432519	−	0.314243i
$115$		0			0
$116$	−6.85410	−	4.97980i	−0.636387	−	0.462363i
$117$	−6.15537	+	2.00000i	−0.569064	+	0.184900i
$118$		−	3.61803i		−	0.333067i
$119$	−1.00000	−	3.07768i	−0.0916698	−	0.282131i
$120$		0			0
$121$	0.645898	−	1.98787i	0.0587180	−	0.180715i
$122$	−2.62866	−	0.854102i	−0.237987	−	0.0773268i
$123$	3.35520	+	4.61803i	0.302528	+	0.416394i
$124$	−6.61803			−0.594317
$125$		0			0
$126$	2.61803			0.233233
$127$	8.00448	+	11.0172i	0.710283	+	0.977620i	0.999791	+	0.0204448i	$0.00650822\pi$
$127$	8.00448	+	11.0172i	0.710283	+	0.977620i	−0.289508	+	0.957176i	$0.593492\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−2.38197	+	7.33094i	−0.209720	+	0.645453i
$130$		0			0
$131$	−5.52786	−	17.0130i	−0.482972	−	1.48643i	−0.834897	−	0.550406i	$-0.814473\pi$
$131$	−5.52786	−	17.0130i	−0.482972	−	1.48643i	0.351925	−	0.936028i	$-0.385527\pi$
$132$			3.61803i			0.314909i
$133$	14.2128	−	4.61803i	1.23241	−	0.400434i
$134$	−1.23607	−	0.898056i	−0.106780	−	0.0775802i
$135$		0			0
$136$	−1.00000	+	0.726543i	−0.0857493	+	0.0623005i
$137$	7.15942	−	9.85410i	0.611671	−	0.841893i	−0.385043	−	0.922899i	$-0.625813\pi$
$137$	7.15942	−	9.85410i	0.611671	−	0.841893i	0.996714	+	0.0810060i	$0.0258133\pi$
$138$	−2.62866	+	3.61803i	−0.223766	+	0.307988i
$139$	8.47214	−	6.15537i	0.718597	−	0.522091i	−0.167339	−	0.985899i	$-0.553517\pi$
$139$	8.47214	−	6.15537i	0.718597	−	0.522091i	0.885936	+	0.463808i	$0.153517\pi$
$140$		0			0
$141$	1.38197	+	1.00406i	0.116383	+	0.0845569i
$142$	5.25731	−	1.70820i	0.441184	−	0.143349i
$143$		−	23.4164i		−	1.95818i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$		0			0
$146$	1.09017	−	3.35520i	0.0902231	−	0.277678i
$147$	−0.138757	−	0.0450850i	−0.0114445	−	0.00371855i
$148$	−4.70228	−	6.47214i	−0.386525	−	0.532006i
$149$	−22.0902			−1.80970			−0.904849	−	0.425733i	$-0.860016\pi$
$149$	−22.0902			−1.80970			−0.904849	+	0.425733i	$0.860016\pi$
$150$		0			0
$151$	18.3262			1.49137			0.745684	−	0.666300i	$-0.232123\pi$
$151$	18.3262			1.49137			0.745684	+	0.666300i	$0.232123\pi$
$152$	−3.35520	−	4.61803i	−0.272143	−	0.374572i
$153$	1.17557	+	0.381966i	0.0950392	+	0.0308801i
$154$	−2.92705	+	9.00854i	−0.235868	+	0.725929i
$155$		0			0
$156$	2.00000	+	6.15537i	0.160128	+	0.492824i
$157$		−	8.65248i		−	0.690543i	−0.938503	−	0.345271i	$-0.887787\pi$
$157$		−	8.65248i		−	0.690543i	0.938503	−	0.345271i	$-0.112213\pi$
$158$	5.34307	−	1.73607i	0.425072	−	0.138114i
$159$	1.69098	+	1.22857i	0.134104	+	0.0974320i
$160$		0			0
$161$	−9.47214	+	6.88191i	−0.746509	+	0.542370i
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−0.277515	+	0.381966i	−0.0217366	+	0.0299179i	−0.819747	−	0.572726i	$-0.805886\pi$
$163$	−0.277515	+	0.381966i	−0.0217366	+	0.0299179i	0.798010	+	0.602644i	$0.205886\pi$
$164$	4.61803	−	3.35520i	0.360608	−	0.261997i
$165$		0			0
$166$	−1.73607	−	1.26133i	−0.134745	−	0.0978980i
$167$	11.1352	−	3.61803i	0.861665	−	0.279972i	0.155341	−	0.987861i	$-0.450352\pi$
$167$	11.1352	−	3.61803i	0.861665	−	0.279972i	0.706324	+	0.707889i	$0.250352\pi$
$168$		−	2.61803i		−	0.201986i
$169$	−8.92705	−	27.4746i	−0.686696	−	2.11343i
$170$		0			0
$171$	−1.76393	+	5.42882i	−0.134891	+	0.415153i
$172$	7.33094	+	2.38197i	0.558979	+	0.181623i
$173$	−2.99193	−	4.11803i	−0.227472	−	0.313088i	0.679991	−	0.733221i	$-0.261984\pi$
$173$	−2.99193	−	4.11803i	−0.227472	−	0.313088i	−0.907463	+	0.420132i	$0.861984\pi$
$174$	8.47214			0.642271
$175$		0			0
$176$	3.61803			0.272720
$177$	2.12663	+	2.92705i	0.159847	+	0.220011i
$178$	3.35520	+	1.09017i	0.251483	+	0.0817117i
$179$	−3.04508	+	9.37181i	−0.227600	+	0.700482i	0.770417	+	0.637540i	$0.220048\pi$
$179$	−3.04508	+	9.37181i	−0.227600	+	0.700482i	−0.998017	+	0.0629414i	$0.979952\pi$
$180$		0			0
$181$	−2.05573	−	6.32688i	−0.152801	−	0.470273i	0.845130	−	0.534560i	$-0.179523\pi$
$181$	−2.05573	−	6.32688i	−0.152801	−	0.470273i	−0.997931	+	0.0642869i	$0.979523\pi$
$182$			16.9443i			1.25599i
$183$	2.62866	−	0.854102i	0.194316	−	0.0631370i
$184$	3.61803	+	2.62866i	0.266725	+	0.193787i
$185$		0			0
$186$	5.35410	−	3.88998i	0.392582	−	0.285227i
$187$	−2.62866	+	3.61803i	−0.192226	+	0.264577i
$188$	1.00406	−	1.38197i	0.0732284	−	0.100790i
$189$	−2.11803	+	1.53884i	−0.154064	+	0.111934i
$190$		0			0
$191$	−3.47214	−	2.52265i	−0.251235	−	0.182533i	0.455039	−	0.890472i	$-0.349625\pi$
$191$	−3.47214	−	2.52265i	−0.251235	−	0.182533i	−0.706274	+	0.707939i	$0.749625\pi$
$192$	−0.951057	+	0.309017i	−0.0686366	+	0.0223014i
$193$			17.8541i			1.28517i	0.766216	+	0.642583i	$0.222137\pi$
$193$			17.8541i			1.28517i	−0.766216	+	0.642583i	$0.777863\pi$
$194$	1.04508	+	3.21644i	0.0750327	+	0.230927i
$195$		0			0
$196$	−0.0450850	+	0.138757i	−0.00322036	+	0.00991123i
$197$	16.2537	+	5.28115i	1.15803	+	0.376267i	0.824162	−	0.566354i	$-0.191646\pi$
$197$	16.2537	+	5.28115i	1.15803	+	0.376267i	0.333867	+	0.942620i	$0.391646\pi$
$198$	−2.12663	−	2.92705i	−0.151133	−	0.208016i
$199$	−19.5066			−1.38278			−0.691392	−	0.722480i	$-0.743002\pi$
$199$	−19.5066			−1.38278			−0.691392	+	0.722480i	$0.743002\pi$
$200$		0			0
$201$	1.52786			0.107767
$202$	2.57565	+	3.54508i	0.181222	+	0.249431i
$203$	21.0948	+	6.85410i	1.48056	+	0.481064i
$204$	0.381966	−	1.17557i	0.0267430	−	0.0823064i
$205$		0			0
$206$	4.42705	+	13.6251i	0.308447	+	0.949303i
$207$		−	4.47214i		−	0.310835i
$208$	6.15537	−	2.00000i	0.426798	−	0.138675i
$209$	−16.7082	−	12.1392i	−1.15573	−	0.839687i
$210$		0			0
$211$	2.76393	−	2.00811i	0.190277	−	0.138244i	−0.488568	−	0.872526i	$-0.662481\pi$
$211$	2.76393	−	2.00811i	0.190277	−	0.138244i	0.678845	+	0.734281i	$0.262481\pi$
$212$	1.22857	−	1.69098i	0.0843786	−	0.116137i
$213$	−3.24920	+	4.47214i	−0.222631	+	0.306426i
$214$	−9.39919	+	6.82891i	−0.642515	+	0.466815i
$215$		0			0
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	16.4782	−	5.35410i	1.11862	−	0.363460i
$218$			17.2361i			1.16737i
$219$	1.09017	+	3.35520i	0.0736669	+	0.226723i
$220$		0			0
$221$	−2.47214	+	7.60845i	−0.166294	+	0.511800i
$222$	7.60845	+	2.47214i	0.510646	+	0.165919i
$223$	4.75528	+	6.54508i	0.318437	+	0.438291i	0.937989	−	0.346664i	$-0.112686\pi$
$223$	4.75528	+	6.54508i	0.318437	+	0.438291i	−0.619552	+	0.784956i	$0.712686\pi$
$224$	−2.61803			−0.174925
$225$		0			0
$226$	−19.2361			−1.27956
$227$	−13.0903	−	18.0172i	−0.868832	−	1.19584i	−0.979391	−	0.201975i	$-0.935264\pi$
$227$	−13.0903	−	18.0172i	−0.868832	−	1.19584i	0.110558	−	0.993870i	$-0.464736\pi$
$228$	5.42882	+	1.76393i	0.359533	+	0.116819i
$229$	1.70820	−	5.25731i	0.112881	−	0.347413i	−0.878618	−	0.477525i	$-0.841534\pi$
$229$	1.70820	−	5.25731i	0.112881	−	0.347413i	0.991499	+	0.130113i	$0.0415339\pi$
$230$		0			0
