LMFDB - Embedded newform 750.2.h.b.349.2

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			349.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	750.349
Dual form			750.2.h.b.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} -0.381966i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} -0.381966i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(0.427051 + 1.31433i) q^{11} +(0.951057 + 0.309017i) q^{12} +(2.35114 + 0.763932i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(0.309017 - 0.951057i) q^{16} +(1.90211 - 2.61803i) q^{17} +1.00000i q^{18} +(6.23607 + 4.53077i) q^{19} +(0.309017 - 0.224514i) q^{21} +(0.812299 + 1.11803i) q^{22} +(4.25325 - 1.38197i) q^{23} +1.00000 q^{24} +2.47214 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.224514 - 0.309017i) q^{28} +(-0.381966 + 0.277515i) q^{29} +(-3.54508 - 2.57565i) q^{31} -1.00000i q^{32} +(-0.812299 + 1.11803i) q^{33} +(1.00000 - 3.07768i) q^{34} +(0.309017 + 0.951057i) q^{36} +(-7.60845 - 2.47214i) q^{37} +(7.33094 + 2.38197i) q^{38} +(0.763932 + 2.35114i) q^{39} +(-2.38197 + 7.33094i) q^{41} +(0.224514 - 0.309017i) q^{42} +5.70820i q^{43} +(1.11803 + 0.812299i) q^{44} +(3.61803 - 2.62866i) q^{46} +(-6.88191 - 9.47214i) q^{47} +(0.951057 - 0.309017i) q^{48} +6.85410 q^{49} +3.23607 q^{51} +(2.35114 - 0.763932i) q^{52} +(-5.34307 - 7.35410i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.309017 - 0.224514i) q^{56} +7.70820i q^{57} +(-0.277515 + 0.381966i) q^{58} +(0.427051 - 1.31433i) q^{59} +(2.23607 + 6.88191i) q^{61} +(-4.16750 - 1.35410i) q^{62} +(0.363271 + 0.118034i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.427051 + 1.31433i) q^{66} +(6.15537 - 8.47214i) q^{67} -3.23607i q^{68} +(3.61803 + 2.62866i) q^{69} +(-11.7082 + 8.50651i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-11.8617 + 3.85410i) q^{73} -8.00000 q^{74} +7.70820 q^{76} +(0.502029 - 0.163119i) q^{77} +(1.45309 + 2.00000i) q^{78} +(-2.73607 + 1.98787i) q^{79} +(-0.809017 - 0.587785i) q^{81} +7.70820i q^{82} +(5.20431 - 7.16312i) q^{83} +(0.118034 - 0.363271i) q^{84} +(1.76393 + 5.42882i) q^{86} +(-0.449028 - 0.145898i) q^{87} +(1.31433 + 0.427051i) q^{88} +(-3.85410 - 11.8617i) q^{89} +(0.291796 - 0.898056i) q^{91} +(2.62866 - 3.61803i) q^{92} -4.38197i q^{93} +(-9.47214 - 6.88191i) q^{94} +(0.809017 - 0.587785i) q^{96} +(-3.30220 - 4.54508i) q^{97} +(6.51864 - 2.11803i) q^{98} -1.38197 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$		−	0.381966i		−	0.144370i	−0.997391	−	0.0721848i	$-0.977003\pi$
$7$		−	0.381966i		−	0.144370i	0.997391	−	0.0721848i	$-0.0229971\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	0.427051	+	1.31433i	0.128761	+	0.396285i	0.994567	−	0.104094i	$-0.0331942\pi$
$11$	0.427051	+	1.31433i	0.128761	+	0.396285i	−0.865807	+	0.500378i	$0.833194\pi$
$12$	0.951057	+	0.309017i	0.274546	+	0.0892055i
$13$	2.35114	+	0.763932i	0.652089	+	0.211877i	0.616335	−	0.787484i	$-0.288617\pi$