$231$	−2.92705	−	9.00854i	−0.192586	−	0.592718i
$232$		−	8.47214i		−	0.556223i
$233$	−17.7396	+	5.76393i	−1.16216	+	0.377608i	−0.825710	−	0.564095i	$-0.809225\pi$
$233$	−17.7396	+	5.76393i	−1.16216	+	0.377608i	−0.336447	+	0.941702i	$0.609225\pi$
$234$	−5.23607	−	3.80423i	−0.342292	−	0.248690i
$235$		0			0
$236$	2.92705	−	2.12663i	0.190535	−	0.138432i
$237$	−3.30220	+	4.54508i	−0.214501	+	0.295235i
$238$	1.90211	−	2.61803i	0.123296	−	0.169702i
$239$	9.94427	−	7.22494i	0.643241	−	0.467342i	−0.217721	−	0.976011i	$-0.569862\pi$
$239$	9.94427	−	7.22494i	0.643241	−	0.467342i	0.860962	+	0.508669i	$0.169862\pi$
$240$		0			0
$241$	−7.73607	−	5.62058i	−0.498324	−	0.362054i	0.310052	−	0.950719i	$-0.399653\pi$
$241$	−7.73607	−	5.62058i	−0.498324	−	0.362054i	−0.808376	+	0.588666i	$0.799653\pi$
$242$	1.98787	−	0.645898i	0.127785	−	0.0415199i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.854102	−	2.62866i	−0.0546783	−	0.168282i
$245$		0			0
$246$	−1.76393	+	5.42882i	−0.112464	+	0.346129i
$247$	−35.1361	−	11.4164i	−2.23566	−	0.726409i
$248$	−3.88998	−	5.35410i	−0.247014	−	0.339986i
$249$	2.14590			0.135991
$250$		0			0
$251$	13.5623			0.856045			0.428023	−	0.903768i	$-0.359210\pi$
$251$	13.5623			0.856045			0.428023	+	0.903768i	$0.359210\pi$
$252$	1.53884	+	2.11803i	0.0969379	+	0.133424i
$253$	15.3884	+	5.00000i	0.967462	+	0.314347i
$254$	−4.20820	+	12.9515i	−0.264046	+	0.812651i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			22.0000i			1.37232i	0.727450	+	0.686161i	$0.240706\pi$
$257$			22.0000i			1.37232i	−0.727450	+	0.686161i	$0.759294\pi$
$258$	−7.33094	+	2.38197i	−0.456404	+	0.148295i
$259$	16.9443	+	12.3107i	1.05287	+	0.764952i
$260$		0			0
$261$	−6.85410	+	4.97980i	−0.424258	+	0.308242i
$262$	10.5146	−	14.4721i	0.649596	−	0.894092i
$263$	−6.88191	+	9.47214i	−0.424357	+	0.584077i	−0.966646	−	0.256115i	$-0.917558\pi$
$263$	−6.88191	+	9.47214i	−0.424357	+	0.584077i	0.542290	+	0.840192i	$0.317558\pi$
$264$	−2.92705	+	2.12663i	−0.180148	+	0.130885i
$265$		0			0
$266$	12.0902	+	8.78402i	0.741296	+	0.538583i
$267$	−3.35520	+	1.09017i	−0.205335	+	0.0667173i
$268$		−	1.52786i		−	0.0933292i
$269$	2.80902	+	8.64527i	0.171269	+	0.527111i	0.999443	−	0.0333590i	$-0.0106205\pi$
$269$	2.80902	+	8.64527i	0.171269	+	0.527111i	−0.828175	+	0.560470i	$0.810620\pi$
$270$		0			0
$271$	−5.57295	+	17.1518i	−0.338533	+	1.04190i	0.626423	+	0.779483i	$0.284518\pi$
$271$	−5.57295	+	17.1518i	−0.338533	+	1.04190i	−0.964956	+	0.262413i	$0.915482\pi$
$272$	−1.17557	−	0.381966i	−0.0712794	−	0.0231601i
$273$	−9.95959	−	13.7082i	−0.602782	−	0.829658i
$274$	12.1803			0.735841
$275$		0			0
$276$	−4.47214			−0.269191
$277$	9.95959	+	13.7082i	0.598414	+	0.823646i	0.995562	−	0.0941084i	$-0.0300000\pi$
$277$	9.95959	+	13.7082i	0.598414	+	0.823646i	−0.397148	+	0.917755i	$0.630000\pi$
$278$	9.95959	+	3.23607i	0.597337	+	0.194086i
$279$	−2.04508	+	6.29412i	−0.122436	+	0.376819i
$280$		0			0
$281$	1.81966	+	5.60034i	0.108552	+	0.334088i	0.990548	−	0.137169i	$-0.0438004\pi$
$281$	1.81966	+	5.60034i	0.108552	+	0.334088i	−0.881996	+	0.471257i	$0.843800\pi$
$282$			1.70820i			0.101722i
$283$	−4.35926	+	1.41641i	−0.259131	+	0.0841967i	−0.435701	−	0.900091i	$-0.643500\pi$
$283$	−4.35926	+	1.41641i	−0.259131	+	0.0841967i	0.176571	+	0.984288i	$0.443500\pi$
$284$	4.47214	+	3.24920i	0.265372	+	0.192804i
$285$		0			0
$286$	18.9443	−	13.7638i	1.12020	−	0.813872i
$287$	−8.78402	+	12.0902i	−0.518504	+	0.713660i
$288$	0.587785	−	0.809017i	0.0346356	−	0.0476718i
$289$	−12.5172	+	9.09429i	−0.736307	+	0.534958i
$290$		0			0
$291$	−2.73607	−	1.98787i	−0.160391	−	0.116531i
$292$	3.35520	−	1.09017i	0.196348	−	0.0637974i
$293$		−	22.0902i		−	1.29052i	−0.763962	−	0.645261i	$-0.776749\pi$
$293$		−	22.0902i		−	1.29052i	0.763962	−	0.645261i	$-0.223251\pi$
$294$	−0.0450850	−	0.138757i	−0.00262941	−	0.00809249i
$295$		0			0
$296$	2.47214	−	7.60845i	0.143690	−	0.442232i
$297$	3.44095	+	1.11803i	0.199664	+	0.0648749i
$298$	−12.9843	−	17.8713i	−0.752159	−	1.03526i
$299$	28.9443			1.67389
$300$		0			0
$301$	−20.1803			−1.16318
$302$	10.7719	+	14.8262i	0.619853	+	0.853154i
$303$	−4.16750	−	1.35410i	−0.239416	−	0.0777911i
$304$	1.76393	−	5.42882i	0.101168	−	0.311364i
$305$		0			0
$306$	0.381966	+	1.17557i	0.0218355	+	0.0672029i
$307$		−	10.0000i		−	0.570730i	−0.958419	−	0.285365i	$-0.907885\pi$
$307$		−	10.0000i		−	0.570730i	0.958419	−	0.285365i	$-0.0921148\pi$
$308$	−9.00854	+	2.92705i	−0.513309	+	0.166784i
$309$	−11.5902	−	8.42075i	−0.659342	−	0.479040i
$310$		0			0
$311$	0.854102	−	0.620541i	0.0484317	−	0.0351877i	−0.563306	−	0.826248i	$-0.690471\pi$
$311$	0.854102	−	0.620541i	0.0484317	−	0.0351877i	0.611738	+	0.791061i	$0.290471\pi$
$312$	−3.80423	+	5.23607i	−0.215372	+	0.296434i
$313$	−9.56357	+	13.1631i	−0.540565	+	0.744023i	−0.988694	−	0.149945i	$-0.952090\pi$
$313$	−9.56357	+	13.1631i	−0.540565	+	0.744023i	0.448130	+	0.893969i	$0.352090\pi$
$314$	7.00000	−	5.08580i	0.395033	−	0.287008i
$315$		0			0
$316$	4.54508	+	3.30220i	0.255681	+	0.185763i
$317$	−19.5559	+	6.35410i	−1.09837	+	0.356882i	−0.801475	−	0.598028i	$-0.795951\pi$
$317$	−19.5559	+	6.35410i	−1.09837	+	0.356882i	−0.296895	+	0.954910i	$0.595951\pi$
$318$			2.09017i			0.117211i
$319$	−9.47214	−	29.1522i	−0.530338	−	1.63221i
$320$		0			0
$321$	3.59017	−	11.0494i	0.200384	−	0.616718i
$322$	−11.1352	−	3.61803i	−0.620538	−	0.201625i
$323$	4.14725	+	5.70820i	0.230759	+	0.317613i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−0.472136			−0.0261492
$327$	−10.1311	−	13.9443i	−0.560251	−	0.771120i
$328$	5.42882	+	1.76393i	0.299757	+	0.0973969i
$329$	−1.38197	+	4.25325i	−0.0761903	+	0.234489i
$330$		0			0
$331$	−5.56231	−	17.1190i	−0.305732	−	0.940946i	−0.979403	−	0.201915i	$-0.935284\pi$
$331$	−5.56231	−	17.1190i	−0.305732	−	0.940946i	0.673671	−	0.739031i	$-0.264716\pi$
$332$		−	2.14590i		−	0.117771i
$333$	−7.60845	+	2.47214i	−0.416941	+	0.135472i
$334$	9.47214	+	6.88191i	0.518292	+	0.376561i
$335$		0			0
$336$	2.11803	−	1.53884i	0.115548	−	0.0839507i
$337$	−0.534785	+	0.736068i	−0.0291316	+	0.0400962i	−0.823334	−	0.567557i	$-0.807889\pi$
$337$	−0.534785	+	0.736068i	−0.0291316	+	0.0400962i	0.794203	+	0.607653i	$0.207889\pi$
$338$	16.9803	−	23.3713i	0.923604	−	1.27123i
$339$	15.5623	−	11.3067i	0.845228	−	0.614094i
$340$		0			0
$341$	−19.3713	−	14.0741i	−1.04902	−	0.762155i
$342$	−5.42882	+	1.76393i	−0.293557	+	0.0953825i
$343$		−	18.7082i		−	1.01015i
$344$	2.38197	+	7.33094i	0.128427	+	0.395258i
$345$		0			0
$346$	1.57295	−	4.84104i	0.0845623	−	0.260256i
$347$	−19.5559	−	6.35410i	−1.04982	−	0.341106i	−0.267220	−	0.963636i	$-0.586105\pi$
$347$	−19.5559	−	6.35410i	−1.04982	−	0.341106i	−0.782596	+	0.622529i	$0.786105\pi$