$13$	2.35114	+	0.763932i	0.652089	+	0.211877i	0.0357541	+	0.999361i	$0.488617\pi$
$14$	−0.118034	−	0.363271i	−0.0315459	−	0.0970883i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.90211	−	2.61803i	0.461330	−	0.634967i	−0.513454	−	0.858117i	$-0.671634\pi$
$17$	1.90211	−	2.61803i	0.461330	−	0.634967i	0.974784	+	0.223151i	$0.0716342\pi$
$18$			1.00000i			0.235702i
$19$	6.23607	+	4.53077i	1.43065	+	1.03943i	0.989895	+	0.141803i	$0.0452900\pi$
$19$	6.23607	+	4.53077i	1.43065	+	1.03943i	0.440757	+	0.897626i	$0.354710\pi$
$20$		0			0
$21$	0.309017	−	0.224514i	0.0674330	−	0.0489930i
$22$	0.812299	+	1.11803i	0.173183	+	0.238366i
$23$	4.25325	−	1.38197i	0.886865	−	0.288160i	0.170060	−	0.985434i	$-0.445604\pi$
$23$	4.25325	−	1.38197i	0.886865	−	0.288160i	0.716805	+	0.697274i	$0.245604\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	2.47214			0.484826
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−0.224514	−	0.309017i	−0.0424292	−	0.0583987i
$29$	−0.381966	+	0.277515i	−0.0709293	+	0.0515332i	−0.622685	−	0.782473i	$-0.713958\pi$
$29$	−0.381966	+	0.277515i	−0.0709293	+	0.0515332i	0.551756	+	0.834006i	$0.313958\pi$
$30$		0			0
$31$	−3.54508	−	2.57565i	−0.636716	−	0.462601i	0.222004	−	0.975046i	$-0.428740\pi$
$31$	−3.54508	−	2.57565i	−0.636716	−	0.462601i	−0.858720	+	0.512444i	$0.828740\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.812299	+	1.11803i	−0.141403	+	0.194625i
$34$	1.00000	−	3.07768i	0.171499	−	0.527818i
$35$		0			0
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−7.60845	−	2.47214i	−1.25082	−	0.406417i	−0.392607	−	0.919707i	$-0.628427\pi$
$37$	−7.60845	−	2.47214i	−1.25082	−	0.406417i	−0.858215	+	0.513290i	$0.828427\pi$
$38$	7.33094	+	2.38197i	1.18924	+	0.386406i
$39$	0.763932	+	2.35114i	0.122327	+	0.376484i
$40$		0			0
$41$	−2.38197	+	7.33094i	−0.372001	+	1.14490i	0.573479	+	0.819220i	$0.305593\pi$
$41$	−2.38197	+	7.33094i	−0.372001	+	1.14490i	−0.945480	+	0.325680i	$0.894407\pi$
$42$	0.224514	−	0.309017i	0.0346433	−	0.0476824i
$43$			5.70820i			0.870493i	0.900311	+	0.435246i	$0.143339\pi$
$43$			5.70820i			0.870493i	−0.900311	+	0.435246i	$0.856661\pi$
$44$	1.11803	+	0.812299i	0.168550	+	0.122459i
$45$		0			0
$46$	3.61803	−	2.62866i	0.533450	−	0.387574i
$47$	−6.88191	−	9.47214i	−1.00383	−	1.38165i	−0.922946	−	0.384929i	$-0.874226\pi$
$47$	−6.88191	−	9.47214i	−1.00383	−	1.38165i	−0.0808837	−	0.996724i	$-0.525774\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	6.85410			0.979157
$50$		0			0
$51$	3.23607			0.453140
$52$	2.35114	−	0.763932i	0.326045	−	0.105938i
$53$	−5.34307	−	7.35410i	−0.733927	−	1.01016i	−0.998945	−	0.0459202i	$-0.985378\pi$
$53$	−5.34307	−	7.35410i	−0.733927	−	1.01016i	0.265018	−	0.964243i	$-0.414622\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$		0			0
$56$	−0.309017	−	0.224514i	−0.0412941	−	0.0300019i
$57$			7.70820i			1.02098i
$58$	−0.277515	+	0.381966i	−0.0364394	+	0.0501546i
$59$	0.427051	−	1.31433i	0.0555973	−	0.171111i	−0.919402	−	0.393320i	$-0.871327\pi$