$348$	4.97980	+	6.85410i	0.266945	+	0.367418i
$349$	27.8885			1.49284			0.746420	−	0.665475i	$-0.231771\pi$
$349$	27.8885			1.49284			0.746420	+	0.665475i	$0.231771\pi$
$350$		0			0
$351$	6.47214			0.345457
$352$	2.12663	+	2.92705i	0.113350	+	0.156012i
$353$	−12.5882	−	4.09017i	−0.670005	−	0.217698i	−0.0457907	−	0.998951i	$-0.514581\pi$
$353$	−12.5882	−	4.09017i	−0.670005	−	0.217698i	−0.624214	+	0.781253i	$0.714581\pi$
$354$	−1.11803	+	3.44095i	−0.0594228	+	0.182885i
$355$		0			0
$356$	1.09017	+	3.35520i	0.0577789	+	0.177825i
$357$			3.23607i			0.171271i
$358$	−9.37181	+	3.04508i	−0.495315	+	0.160938i
$359$	17.9443	+	13.0373i	0.947062	+	0.688081i	0.950110	−	0.311914i	$-0.100970\pi$
$359$	17.9443	+	13.0373i	0.947062	+	0.688081i	−0.00304782	+	0.999995i	$0.500970\pi$
$360$		0			0
$361$	−10.9894	+	7.98424i	−0.578387	+	0.420223i
$362$	3.91023	−	5.38197i	0.205517	−	0.282870i
$363$	−1.22857	+	1.69098i	−0.0644833	+	0.0887536i
$364$	−13.7082	+	9.95959i	−0.718505	+	0.522025i
$365$		0			0
$366$	2.23607	+	1.62460i	0.116881	+	0.0849191i
$367$	−29.1195	+	9.46149i	−1.52002	+	0.493886i	−0.945783	−	0.324800i	$-0.894703\pi$
$367$	−29.1195	+	9.46149i	−1.52002	+	0.493886i	−0.574242	+	0.818686i	$0.694703\pi$
$368$			4.47214i			0.233126i
$369$	−1.76393	−	5.42882i	−0.0918266	−	0.282613i
$370$		0			0
$371$	−1.69098	+	5.20431i	−0.0877915	+	0.270194i
$372$	6.29412	+	2.04508i	0.326335	+	0.106033i
$373$	6.77591	+	9.32624i	0.350843	+	0.482894i	0.947569	−	0.319551i	$-0.103532\pi$
$373$	6.77591	+	9.32624i	0.350843	+	0.482894i	−0.596726	+	0.802445i	$0.703532\pi$
$374$	−4.47214			−0.231249
$375$		0			0
$376$	1.70820			0.0880939
$377$	−32.2299	−	44.3607i	−1.65993	−	2.28469i
$378$	−2.48990	−	0.809017i	−0.128067	−	0.0416113i
$379$	6.23607	−	19.1926i	0.320325	−	0.985860i	−0.653181	−	0.757201i	$-0.726566\pi$
$379$	6.23607	−	19.1926i	0.320325	−	0.985860i	0.973507	−	0.228658i	$-0.0734339\pi$
$380$		0			0
$381$	−4.20820	−	12.9515i	−0.215593	−	0.663526i
$382$		−	4.29180i		−	0.219587i
$383$	19.0211	−	6.18034i	0.971934	−	0.315801i	0.220338	−	0.975424i	$-0.429284\pi$
$383$	19.0211	−	6.18034i	0.971934	−	0.315801i	0.751597	+	0.659623i	$0.229284\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$		0			0
$386$	−14.4443	+	10.4944i	−0.735194	+	0.534150i
$387$	4.53077	−	6.23607i	0.230312	−	0.316997i
$388$	−1.98787	+	2.73607i	−0.100919	+	0.138903i
$389$	−10.0172	+	7.27794i	−0.507893	+	0.369006i	−0.812024	−	0.583624i	$-0.801634\pi$
$389$	−10.0172	+	7.27794i	−0.507893	+	0.369006i	0.304131	+	0.952630i	$0.401634\pi$
$390$		0			0
$391$	−4.47214	−	3.24920i	−0.226166	−	0.164319i
$392$	−0.138757	+	0.0450850i	−0.00700830	+	0.00227713i
$393$			17.8885i			0.902358i
$394$	5.28115	+	16.2537i	0.266061	+	0.818850i
$395$		0			0
$396$	1.11803	−	3.44095i	0.0561833	−	0.172914i
$397$	29.2582	+	9.50658i	1.46843	+	0.477121i	0.930633	−	0.365954i	$-0.119257\pi$
$397$	29.2582	+	9.50658i	1.46843	+	0.477121i	0.537796	+	0.843075i	$0.319257\pi$
$398$	−11.4657	−	15.7812i	−0.574723	−	0.791038i
$399$	−14.9443			−0.748149
$400$		0			0
$401$	25.7082			1.28381			0.641903	−	0.766786i	$-0.278145\pi$
$401$	25.7082			1.28381			0.641903	+	0.766786i	$0.278145\pi$
$402$	0.898056	+	1.23607i	0.0447910	+	0.0616495i
$403$	−40.7364	−	13.2361i	−2.02923	−	0.659336i
$404$	−1.35410	+	4.16750i	−0.0673691	+	0.207341i
$405$		0			0
$406$	6.85410	+	21.0948i	0.340163	+	1.04692i
$407$		−	28.9443i		−	1.43471i
$408$	1.17557	−	0.381966i	0.0581994	−	0.0189101i
$409$	4.69098	+	3.40820i	0.231954	+	0.168525i	0.697691	−	0.716399i	$-0.254211\pi$
$409$	4.69098	+	3.40820i	0.231954	+	0.168525i	−0.465737	+	0.884923i	$0.654211\pi$
$410$		0			0
$411$	−9.85410	+	7.15942i	−0.486067	+	0.353148i
$412$	−8.42075	+	11.5902i	−0.414861	+	0.571007i
$413$	−5.56758	+	7.66312i	−0.273963	+	0.377077i
$414$	3.61803	−	2.62866i	0.177817	−	0.129191i
$415$		0			0
$416$	5.23607	+	3.80423i	0.256719	+	0.186518i
$417$	−9.95959	+	3.23607i	−0.487723	+	0.158471i
$418$		−	20.6525i		−	1.01015i
$419$	0.954915	+	2.93893i	0.0466507	+	0.143576i	0.971669	−	0.236347i	$-0.0759504\pi$
$419$	0.954915	+	2.93893i	0.0466507	+	0.143576i	−0.925018	+	0.379923i	$0.875950\pi$
$420$		0			0
$421$	−7.03444	+	21.6498i	−0.342838	+	1.05515i	0.619893	+	0.784686i	$0.287176\pi$
$421$	−7.03444	+	21.6498i	−0.342838	+	1.05515i	−0.962731	+	0.270460i	$0.912824\pi$
$422$	3.24920	+	1.05573i	0.158168	+	0.0513920i
$423$	−1.00406	−	1.38197i	−0.0488189	−	0.0671935i
$424$	2.09017			0.101508
$425$		0			0
$426$	−5.52786			−0.267826
$427$	4.25325	+	5.85410i	0.205829	+	0.283300i
$428$	−11.0494	−	3.59017i	−0.534093	−	0.173537i
$429$	−7.23607	+	22.2703i	−0.349361	+	1.07522i
$430$		0			0
$431$	5.20163	+	16.0090i	0.250554	+	0.771124i	0.994673	+	0.103078i	$0.0328692\pi$
$431$	5.20163	+	16.0090i	0.250554	+	0.771124i	−0.744120	+	0.668046i	$0.767131\pi$
$432$			1.00000i			0.0481125i
$433$	−14.7476	+	4.79180i	−0.708726	+	0.230279i	−0.641128	−	0.767434i	$-0.721533\pi$
$433$	−14.7476	+	4.79180i	−0.708726	+	0.230279i	−0.0675976	+	0.997713i	$0.521533\pi$
$434$	14.0172	+	10.1841i	0.672848	+	0.488853i
$435$		0			0
$436$	−13.9443	+	10.1311i	−0.667810	+	0.485192i
$437$	15.0049	−	20.6525i	0.717782	−	0.987942i
$438$	−2.07363	+	2.85410i	−0.0990817	+	0.136374i
$439$	−19.0172	+	13.8168i	−0.907642	+	0.659441i	−0.940418	−	0.340022i	$-0.889566\pi$
$439$	−19.0172	+	13.8168i	−0.907642	+	0.659441i	0.0327751	+	0.999463i	$0.489566\pi$
$440$		0			0
$441$	0.118034	+	0.0857567i	0.00562067	+	0.00408365i
$442$	−7.60845	+	2.47214i	−0.361897	+	0.117588i
$443$			16.6180i			0.789547i	0.918779	+	0.394773i	$0.129177\pi$
$443$			16.6180i			0.789547i	−0.918779	+	0.394773i	$0.870823\pi$
$444$	2.47214	+	7.60845i	0.117322	+	0.361081i
$445$		0			0
$446$	−2.50000	+	7.69421i	−0.118378	+	0.364331i
$447$	21.0090	+	6.82624i	0.993692	+	0.322870i
$448$	−1.53884	−	2.11803i	−0.0727034	−	0.100068i
$449$	27.7082			1.30763			0.653815	−	0.756654i	$-0.273167\pi$
$449$	27.7082			1.30763			0.653815	+	0.756654i	$0.273167\pi$
$450$		0			0
$451$	20.6525			0.972487
$452$	−11.3067	−	15.5623i	−0.531821	−	0.731989i
$453$	−17.4293	−	5.66312i	−0.818899	−	0.266077i
$454$	6.88197	−	21.1805i	0.322987	−	0.994051i
$455$		0			0
$456$	1.76393	+	5.42882i	0.0826037	+	0.254228i
$457$			4.09017i			0.191330i	0.995414	+	0.0956650i	$0.0304978\pi$
$457$			4.09017i			0.191330i	−0.995414	+	0.0956650i	$0.969502\pi$
$458$	5.25731	−	1.70820i	0.245658	−	0.0798191i
$459$	−1.00000	−	0.726543i	−0.0466760	−	0.0339121i
$460$		0			0
$461$	−6.11803	+	4.44501i	−0.284945	+	0.207025i	−0.721072	−	0.692861i	$-0.756350\pi$
$461$	−6.11803	+	4.44501i	−0.284945	+	0.207025i	0.436126	+	0.899885i	$0.356350\pi$
$462$	5.56758	−	7.66312i	0.259027	−	0.356521i
$463$	−13.4208	+	18.4721i	−0.623717	+	0.858473i	−0.997617	−	0.0689961i	$-0.978020\pi$
$463$	−13.4208	+	18.4721i	−0.623717	+	0.858473i	0.373900	+	0.927469i	$0.378020\pi$
$464$	6.85410	−	4.97980i	0.318194	−	0.231181i
$465$		0			0
$466$	−15.0902	−	10.9637i	−0.699039	−	0.507881i
$467$	10.1514	−	3.29837i	0.469749	−	0.152631i	−0.0645710	−	0.997913i	$-0.520568\pi$
$467$	10.1514	−	3.29837i	0.469749	−	0.152631i	0.534320	+	0.845283i	$0.320568\pi$
$468$		−	6.47214i		−	0.299175i
$469$	1.23607	+	3.80423i	0.0570763	+	0.175663i
$470$		0			0
$471$	−2.67376	+	8.22899i	−0.123200	+	0.379172i
$472$	3.44095	+	1.11803i	0.158383	+	0.0514617i
$473$	16.3925	+	22.5623i	0.753727	+	1.03742i
$474$	−5.61803			−0.258045
$475$		0			0
$476$	3.23607			0.148325
$477$	−1.22857	−	1.69098i	−0.0562524	−	0.0774248i
$478$	11.6902	+	3.79837i	0.534697	+	0.173734i
$479$	9.00000	−	27.6992i	0.411220	−	1.26561i	−0.504368	−	0.863489i	$-0.668274\pi$
$479$	9.00000	−	27.6992i	0.411220	−	1.26561i	0.915588	−	0.402117i	$-0.131726\pi$
$480$		0			0
$481$	−16.0000	−	49.2429i	−0.729537	−	2.24528i
$482$		−	9.56231i		−	0.435551i
$483$	11.1352	−	3.61803i	0.506667	−	0.164626i
$484$	1.69098	+	1.22857i	0.0768629	+	0.0558441i
$485$		0			0
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−10.4616	+	14.3992i	−0.474061	+	0.652489i	−0.977350	−	0.211629i	$-0.932123\pi$
$487$	−10.4616	+	14.3992i	−0.474061	+	0.652489i	0.503289	+	0.864118i	$0.332123\pi$
$488$	1.62460	−	2.23607i	0.0735421	−	0.101222i
$489$	0.381966	−	0.277515i	0.0172731	−	0.0125496i
$490$		0			0
$491$	20.4443	+	14.8536i	0.922637	+	0.670335i	0.944179	−	0.329433i	$-0.106858\pi$
$491$	20.4443	+	14.8536i	0.922637	+	0.670335i	−0.0215419	+	0.999768i	$0.506858\pi$
$492$	−5.42882	+	1.76393i	−0.244750	+	0.0795242i
$493$			10.4721i			0.471641i
$494$	−11.4164	−	35.1361i	−0.513648	−	1.58085i
$495$		0			0
$496$	2.04508	−	6.29412i	0.0918270	−	0.282615i
$497$	−13.7638	−	4.47214i	−0.617392	−	0.200603i
$498$	1.26133	+	1.73607i	0.0565214	+	0.0777951i
$499$	−35.5967			−1.59353			−0.796765	−	0.604290i	$-0.793457\pi$
$499$	−35.5967			−1.59353			−0.796765	+	0.604290i	$0.793457\pi$
$500$		0			0
$501$	−11.7082			−0.523084
$502$	7.97172	+	10.9721i	0.355795	+	0.489710i
$503$	22.7194	+	7.38197i	1.01301	+	0.329146i	0.768051	−	0.640389i	$-0.221227\pi$
$503$	22.7194	+	7.38197i	1.01301	+	0.329146i	0.244955	+	0.969534i	$0.421227\pi$
$504$	−0.809017	+	2.48990i	−0.0360365	+	0.110909i
$505$		0			0
$506$	5.00000	+	15.3884i	0.222277	+	0.684099i
$507$			28.8885i			1.28299i
$508$	−12.9515	+	4.20820i	−0.574631	+	0.186709i
$509$	−14.1631	−	10.2901i	−0.627769	−	0.456101i	0.227857	−	0.973694i	$-0.426828\pi$
$509$	−14.1631	−	10.2901i	−0.627769	−	0.456101i	−0.855627	+	0.517593i	$0.826828\pi$
$510$		0			0
$511$	−7.47214	+	5.42882i	−0.330548	+	0.240157i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	3.35520	−	4.61803i	0.148136	−	0.203891i
$514$	−17.7984	+	12.9313i	−0.785053	+	0.570374i
$515$		0			0
$516$	−6.23607	−	4.53077i	−0.274528	−	0.199456i
$517$	5.87785	−	1.90983i	0.258508	−	0.0839942i
$518$			20.9443i			0.920238i
$519$	1.57295	+	4.84104i	0.0690448	+	0.212498i
$520$		0			0
$521$	4.38197	−	13.4863i	0.191977	−	0.590846i	−0.808021	−	0.589153i	$-0.799461\pi$
$521$	4.38197	−	13.4863i	0.191977	−	0.590846i	0.999999	−	0.00169226i	$-0.000538663\pi$
$522$	−8.05748	−	2.61803i	−0.352666	−	0.114588i
$523$	−6.49839	−	8.94427i	−0.284155	−	0.391106i	0.642950	−	0.765908i	$-0.277710\pi$
$523$	−6.49839	−	8.94427i	−0.284155	−	0.391106i	−0.927105	+	0.374803i	$0.877710\pi$
$524$	17.8885			0.781465
$525$		0			0
$526$	−11.7082			−0.510502
$527$	4.80828	+	6.61803i	0.209452	+	0.288286i
$528$	−3.44095	−	1.11803i	−0.149748	−	0.0486562i
$529$	0.927051	−	2.85317i	0.0403066	−	0.124051i
$530$		0			0
$531$	−1.11803	−	3.44095i	−0.0485185	−	0.149325i
$532$			14.9443i			0.647916i
$533$	35.1361	−	11.4164i	1.52191	−	0.494500i
$534$	−2.85410	−	2.07363i	−0.123509	−	0.0897346i
$535$		0			0
$536$	1.23607	−	0.898056i	0.0533900	−	0.0387901i
$537$	5.79210	−	7.97214i	0.249947	−	0.344023i
$538$	−5.34307	+	7.35410i	−0.230356	+	0.317058i
$539$	−0.427051	+	0.310271i	−0.0183944	+	0.0133643i
$540$		0			0
$541$	21.1803	+	15.3884i	0.910614	+	0.661600i	0.941170	−	0.337933i	$-0.109728\pi$
$541$	21.1803	+	15.3884i	0.910614	+	0.661600i	−0.0305561	+	0.999533i	$0.509728\pi$
$542$	−17.1518	+	5.57295i	−0.736732	+	0.239379i
$543$			6.65248i			0.285485i
$544$	−0.381966	−	1.17557i	−0.0163767	−	0.0504022i
$545$		0			0
$546$	5.23607	−	16.1150i	0.224083	−	0.689657i
$547$	−9.23305	−	3.00000i	−0.394777	−	0.128271i	0.104900	−	0.994483i	$-0.466548\pi$
$547$	−9.23305	−	3.00000i	−0.394777	−	0.128271i	−0.499677	+	0.866212i	$0.666548\pi$
$548$	7.15942	+	9.85410i	0.305835	+	0.420946i
$549$	−2.76393			−0.117962
$550$		0			0
$551$	−48.3607			−2.06023
$552$	−2.62866	−	3.61803i	−0.111883	−	0.153994i
$553$	−13.9883	−	4.54508i	−0.594844	−	0.193277i
$554$	−5.23607	+	16.1150i	−0.222459	+	0.684659i
$555$		0			0
$556$	3.23607	+	9.95959i	0.137240	+	0.422381i
$557$			18.3262i			0.776508i	0.921552	+	0.388254i	$0.126922\pi$
$557$			18.3262i			0.776508i	−0.921552	+	0.388254i	$0.873078\pi$
$558$	−6.29412	+	2.04508i	−0.266452	+	0.0865754i
$559$	40.3607	+	29.3238i	1.70707	+	1.24026i
$560$		0			0
$561$	3.61803	−	2.62866i	0.152754	−	0.110982i
$562$	−3.46120	+	4.76393i	−0.146002	+	0.200954i
$563$	12.5025	−	17.2082i	0.526917	−	0.725239i	−0.459739	−	0.888054i	$-0.652057\pi$
$563$	12.5025	−	17.2082i	0.526917	−	0.725239i	0.986657	+	0.162815i	$0.0520572\pi$
$564$	−1.38197	+	1.00406i	−0.0581913	+	0.0422784i
$565$		0			0
$566$	−3.70820	−	2.69417i	−0.155867	−	0.113244i
$567$	2.48990	−	0.809017i	0.104566	−	0.0339755i
$568$			5.52786i			0.231944i
$569$	8.58359	+	26.4176i	0.359843	+	1.10748i	0.953148	+	0.302505i	$0.0978228\pi$
$569$	8.58359	+	26.4176i	0.359843	+	1.10748i	−0.593305	+	0.804978i	$0.702177\pi$
$570$		0			0
$571$	2.43769	−	7.50245i	0.102014	−	0.313968i	−0.887004	−	0.461762i	$-0.847217\pi$
$571$	2.43769	−	7.50245i	0.102014	−	0.313968i	0.989018	+	0.147794i	$0.0472174\pi$
$572$	22.2703	+	7.23607i	0.931169	+	0.302555i
$573$	2.52265	+	3.47214i	0.105385	+	0.145051i
$574$	−14.9443			−0.623762
$575$		0			0
$576$	1.00000			0.0416667
$577$	5.27756	+	7.26393i	0.219708	+	0.302401i	0.904616	−	0.426228i	$-0.140158\pi$
$577$	5.27756	+	7.26393i	0.219708	+	0.302401i	−0.684908	+	0.728629i	$0.740158\pi$
$578$	−14.7149	−	4.78115i	−0.612058	−	0.198870i
$579$	5.51722	−	16.9803i	0.229288	−	0.705676i
$580$		0			0
$581$	1.73607	+	5.34307i	0.0720242	+	0.221668i
$582$		−	3.38197i		−	0.140187i
$583$	7.19218	−	2.33688i	0.297870	−	0.0967837i
$584$	2.85410	+	2.07363i	0.118104	+	0.0858073i
$585$		0			0
$586$	17.8713	−	12.9843i	0.738258	−	0.536376i
$587$	0.567541	−	0.781153i	0.0234249	−	0.0322416i	−0.797144	−	0.603789i	$-0.793657\pi$