$59$	0.427051	−	1.31433i	0.0555973	−	0.171111i	0.974999	+	0.222209i	$0.0713266\pi$
$60$		0			0
$61$	2.23607	+	6.88191i	0.286299	+	0.881138i	0.986006	+	0.166708i	$0.0533138\pi$
$61$	2.23607	+	6.88191i	0.286299	+	0.881138i	−0.699707	+	0.714430i	$0.746686\pi$
$62$	−4.16750	−	1.35410i	−0.529273	−	0.171971i
$63$	0.363271	+	0.118034i	0.0457679	+	0.0148709i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$		0			0
$66$	−0.427051	+	1.31433i	−0.0525663	+	0.161783i
$67$	6.15537	−	8.47214i	0.751998	−	1.03504i	−0.245840	−	0.969310i	$-0.579064\pi$
$67$	6.15537	−	8.47214i	0.751998	−	1.03504i	0.997838	−	0.0657257i	$-0.0209362\pi$
$68$		−	3.23607i		−	0.392431i
$69$	3.61803	+	2.62866i	0.435560	+	0.316453i
$70$		0			0
$71$	−11.7082	+	8.50651i	−1.38951	+	1.00954i	−0.393589	+	0.919286i	$0.628767\pi$
$71$	−11.7082	+	8.50651i	−1.38951	+	1.00954i	−0.995919	+	0.0902503i	$0.971233\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	−11.8617	+	3.85410i	−1.38831	+	0.451089i	−0.905391	−	0.424578i	$-0.860422\pi$
$73$	−11.8617	+	3.85410i	−1.38831	+	0.451089i	−0.482916	+	0.875667i	$0.660422\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$	7.70820			0.884192
$77$	0.502029	−	0.163119i	0.0572115	−	0.0185891i
$78$	1.45309	+	2.00000i	0.164529	+	0.226455i
$79$	−2.73607	+	1.98787i	−0.307832	+	0.223653i	−0.730966	−	0.682414i	$-0.760930\pi$
$79$	−2.73607	+	1.98787i	−0.307832	+	0.223653i	0.423134	+	0.906067i	$0.360930\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			7.70820i			0.851229i
$83$	5.20431	−	7.16312i	0.571247	−	0.786254i	−0.421454	−	0.906850i	$-0.638480\pi$
$83$	5.20431	−	7.16312i	0.571247	−	0.786254i	0.992702	+	0.120595i	$0.0384803\pi$
$84$	0.118034	−	0.363271i	0.0128786	−	0.0396361i
$85$		0			0
$86$	1.76393	+	5.42882i	0.190210	+	0.585405i
$87$	−0.449028	−	0.145898i	−0.0481409	−	0.0156419i
$88$	1.31433	+	0.427051i	0.140108	+	0.0455238i
$89$	−3.85410	−	11.8617i	−0.408534	−	1.25734i	−0.917908	−	0.396793i	$-0.870123\pi$
$89$	−3.85410	−	11.8617i	−0.408534	−	1.25734i	0.509374	−	0.860545i	$-0.329877\pi$
$90$		0			0
$91$	0.291796	−	0.898056i	0.0305885	−	0.0941418i
$92$	2.62866	−	3.61803i	0.274056	−	0.377206i
$93$		−	4.38197i		−	0.454389i
$94$	−9.47214	−	6.88191i	−0.976976	−	0.709815i
$95$		0			0
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−3.30220	−	4.54508i	−0.335287	−	0.461483i	0.607770	−	0.794113i	$-0.292064\pi$
$97$	−3.30220	−	4.54508i	−0.335287	−	0.461483i	−0.943058	+	0.332629i	$0.892064\pi$
$98$	6.51864	−	2.11803i	0.658482	−	0.213954i
$99$	−1.38197			−0.138893
$100$		0			0
$101$	6.61803			0.658519			0.329259	−	0.944239i	$-0.393201\pi$
$101$	6.61803			0.658519			0.329259	+	0.944239i	$0.393201\pi$
$102$	3.07768	−	1.00000i	0.304736	−	0.0990148i
$103$	0.779543	+	1.07295i	0.0768107	+	0.105721i	0.845694	−	0.533669i	$-0.179187\pi$
$103$	0.779543	+	1.07295i	0.0768107	+	0.105721i	−0.768883	+	0.639390i	$0.779187\pi$
$104$	2.00000	−	1.45309i	0.196116	−	0.142487i
$105$		0			0
$106$	−7.35410	−	5.34307i	−0.714294	−	0.518965i
$107$			9.38197i			0.906989i	0.891259	+	0.453494i	$0.149823\pi$
$107$			9.38197i			0.906989i	−0.891259	+	0.453494i	$0.850177\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	−3.94427	+	12.1392i	−0.377793	+	1.16273i	0.563782	+	0.825923i	$0.309346\pi$
$109$	−3.94427	+	12.1392i	−0.377793	+	1.16273i	−0.941575	+	0.336803i	$0.890654\pi$
$110$		0			0
$111$	−2.47214	−	7.60845i	−0.234645	−	0.722162i
$112$	−0.363271	−	0.118034i	−0.0343259	−	0.0111532i
$113$	−14.0413	−	4.56231i	−1.32090	−	0.429186i	−0.438095	−	0.898929i	$-0.644346\pi$
$113$	−14.0413	−	4.56231i	−1.32090	−	0.429186i	−0.882803	+	0.469743i	$0.844346\pi$
$114$	2.38197	+	7.33094i	0.223092	+	0.686605i
$115$		0			0
$116$	−0.145898	+	0.449028i	−0.0135463	+	0.0416912i
$117$	−1.45309	+	2.00000i	−0.134338	+	0.184900i
$118$		−	1.38197i		−	0.127220i
$119$	−1.00000	−	0.726543i	−0.0916698	−	0.0666020i
$120$		0			0
$121$	7.35410	−	5.34307i	0.668555	−	0.485733i
$122$	4.25325	+	5.85410i	0.385072	+	0.530005i
$123$	−7.33094	+	2.38197i	−0.661008	+	0.214775i
$124$	−4.38197			−0.393512
$125$		0			0
$126$	0.381966			0.0340282
$127$	10.8249	−	3.51722i	0.960554	−	0.312103i	0.213557	−	0.976931i	$-0.431495\pi$
$127$	10.8249	−	3.51722i	0.960554	−	0.312103i	0.746997	+	0.664828i	$0.231495\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−4.61803	+	3.35520i	−0.406595	+	0.295409i
$130$		0			0
$131$	−14.4721	−	10.5146i	−1.26444	−	0.918667i	−0.265470	−	0.964119i	$-0.585527\pi$
$131$	−14.4721	−	10.5146i	−1.26444	−	0.918667i	−0.998967	+	0.0454523i	$0.985527\pi$
$132$			1.38197i			0.120285i
$133$	1.73060	−	2.38197i	0.150062	−	0.206543i
$134$	3.23607	−	9.95959i	0.279554	−	0.860378i
$135$		0			0
$136$	−1.00000	−	3.07768i	−0.0857493	−	0.263909i
$137$	−9.68208	−	3.14590i	−0.827196	−	0.268772i	−0.135332	−	0.990800i	$-0.543210\pi$
$137$	−9.68208	−	3.14590i	−0.827196	−	0.268772i	−0.691864	+	0.722028i	$0.743210\pi$
$138$	4.25325	+	1.38197i	0.362061	+	0.117641i
$139$	−0.472136	−	1.45309i	−0.0400460	−	0.123249i	0.929035	−	0.369992i	$-0.120640\pi$
$139$	−0.472136	−	1.45309i	−0.0400460	−	0.123249i	−0.969081	+	0.246743i	$0.920640\pi$
$140$		0			0
$141$	3.61803	−	11.1352i	0.304693	−	0.937750i
$142$	−8.50651	+	11.7082i	−0.713850	+	0.982531i
$143$			3.41641i			0.285694i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$		0			0
$146$	−10.0902	+	7.33094i	−0.835068	+	0.606713i
$147$	4.02874	+	5.54508i	0.332285	+	0.457351i
$148$	−7.60845	+	2.47214i	−0.625411	+	0.203208i
$149$	−10.9098			−0.893768			−0.446884	−	0.894592i	$-0.647466\pi$
$149$	−10.9098			−0.893768			−0.446884	+	0.894592i	$0.647466\pi$
$150$		0			0
$151$	2.67376			0.217588			0.108794	−	0.994064i	$-0.465301\pi$
$151$	2.67376			0.217588			0.108794	+	0.994064i	$0.465301\pi$
$152$	7.33094	−	2.38197i	0.594618	−	0.193203i
$153$	1.90211	+	2.61803i	0.153777	+	0.211656i
$154$	0.427051	−	0.310271i	0.0344127	−	0.0250023i
$155$		0			0
$156$	2.00000	+	1.45309i	0.160128	+	0.116340i
$157$			22.6525i			1.80786i	0.427676	+	0.903932i	$0.359332\pi$