$587$	0.567541	−	0.781153i	0.0234249	−	0.0322416i	0.820569	+	0.571548i	$0.193657\pi$
$588$	0.0857567	−	0.118034i	0.00353655	−	0.00486764i
$589$	−30.5623	+	22.2048i	−1.25930	+	0.914933i
$590$		0			0
$591$	−13.8262	−	10.0453i	−0.568735	−	0.413210i
$592$	7.60845	−	2.47214i	0.312705	−	0.101604i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	1.11803	+	3.44095i	0.0458735	+	0.141184i
$595$		0			0
$596$	6.82624	−	21.0090i	0.279614	−	0.860562i
$597$	18.5519	+	6.02786i	0.759277	+	0.246704i
$598$	17.0130	+	23.4164i	0.695714	+	0.957568i
$599$	−0.472136			−0.0192910			−0.00964548	−	0.999953i	$-0.503070\pi$
$599$	−0.472136			−0.0192910			−0.00964548	+	0.999953i	$0.503070\pi$
$600$		0			0
$601$	−7.72949			−0.315292			−0.157646	−	0.987496i	$-0.550391\pi$
$601$	−7.72949			−0.315292			−0.157646	+	0.987496i	$0.550391\pi$
$602$	−11.8617	−	16.3262i	−0.483447	−	0.665408i
$603$	−1.45309	−	0.472136i	−0.0591742	−	0.0192269i
$604$	−5.66312	+	17.4293i	−0.230429	+	0.709188i
$605$		0			0
$606$	−1.35410	−	4.16750i	−0.0550066	−	0.169293i
$607$		−	6.56231i		−	0.266356i	−0.991092	−	0.133178i	$-0.957482\pi$
$607$		−	6.56231i		−	0.266356i	0.991092	−	0.133178i	$-0.0425182\pi$
$608$	5.42882	−	1.76393i	0.220168	−	0.0715369i
$609$	−17.9443	−	13.0373i	−0.727139	−	0.528297i
$610$		0			0
$611$	8.94427	−	6.49839i	0.361847	−	0.262897i
$612$	−0.726543	+	1.00000i	−0.0293687	+	0.0404226i
$613$	28.3602	−	39.0344i	1.14546	−	1.57659i	0.390788	−	0.920481i	$-0.372203\pi$
$613$	28.3602	−	39.0344i	1.14546	−	1.57659i	0.754669	−	0.656105i	$-0.227797\pi$
$614$	8.09017	−	5.87785i	0.326493	−	0.237211i
$615$		0			0
$616$	−7.66312	−	5.56758i	−0.308756	−	0.224324i
$617$	2.00811	−	0.652476i	0.0808436	−	0.0262677i	−0.268316	−	0.963331i	$-0.586467\pi$
$617$	2.00811	−	0.652476i	0.0808436	−	0.0262677i	0.349160	+	0.937063i	$0.386467\pi$
$618$		−	14.3262i		−	0.576286i
$619$	2.90983	+	8.95554i	0.116956	+	0.359953i	0.992350	−	0.123457i	$-0.0393980\pi$
$619$	2.90983	+	8.95554i	0.116956	+	0.359953i	−0.875394	+	0.483410i	$0.839398\pi$
$620$		0			0
$621$	−1.38197	+	4.25325i	−0.0554564	+	0.170677i
$622$	1.00406	+	0.326238i	0.0402590	+	0.0130809i
$623$	−5.42882	−	7.47214i	−0.217501	−	0.299365i
$624$	−6.47214			−0.259093
$625$		0			0
$626$	−16.2705			−0.650300
$627$	12.1392	+	16.7082i	0.484794	+	0.667261i
$628$	8.22899	+	2.67376i	0.328373	+	0.106695i
$629$	−3.05573	+	9.40456i	−0.121840	+	0.374985i
$630$		0			0
$631$	14.3607	+	44.1976i	0.571690	+	1.75948i	0.647184	+	0.762334i	$0.275946\pi$
$631$	14.3607	+	44.1976i	0.571690	+	1.75948i	−0.0754947	+	0.997146i	$0.524054\pi$
$632$			5.61803i			0.223473i
$633$	−3.24920	+	1.05573i	−0.129144	+	0.0419614i
$634$	−16.6353	−	12.0862i	−0.660670	−	0.480005i
$635$		0			0
$636$	−1.69098	+	1.22857i	−0.0670518	+	0.0487160i
$637$	−0.555029	+	0.763932i	−0.0219911	+	0.0302681i
$638$	18.0171	−	24.7984i	0.713303	−	0.981777i
$639$	4.47214	−	3.24920i	0.176915	−	0.128536i
$640$		0			0
$641$	11.1803	+	8.12299i	0.441597	+	0.320839i	0.786269	−	0.617884i	$-0.212010\pi$
$641$	11.1803	+	8.12299i	0.441597	+	0.320839i	−0.344672	+	0.938723i	$0.612010\pi$
$642$	11.0494	−	3.59017i	0.436085	−	0.141693i
$643$			21.8885i			0.863200i	0.902065	+	0.431600i	$0.142051\pi$
$643$			21.8885i			0.863200i	−0.902065	+	0.431600i	$0.857949\pi$
$644$	−3.61803	−	11.1352i	−0.142571	−	0.438787i
$645$		0			0
$646$	−2.18034	+	6.71040i	−0.0857843	+	0.264017i
$647$	21.8213	+	7.09017i	0.857884	+	0.278743i	0.704744	−	0.709461i	$-0.251062\pi$
$647$	21.8213	+	7.09017i	0.857884	+	0.278743i	0.153139	+	0.988205i	$0.451062\pi$
$648$	−0.587785	−	0.809017i	−0.0230904	−	0.0317812i
$649$	13.0902			0.513834
$650$		0			0
$651$	−17.3262			−0.679069
$652$	−0.277515	−	0.381966i	−0.0108683	−	0.0149589i
$653$	−3.66547	−	1.19098i	−0.143441	−	0.0466068i	0.236417	−	0.971652i	$-0.424027\pi$
$653$	−3.66547	−	1.19098i	−0.143441	−	0.0466068i	−0.379858	+	0.925045i	$0.624027\pi$
$654$	5.32624	−	16.3925i	0.208272	−	0.640996i
$655$		0			0
$656$	1.76393	+	5.42882i	0.0688700	+	0.211960i
$657$		−	3.52786i		−	0.137635i
$658$	−4.25325	+	1.38197i	−0.165809	+	0.0538746i
$659$	−16.6803	−	12.1190i	−0.649774	−	0.472088i	0.213420	−	0.976960i	$-0.431540\pi$
$659$	−16.6803	−	12.1190i	−0.649774	−	0.472088i	−0.863194	+	0.504872i	$0.831540\pi$
$660$		0			0
$661$	24.6525	−	17.9111i	0.958870	−	0.696660i	0.00598211	−	0.999982i	$-0.498096\pi$
$661$	24.6525	−	17.9111i	0.958870	−	0.696660i	0.952888	+	0.303322i	$0.0980958\pi$
$662$	10.5801	−	14.5623i	0.411209	−	0.565980i
$663$	4.70228	−	6.47214i	0.182622	−	0.251357i
$664$	1.73607	−	1.26133i	0.0673725	−	0.0489490i
$665$		0			0
$666$	−6.47214	−	4.70228i	−0.250790	−	0.182210i
$667$	36.0341	−	11.7082i	1.39525	−	0.453343i
$668$			11.7082i			0.453004i
$669$	−2.50000	−	7.69421i	−0.0966556	−	0.297475i
$670$		0			0
$671$	3.09017	−	9.51057i	0.119295	−	0.367151i
$672$	2.48990	+	0.809017i	0.0960499	+	0.0312085i
$673$	18.4863	+	25.4443i	0.712596	+	0.980805i	0.999737	+	0.0229163i	$0.00729513\pi$
$673$	18.4863	+	25.4443i	0.712596	+	0.980805i	−0.287141	+	0.957888i	$0.592705\pi$
$674$	−0.909830			−0.0350453
$675$		0			0
$676$	28.8885			1.11110
$677$	17.0988	+	23.5344i	0.657159	+	0.904502i	0.999383	−	0.0351163i	$-0.0111802\pi$
$677$	17.0988	+	23.5344i	0.657159	+	0.904502i	−0.342224	+	0.939618i	$0.611180\pi$
$678$	18.2946	+	5.94427i	0.702599	+	0.228288i
$679$	2.73607	−	8.42075i	0.105001	−	0.323159i
$680$		0			0
$681$	6.88197	+	21.1805i	0.263718	+	0.811639i
$682$		−	23.9443i		−	0.916874i
$683$	−31.8666	+	10.3541i	−1.21934	+	0.396189i	−0.846843	−	0.531843i	$-0.821500\pi$
$683$	−31.8666	+	10.3541i	−1.21934	+	0.396189i	−0.372501	+	0.928032i	$0.621500\pi$
$684$	−4.61803	−	3.35520i	−0.176575	−	0.128289i
$685$		0			0
$686$	15.1353	−	10.9964i	0.577867	−	0.419845i
$687$	−3.24920	+	4.47214i	−0.123965	+	0.170623i
$688$	−4.53077	+	6.23607i	−0.172734	+	0.237748i
$689$	10.9443	−	7.95148i	0.416944	−	0.302927i
$690$		0			0
$691$	−9.09017	−	6.60440i	−0.345806	−	0.251243i	0.401301	−	0.915946i	$-0.368558\pi$
$691$	−9.09017	−	6.60440i	−0.345806	−	0.251243i	−0.747108	+	0.664703i	$0.768558\pi$
$692$	4.84104	−	1.57295i	0.184029	−	0.0597945i
$693$			9.47214i			0.359817i
$694$	−6.35410	−	19.5559i	−0.241198	−	0.742332i
$695$		0			0
$696$	−2.61803	+	8.05748i	−0.0992363	+	0.305418i
$697$	−6.71040	−	2.18034i	−0.254174	−	0.0825863i
$698$	16.3925	+	22.5623i	0.620464	+	0.853996i
$699$	18.6525			0.705501
$700$		0			0
$701$	40.8328			1.54223			0.771117	−	0.636693i	$-0.219698\pi$
$701$	40.8328			1.54223			0.771117	+	0.636693i	$0.219698\pi$
$702$	3.80423	+	5.23607i	0.143581	+	0.197623i
$703$	−43.4306	−	14.1115i	−1.63802	−	0.532224i
$704$	−1.11803	+	3.44095i	−0.0421375	+	0.129686i
$705$		0			0
$706$	−4.09017	−	12.5882i	−0.153936	−	0.473765i
$707$		−	11.4721i		−	0.431454i
$708$	−3.44095	+	1.11803i	−0.129319	+	0.0420183i
$709$	−35.3607	−	25.6910i	−1.32800	−	0.964847i	−0.999795	−	0.0202400i	$-0.993557\pi$
$709$	−35.3607	−	25.6910i	−1.32800	−	0.964847i	−0.328203	−	0.944607i	$-0.606443\pi$
$710$		0			0
$711$	4.54508	−	3.30220i	0.170454	−	0.123842i
$712$	−2.07363	+	2.85410i	−0.0777124	+	0.106962i
$713$	17.3965	−	23.9443i	0.651505	−	0.896720i
$714$	−2.61803	+	1.90211i	−0.0979775	+	0.0711848i
$715$		0			0
$716$	−7.97214	−	5.79210i	−0.297933	−	0.216461i
$717$	−11.6902	+	3.79837i	−0.436578	+	0.141853i
$718$			22.1803i			0.827763i
$719$	5.12461	+	15.7719i	0.191116	+	0.588194i	1.00000		0.000225882i	$7.19006e-5\pi$
$719$	5.12461	+	15.7719i	0.191116	+	0.588194i	−0.808884	+	0.587968i	$0.799928\pi$
$720$		0			0
$721$	11.5902	−	35.6709i	0.431640	−	1.32845i
$722$	−12.9188	−	4.19756i	−0.480787	−	0.156217i
$723$	5.62058	+	7.73607i	0.209032	+	0.287707i
$724$	6.65248			0.247237
$725$		0			0
$726$	−2.09017			−0.0775735
$727$	−5.04531	−	6.94427i	−0.187120	−	0.257549i	0.705142	−	0.709066i	$-0.250883\pi$
$727$	−5.04531	−	6.94427i	−0.187120	−	0.257549i	−0.892263	+	0.451517i	$0.850883\pi$
$728$	−16.1150	−	5.23607i	−0.597260	−	0.194062i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	−2.94427	−	9.06154i	−0.108898	−	0.335153i
$732$			2.76393i			0.102158i
$733$	34.1320	−	11.0902i	1.26070	−	0.409625i	0.398953	−	0.916971i	$-0.369374\pi$
$733$	34.1320	−	11.0902i	1.26070	−	0.409625i	0.861742	+	0.507346i	$0.169374\pi$
$734$	−24.7705	−	17.9968i	−0.914296	−	0.664275i
$735$		0			0
$736$	−3.61803	+	2.62866i	−0.133363	+	0.0968935i
$737$	3.24920	−	4.47214i	0.119686	−	0.164733i
$738$	3.35520	−	4.61803i	0.123507	−	0.169992i
$739$	−38.9787	+	28.3197i	−1.43386	+	1.04176i	−0.444573	+	0.895743i	$0.646644\pi$
$739$	−38.9787	+	28.3197i	−1.43386	+	1.04176i	−0.989283	+	0.146014i	$0.953356\pi$
$740$		0			0
$741$	29.8885	+	21.7153i	1.09798	+	0.797731i
$742$	−5.20431	+	1.69098i	−0.191056	+	0.0620779i
$743$		−	39.0132i		−	1.43125i	−0.698483	−	0.715627i	$-0.746141\pi$
$743$		−	39.0132i		−	1.43125i	0.698483	−	0.715627i	$-0.253859\pi$
$744$	2.04508	+	6.29412i	0.0749765	+	0.230754i
$745$		0			0
$746$	−3.56231	+	10.9637i	−0.130425	+	0.401408i
$747$	−2.04087	−	0.663119i	−0.0746715	−	0.0242623i
$748$	−2.62866	−	3.61803i	−0.0961132	−	0.132288i
$749$	30.4164			1.11139
$750$		0			0
$751$	24.7984			0.904906			0.452453	−	0.891788i	$-0.350549\pi$
$751$	24.7984			0.904906			0.452453	+	0.891788i	$0.350549\pi$
$752$	1.00406	+	1.38197i	0.0366142	+	0.0503951i
$753$	−12.8985	−	4.19098i	−0.470048	−	0.152728i
$754$	16.9443	−	52.1491i	0.617074	−	1.89916i
$755$		0			0
$756$	−0.809017	−	2.48990i	−0.0294237	−	0.0905567i
$757$			17.1246i			0.622405i	0.950344	+	0.311202i	$0.100732\pi$
$757$			17.1246i			0.622405i	−0.950344	+	0.311202i	$0.899268\pi$
$758$	19.1926	−	6.23607i	0.697108	−	0.226504i
$759$	−13.0902	−	9.51057i	−0.475143	−	0.345212i
$760$		0			0
$761$	−1.14590	+	0.832544i	−0.0415388	+	0.0301797i	−0.608361	−	0.793661i	$-0.708173\pi$
$761$	−1.14590	+	0.832544i	−0.0415388	+	0.0301797i	0.566822	+	0.823840i	$0.308173\pi$
$762$	8.00448	−	11.0172i	0.289972	−	0.399112i
$763$	26.5236	−	36.5066i	0.960218	−	1.32163i
$764$	3.47214	−	2.52265i	0.125617	−	0.0912664i
$765$		0			0
$766$	16.1803	+	11.7557i	0.584619	+	0.424751i
$767$	22.2703	−	7.23607i	0.804135	−	0.261279i
$768$		−	1.00000i		−	0.0360844i
$769$	−7.62868	−	23.4787i	−0.275097	−	0.846662i	−0.989194	−	0.146615i	$-0.953162\pi$
$769$	−7.62868	−	23.4787i	−0.275097	−	0.846662i	0.714097	−	0.700047i	$-0.246838\pi$
$770$		0			0
$771$	6.79837	−	20.9232i	0.244837	−	0.753532i
$772$	−16.9803	−	5.51722i	−0.611133	−	0.198569i
$773$	0.673542	+	0.927051i	0.0242256	+	0.0333437i	0.820958	−	0.570989i	$-0.193440\pi$
$773$	0.673542	+	0.927051i	0.0242256	+	0.0333437i	−0.796732	+	0.604332i	$0.793440\pi$
$774$	7.70820			0.277066
$775$		0			0
$776$	−3.38197			−0.121406
$777$	−12.3107	−	16.9443i	−0.441645	−	0.607872i
$778$	−11.7759	−	3.82624i	−0.422188	−	0.137177i
$779$	10.0689	−	30.9888i	0.360755	−	1.11029i
$780$		0			0
$781$	6.18034	+	19.0211i	0.221150	+	0.680630i
$782$		−	5.52786i		−	0.197676i
$783$	8.05748	−	2.61803i	0.287951	−	0.0935609i
$784$	−0.118034	−	0.0857567i	−0.00421550	−	0.00306274i
$785$		0			0
$786$	−14.4721	+	10.5146i	−0.516204	+	0.375044i
$787$	−16.4985	+	22.7082i	−0.588107	+	0.809460i	−0.994555	−	0.104214i	$-0.966767\pi$
$787$	−16.4985	+	22.7082i	−0.588107	+	0.809460i	0.406448	+	0.913674i	$0.366767\pi$
$788$	−10.0453	+	13.8262i	−0.357851	+	0.492539i
$789$	9.47214	−	6.88191i	0.337217	−	0.245002i
$790$		0			0
$791$	40.7426	+	29.6013i	1.44864	+	1.05250i
$792$	3.44095	−	1.11803i	0.122269	−	0.0397276i
$793$		−	17.8885i		−	0.635241i
$794$	9.50658	+	29.2582i	0.337376	+	1.03834i
$795$		0			0
$796$	6.02786	−	18.5519i	0.213652	−	0.657553i
$797$	−1.43284	−	0.465558i	−0.0507538	−	0.0164909i	0.283530	−	0.958963i	$-0.408494\pi$
$797$	−1.43284	−	0.465558i	−0.0507538	−	0.0164909i	−0.334284	+	0.942472i	$0.608494\pi$
$798$	−8.78402	−	12.0902i	−0.310951	−	0.427987i
$799$	−2.11146			−0.0746979
$800$		0			0
$801$	3.52786			0.124651
$802$	15.1109	+	20.7984i	0.533585	+	0.734416i
$803$	12.1392	+	3.94427i	0.428384	+	0.139190i
$804$	−0.472136	+	1.45309i	−0.0166510	+	0.0512464i
$805$		0			0
$806$	−13.2361	−	40.7364i	−0.466221	−	1.43488i
$807$		−	9.09017i		−	0.319989i
$808$	−4.16750	+	1.35410i	−0.146612	+	0.0476371i
$809$	−24.9443	−	18.1231i	−0.876994	−	0.637173i	0.0554606	−	0.998461i	$-0.482337\pi$
$809$	−24.9443	−	18.1231i	−0.876994	−	0.637173i	−0.932454	+	0.361288i	$0.882337\pi$
$810$		0			0
$811$	4.61803	−	3.35520i	0.162161	−	0.117817i	−0.503745	−	0.863852i	$-0.668045\pi$
$811$	4.61803	−	3.35520i	0.162161	−	0.117817i	0.665906	+	0.746035i	$0.268045\pi$
$812$	−13.0373	+	17.9443i	−0.457519	+	0.629720i
$813$	10.6004	−	14.5902i	0.371772	−	0.511700i
$814$	23.4164	−	17.0130i	0.820745	−	0.596306i
$815$		0			0
$816$	1.00000	+	0.726543i	0.0350070	+	0.0254341i
$817$	41.8465	−	13.5967i	1.46402	−	0.475690i
$818$			5.79837i			0.202735i
$819$	5.23607	+	16.1150i	0.182963	+	0.563102i
$820$		0			0
$821$	−13.9336	+	42.8833i	−0.486287	+	1.49664i	0.343821	+	0.939035i	$0.388279\pi$
$821$	−13.9336	+	42.8833i	−0.486287	+	1.49664i	−0.830108	+	0.557602i	$0.811721\pi$
$822$	−11.5842	−	3.76393i	−0.404045	−	0.131282i
$823$	−1.74311	−	2.39919i	−0.0607610	−	0.0836304i	0.777555	−	0.628815i	$-0.216460\pi$
$823$	−1.74311	−	2.39919i	−0.0607610	−	0.0836304i	−0.838316	+	0.545184i	$0.816460\pi$
$824$	−14.3262			−0.499078
$825$		0			0
$826$	−9.47214			−0.329578
$827$	25.9233	+	35.6803i	0.901441	+	1.24073i	0.970006	+	0.243080i	$0.0781579\pi$
$827$	25.9233	+	35.6803i	0.901441	+	1.24073i	−0.0685652	+	0.997647i	$0.521842\pi$
$828$	4.25325	+	1.38197i	0.147811	+	0.0480266i
$829$	−8.00000	+	24.6215i	−0.277851	+	0.855139i	0.710599	+	0.703597i	$0.248424\pi$
$829$	−8.00000	+	24.6215i	−0.277851	+	0.855139i	−0.988451	+	0.151542i	$0.951576\pi$
$830$		0			0
$831$	−5.23607	−	16.1150i	−0.181637	−	0.559022i
$832$			6.47214i			0.224381i
$833$	0.171513	−	0.0557281i	0.00594259	−	0.00193086i
$834$	−8.47214	−	6.15537i	−0.293366	−	0.213143i
$835$		0			0
$836$	16.7082	−	12.1392i	0.577865	−	0.419844i
$837$	3.88998	−	5.35410i	0.134457	−	0.185065i
$838$	−1.81636	+	2.50000i	−0.0627450	+	0.0863611i
$839$	5.14590	−	3.73871i	0.177656	−	0.129075i	−0.495403	−	0.868663i	$-0.664980\pi$
$839$	5.14590	−	3.73871i	0.177656	−	0.129075i	0.673060	+	0.739588i	$0.264980\pi$
$840$		0			0
$841$	−34.6074	−	25.1437i	−1.19336	−	0.867026i
$842$	−21.6498	+	7.03444i	−0.746101	+	0.242423i
$843$		−	5.88854i		−	0.202812i
$844$	1.05573	+	3.24920i	0.0363397	+	0.111842i
$845$		0			0
$846$	0.527864	−	1.62460i	0.0181483	−	0.0558548i
$847$	−5.20431	−	1.69098i	−0.178822	−	0.0581029i
$848$	1.22857	+	1.69098i	0.0421893	+	0.0580686i
$849$	4.58359			0.157308
$850$		0			0
$851$	35.7771			1.22642
$852$	−3.24920	−	4.47214i	−0.111316	−	0.153213i
$853$	−41.4630	−	13.4721i	−1.41967	−	0.461277i	−0.504169	−	0.863605i	$-0.668201\pi$
$853$	−41.4630	−	13.4721i	−1.41967	−	0.461277i	−0.915496	+	0.402328i	$0.868201\pi$
$854$	−2.23607	+	6.88191i	−0.0765167	+	0.235494i
$855$		0			0
$856$	−3.59017	−	11.0494i	−0.122709	−	0.377661i
$857$			16.0689i			0.548903i	0.961601	+	0.274451i	$0.0884962\pi$
$857$			16.0689i			0.548903i	−0.961601	+	0.274451i	$0.911504\pi$
$858$	−22.2703	+	7.23607i	−0.760296	+	0.247035i
$859$	−1.85410	−	1.34708i	−0.0632611	−	0.0459619i	0.555705	−	0.831379i	$-0.312448\pi$
$859$	−1.85410	−	1.34708i	−0.0632611	−	0.0459619i	−0.618966	+	0.785417i	$0.712448\pi$
$860$		0			0
$861$	12.0902	−	8.78402i	0.412032	−	0.299359i
$862$	−9.89408	+	13.6180i	−0.336994	+	0.463832i
$863$	−5.98385	+	8.23607i	−0.203693	+	0.280359i	−0.898626	−	0.438715i	$-0.855434\pi$
$863$	−5.98385	+	8.23607i	−0.203693	+	0.280359i	0.694934	+	0.719074i	$0.255434\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$		0			0
$866$	−12.5451	−	9.11454i	−0.426299	−	0.309725i
$867$	14.7149	−	4.78115i	0.499743	−	0.162376i
$868$			17.3262i			0.588091i
$869$	6.28115	+	19.3314i	0.213074	+	0.655773i
$870$		0			0
$871$	3.05573	−	9.40456i	0.103539	−	0.318661i
$872$	−16.3925	−	5.32624i	−0.555119	−	0.180369i
$873$	1.98787	+	2.73607i	0.0672792	+	0.0926019i
$874$	25.5279			0.863493
$875$		0			0
$876$	−3.52786			−0.119195
$877$	−21.8213	−	30.0344i	−0.736853	−	1.01419i	−0.998794	−	0.0491070i	$-0.984362\pi$
$877$	−21.8213	−	30.0344i	−0.736853	−	1.01419i	0.261941	−	0.965084i	$-0.415638\pi$
$878$	−22.3561	−	7.26393i	−0.754481	−	0.245146i
$879$	−6.82624	+	21.0090i	−0.230243	+	0.708616i
$880$		0			0
$881$	−7.29180	−	22.4418i	−0.245667	−	0.756085i	−0.995526	−	0.0944874i	$-0.969879\pi$
$881$	−7.29180	−	22.4418i	−0.245667	−	0.756085i	0.749859	−	0.661597i	$-0.230121\pi$
$882$			0.145898i			0.00491264i
$883$	28.5972	−	9.29180i	0.962373	−	0.312694i	0.214640	−	0.976693i	$-0.431142\pi$
$883$	28.5972	−	9.29180i	0.962373	−	0.312694i	0.747733	+	0.663999i	$0.231142\pi$
$884$	−6.47214	−	4.70228i	−0.217681	−	0.158155i
$885$		0			0
$886$	−13.4443	+	9.76784i	−0.451669	+	0.328157i
$887$	−13.7638	+	18.9443i	−0.462144	+	0.636086i	−0.974952	−	0.222417i	$-0.928605\pi$
$887$	−13.7638	+	18.9443i	−0.462144	+	0.636086i	0.512808	+	0.858503i	$0.328605\pi$
$888$	−4.70228	+	6.47214i	−0.157798	+	0.217191i
$889$	28.8435	−	20.9560i	0.967379	−	0.702842i
$890$		0			0
$891$	−2.92705	−	2.12663i	−0.0980599	−	0.0712447i
$892$	−7.69421	+	2.50000i	−0.257621	+	0.0837062i
$893$		−	9.75078i		−	0.326297i
$894$	6.82624	+	21.0090i	0.228304	+	0.702646i
$895$		0			0
$896$	0.809017	−	2.48990i	0.0270274	−	0.0831817i
$897$	−27.5276	−	8.94427i	−0.919121	−	0.298641i
$898$	16.2865	+	22.4164i	0.543487	+	0.748045i
$899$	−56.0689			−1.87000
$900$		0			0
$901$	−2.58359			−0.0860719
$902$	12.1392	+	16.7082i	0.404192	+	0.556322i
$903$	19.1926	+	6.23607i	0.638691	+	0.207523i
$904$	5.94427	−	18.2946i	0.197704	−	0.608469i
$905$		0			0
$906$	−5.66312	−	17.4293i	−0.188145	−	0.579049i
$907$		−	30.4721i		−	1.01181i	−0.862589	−	0.505905i	$-0.831159\pi$
$907$		−	30.4721i		−	1.01181i	0.862589	−	0.505905i	$-0.168841\pi$
$908$	21.1805	−	6.88197i	0.702900	−	0.228386i
$909$	3.54508	+	2.57565i	0.117583	+	0.0854291i
$910$		0			0
$911$	−14.7082	+	10.6861i	−0.487305	+	0.354047i	−0.804147	−	0.594431i	$-0.797377\pi$
$911$	−14.7082	+	10.6861i	−0.487305	+	0.354047i	0.316842	+	0.948478i	$0.397377\pi$
$912$	−3.35520	+	4.61803i	−0.111102	+	0.152918i
$913$	4.56352	−	6.28115i	0.151031	−	0.207876i
$914$	−3.30902	+	2.40414i	−0.109453	+	0.0795219i
$915$		0			0
$916$	4.47214	+	3.24920i	0.147764	+	0.107356i
$917$	−44.5407	+	14.4721i	−1.47086	+	0.477912i
$918$		−	1.23607i		−	0.0407963i
$919$	12.5836	+	38.7283i	0.415094	+	1.27753i	0.912166	+	0.409820i	$0.134408\pi$
$919$	12.5836	+	38.7283i	0.415094	+	1.27753i	−0.497072	+	0.867709i	$0.665592\pi$
$920$		0			0
$921$	−3.09017	+	9.51057i	−0.101825	+	0.313384i
$922$	−7.19218	−	2.33688i	−0.236862	−	0.0769611i
$923$	21.0292	+	28.9443i	0.692186	+	0.952712i
$924$	9.47214			0.311610
$925$		0			0
$926$	−22.8328			−0.750333
$927$	8.42075	+	11.5902i	0.276574	+	0.380671i
$928$	8.05748	+	2.61803i	0.264500	+	0.0859412i
$929$	5.87539	−	18.0826i	0.192765	−	0.593270i	−0.807230	−	0.590237i	$-0.799034\pi$
$929$	5.87539	−	18.0826i	0.192765	−	0.593270i	0.999995	−	0.00303360i	$-0.000965627\pi$
$930$		0			0
$931$	0.257354	+	0.792055i	0.00843444	+	0.0259585i
$932$		−	18.6525i		−	0.610982i
$933$	−1.00406	+	0.326238i	−0.0328714	+	0.0106806i
$934$	8.63525	+	6.27388i	0.282554	+	0.205288i
$935$		0			0
$936$	5.23607	−	3.80423i	0.171146	−	0.124345i
$937$	5.10604	−	7.02786i	0.166807	−	0.229590i	−0.717428	−	0.696633i	$-0.754681\pi$
$937$	5.10604	−	7.02786i	0.166807	−	0.229590i	0.884235	+	0.467043i	$0.154681\pi$
$938$	−2.35114	+	3.23607i	−0.0767675	+	0.105661i
$939$	13.1631	−	9.56357i	0.429562	−	0.312095i
$940$		0			0
$941$	3.59017	+	2.60841i	0.117036	+	0.0850318i	0.644764	−	0.764382i	$-0.276956\pi$
$941$	3.59017	+	2.60841i	0.117036	+	0.0850318i	−0.527728	+	0.849414i	$0.676956\pi$
$942$	−8.22899	+	2.67376i	−0.268115	+	0.0871159i
$943$			25.5279i			0.831302i
$944$	1.11803	+	3.44095i	0.0363889	+	0.111994i
$945$		0			0
$946$	−8.61803	+	26.5236i	−0.280196	+	0.862356i
$947$	31.9196	+	10.3713i	1.03725	+	0.337023i	0.777652	−	0.628694i	$-0.216410\pi$
$947$	31.9196	+	10.3713i	1.03725	+	0.337023i	0.259597	+	0.965717i	$0.416410\pi$
$948$	−3.30220	−	4.54508i	−0.107250	−	0.147617i
$949$	22.8328			0.741185
$950$		0			0
$951$	20.5623			0.666778
$952$	1.90211	+	2.61803i	0.0616478	+	0.0848510i
$953$	5.04531	+	1.63932i	0.163434	+	0.0531028i	0.389591	−	0.920988i	$-0.372616\pi$
$953$	5.04531	+	1.63932i	0.163434	+	0.0531028i	−0.226157	+	0.974091i	$0.572616\pi$
$954$	0.645898	−	1.98787i	0.0209117	−	0.0643597i
$955$		0			0
$956$	3.79837	+	11.6902i	0.122848	+	0.378088i
$957$			30.6525i			0.990854i
$958$	27.6992	−	9.00000i	0.894919	−	0.290777i
$959$	−25.7984	−	18.7436i	−0.833073	−	0.605263i
$960$		0			0
$961$	−10.3541	+	7.52270i	−0.334003	+	0.242668i
$962$	30.4338	−	41.8885i	0.981225	−	1.35054i
$963$	−6.82891	+	9.39919i	−0.220059	+	0.302885i
$964$	7.73607	−	5.62058i	0.249162	−	0.181027i
$965$		0			0
$966$	9.47214	+	6.88191i	0.304761	+	0.221422i
$967$	10.3759	−	3.37132i	0.333665	−	0.108414i	−0.137393	−	0.990517i	$-0.543872\pi$
$967$	10.3759	−	3.37132i	0.333665	−	0.108414i	0.471058	+	0.882102i	$0.343872\pi$
$968$			2.09017i			0.0671806i
$969$	−2.18034	−	6.71040i	−0.0700426	−	0.215569i
$970$		0			0
$971$	−4.39261	+	13.5191i	−0.140966	+	0.433847i	−0.996470	−	0.0839479i	$-0.973247\pi$
$971$	−4.39261	+	13.5191i	−0.140966	+	0.433847i	0.855505	+	0.517795i	$0.173247\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	−16.1150	−	22.1803i	−0.516622	−	0.711069i
$974$	−17.7984			−0.570297
$975$		0			0
$976$	2.76393			0.0884713
$977$	−0.449028	−	0.618034i	−0.0143657	−	0.0197727i	0.801774	−	0.597628i	$-0.203890\pi$
$977$	−0.449028	−	0.618034i	−0.0143657	−	0.0197727i	−0.816139	+	0.577855i	$0.803890\pi$
$978$	0.449028	+	0.145898i	0.0143583	+	0.00466530i
$979$	−3.94427	+	12.1392i	−0.126059	+	0.387971i
$980$		0			0
$981$	5.32624	+	16.3925i	0.170054	+	0.523371i
$982$			25.2705i			0.806414i
$983$	−38.2138	+	12.4164i	−1.21883	+	0.396022i	−0.846656	−	0.532141i	$-0.821388\pi$
$983$	−38.2138	+	12.4164i	−1.21883	+	0.396022i	−0.372174	+	0.928163i	$0.621388\pi$
$984$	−4.61803	−	3.35520i	−0.147218	−	0.106960i
$985$		0			0
$986$	−8.47214	+	6.15537i	−0.269808	+	0.196027i
$987$	2.62866	−	3.61803i	0.0836710	−	0.115163i
$988$	21.7153	−	29.8885i	0.690856	−	0.950881i
$989$	−27.8885	+	20.2622i	−0.886804	+	0.644301i
$990$		0			0
$991$	−23.8262	−	17.3108i	−0.756865	−	0.549895i	0.141082	−	0.989998i	$-0.454942\pi$
$991$	−23.8262	−	17.3108i	−0.756865	−	0.549895i	−0.897947	+	0.440103i	$0.854942\pi$
$992$	6.29412	−	2.04508i	0.199839	−	0.0649315i
$993$			18.0000i			0.571213i
$994$	−4.47214	−	13.7638i	−0.141848	−	0.436562i
$995$		0			0
$996$	−0.663119	+	2.04087i	−0.0210117	+	0.0646675i
$997$	5.32282	+	1.72949i	0.168576	+	0.0547735i	0.392089	−	0.919927i	$-0.371753\pi$
$997$	5.32282	+	1.72949i	0.168576	+	0.0547735i	−0.223513	+	0.974701i	$0.571753\pi$
$998$	−20.9232	−	28.7984i	−0.662314	−	0.911597i
$999$	8.00000			0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.h.b.199.2		8
5.2	odd	4		150.2.g.a.61.1	✓	4
5.3	odd	4		750.2.g.b.301.1		4
5.4	even	2	inner	750.2.h.b.199.1		8
15.2	even	4		450.2.h.c.361.1		4
25.3	odd	20		3750.2.a.d.1.1		2
25.4	even	10		3750.2.c.b.1249.4		4
25.9	even	10	inner	750.2.h.b.49.2		8
25.12	odd	20		150.2.g.a.91.1	yes	4
25.13	odd	20		750.2.g.b.451.1		4
25.16	even	5	inner	750.2.h.b.49.1		8
25.21	even	5		3750.2.c.b.1249.1		4
25.22	odd	20		3750.2.a.f.1.2		2
75.62	even	20		450.2.h.c.91.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.61.1	✓	4	5.2	odd	4
150.2.g.a.91.1	yes	4	25.12	odd	20
450.2.h.c.91.1		4	75.62	even	20
450.2.h.c.361.1		4	15.2	even	4
750.2.g.b.301.1		4	5.3	odd	4
750.2.g.b.451.1		4	25.13	odd	20
750.2.h.b.49.1		8	25.16	even	5	inner
750.2.h.b.49.2		8	25.9	even	10	inner
750.2.h.b.199.1		8	5.4	even	2	inner
750.2.h.b.199.2		8	1.1	even	1	trivial
3750.2.a.d.1.1		2	25.3	odd	20
3750.2.a.f.1.2		2	25.22	odd	20
3750.2.c.b.1249.1		4	25.21	even	5
3750.2.c.b.1249.4		4	25.4	even	10

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.92705 + 2.12663i) q^{11} +(0.587785 - 0.809017i) q^{12} +(-3.80423 + 5.23607i) q^{13} +(2.11803 - 1.53884i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.17557 - 0.381966i) q^{17} +1.00000i q^{18} +(1.76393 + 5.42882i) q^{19} +(-0.809017 + 2.48990i) q^{21} +(-3.44095 - 1.11803i) q^{22} +(-2.62866 - 3.61803i) q^{23} +1.00000 q^{24} -6.47214 q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.48990 + 0.809017i) q^{28} +(-2.61803 + 8.05748i) q^{29} +(2.04508 + 6.29412i) q^{31} -1.00000i q^{32} +(3.44095 - 1.11803i) q^{33} +(1.00000 + 0.726543i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(-4.70228 + 6.47214i) q^{37} +(-3.35520 + 4.61803i) q^{38} +(5.23607 - 3.80423i) q^{39} +(-4.61803 - 3.35520i) q^{41} +(-2.48990 + 0.809017i) q^{42} -7.70820i q^{43} +(-1.11803 - 3.44095i) q^{44} +(1.38197 - 4.25325i) q^{46} +(-1.62460 - 0.527864i) q^{47} +(0.587785 + 0.809017i) q^{48} +0.145898 q^{49} -1.23607 q^{51} +(-3.80423 - 5.23607i) q^{52} +(-1.98787 - 0.645898i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.809017 + 2.48990i) q^{56} -5.70820i q^{57} +(-8.05748 + 2.61803i) q^{58} +(-2.92705 - 2.12663i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(-3.88998 + 5.35410i) q^{62} +(1.53884 - 2.11803i) q^{63} +(0.809017 - 0.587785i) q^{64} +(2.92705 + 2.12663i) q^{66} +(-1.45309 + 0.472136i) q^{67} +1.23607i q^{68} +(1.38197 + 4.25325i) q^{69} +(1.70820 - 5.25731i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-2.07363 - 2.85410i) q^{73} -8.00000 q^{74} -5.70820 q^{76} +(5.56758 + 7.66312i) q^{77} +(6.15537 + 2.00000i) q^{78} +(1.73607 - 5.34307i) q^{79} +(0.309017 + 0.951057i) q^{81} -5.70820i q^{82} +(-2.04087 + 0.663119i) q^{83} +(-2.11803 - 1.53884i) q^{84} +(6.23607 - 4.53077i) q^{86} +(4.97980 - 6.85410i) q^{87} +(2.12663 - 2.92705i) q^{88} +(2.85410 - 2.07363i) q^{89} +(13.7082 + 9.95959i) q^{91} +(4.25325 - 1.38197i) q^{92} -6.61803i q^{93} +(-0.527864 - 1.62460i) q^{94} +(-0.309017 + 0.951057i) q^{96} +(3.21644 + 1.04508i) q^{97} +(0.0857567 + 0.118034i) q^{98} -3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} - 10 q^{11} + 8 q^{14} - 2 q^{16} + 32 q^{19} - 2 q^{21} + 8 q^{24} - 16 q^{26} - 12 q^{29} - 6 q^{31} + 8 q^{34} - 2 q^{36} + 24 q^{39} - 28 q^{41} + 20 q^{46} + 28 q^{49} + 8 q^{51} - 2 q^{54} + 2 q^{56} - 10 q^{59} + 2 q^{64} + 10 q^{66} + 20 q^{69} - 40 q^{71} - 64 q^{74} + 8 q^{76} - 4 q^{79} - 2 q^{81} - 8 q^{84} + 32 q^{86} - 4 q^{89} + 56 q^{91} - 40 q^{94} + 2 q^{96} - 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 - 10 * q^11 + 8 * q^14 - 2 * q^16 + 32 * q^19 - 2 * q^21 + 8 * q^24 - 16 * q^26 - 12 * q^29 - 6 * q^31 + 8 * q^34 - 2 * q^36 + 24 * q^39 - 28 * q^41 + 20 * q^46 + 28 * q^49 + 8 * q^51 - 2 * q^54 + 2 * q^56 - 10 * q^59 + 2 * q^64 + 10 * q^66 + 20 * q^69 - 40 * q^71 - 64 * q^74 + 8 * q^76 - 4 * q^79 - 2 * q^81 - 8 * q^84 + 32 * q^86 - 4 * q^89 + 56 * q^91 - 40 * q^94 + 2 * q^96 - 20 * q^99

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