$157$			22.6525i			1.80786i	−0.427676	+	0.903932i	$0.640668\pi$
$158$	−1.98787	+	2.73607i	−0.158146	+	0.217670i
$159$	2.80902	−	8.64527i	0.222770	−	0.685614i
$160$		0			0
$161$	−0.527864	−	1.62460i	−0.0416015	−	0.128036i
$162$	−0.951057	−	0.309017i	−0.0747221	−	0.0242787i
$163$	8.05748	+	2.61803i	0.631111	+	0.205060i	0.607067	−	0.794651i	$-0.292346\pi$
$163$	8.05748	+	2.61803i	0.631111	+	0.205060i	0.0240436	+	0.999711i	$0.492346\pi$
$164$	2.38197	+	7.33094i	0.186000	+	0.572450i
$165$		0			0
$166$	2.73607	−	8.42075i	0.212360	−	0.653577i
$167$	1.00406	−	1.38197i	0.0776963	−	0.106940i	−0.768400	−	0.639970i	$-0.778947\pi$
$167$	1.00406	−	1.38197i	0.0776963	−	0.106940i	0.846096	+	0.533030i	$0.178947\pi$
$168$		−	0.381966i		−	0.0294693i
$169$	−5.57295	−	4.04898i	−0.428688	−	0.311460i
$170$		0			0
$171$	−6.23607	+	4.53077i	−0.476884	+	0.346477i
$172$	3.35520	+	4.61803i	0.255831	+	0.352122i
$173$	5.79210	−	1.88197i	0.440365	−	0.143083i	−0.0804391	−	0.996760i	$-0.525632\pi$
$173$	5.79210	−	1.88197i	0.440365	−	0.143083i	0.520804	+	0.853676i	$0.325632\pi$
$174$	−0.472136			−0.0357925
$175$		0			0
$176$	1.38197			0.104170
$177$	1.31433	−	0.427051i	0.0987909	−	0.0320991i
$178$	−7.33094	−	10.0902i	−0.549477	−	0.756290i
$179$	2.54508	−	1.84911i	0.190229	−	0.138209i	−0.488595	−	0.872511i	$-0.662490\pi$
$179$	2.54508	−	1.84911i	0.190229	−	0.138209i	0.678823	+	0.734302i	$0.262490\pi$
$180$		0			0
$181$	−19.9443	−	14.4904i	−1.48245	−	1.07706i	−0.976758	−	0.214344i	$-0.931239\pi$
$181$	−19.9443	−	14.4904i	−1.48245	−	1.07706i	−0.505688	−	0.862717i	$-0.668761\pi$
$182$		−	0.944272i		−	0.0699941i
$183$	−4.25325	+	5.85410i	−0.314410	+	0.432748i
$184$	1.38197	−	4.25325i	0.101880	−	0.313554i
$185$		0			0
$186$	−1.35410	−	4.16750i	−0.0992876	−	0.305576i
$187$	4.25325	+	1.38197i	0.311029	+	0.101059i
$188$	−11.1352	−	3.61803i	−0.812115	−	0.263872i
$189$	0.118034	+	0.363271i	0.00858571	+	0.0264241i
$190$		0			0
$191$	5.47214	−	16.8415i	0.395950	−	1.21861i	−0.532269	−	0.846575i	$-0.678661\pi$
$191$	5.47214	−	16.8415i	0.395950	−	1.21861i	0.928219	−	0.372033i	$-0.121339\pi$
$192$	0.587785	−	0.809017i	0.0424197	−	0.0583858i
$193$			11.1459i			0.802299i	0.916013	+	0.401150i	$0.131389\pi$
$193$			11.1459i			0.802299i	−0.916013	+	0.401150i	$0.868611\pi$
$194$	−4.54508	−	3.30220i	−0.326318	−	0.237084i
$195$		0			0
$196$	5.54508	−	4.02874i	0.396077	−	0.287767i
$197$	−3.47371	−	4.78115i	−0.247492	−	0.340643i	0.667139	−	0.744933i	$-0.267519\pi$
$197$	−3.47371	−	4.78115i	−0.247492	−	0.340643i	−0.914631	+	0.404290i	$0.867519\pi$
$198$	−1.31433	+	0.427051i	−0.0934052	+	0.0303492i
$199$	18.5066			1.31190			0.655948	−	0.754806i	$-0.272269\pi$
$199$	18.5066			1.31190			0.655948	+	0.754806i	$0.272269\pi$
$200$		0			0
$201$	10.4721			0.738648
$202$	6.29412	−	2.04508i	0.442853	−	0.143892i
$203$	0.106001	+	0.145898i	0.00743982	+	0.0102400i
$204$	2.61803	−	1.90211i	0.183299	−	0.133175i
$205$		0			0
$206$	1.07295	+	0.779543i	0.0747559	+	0.0543133i
$207$			4.47214i			0.310835i
$208$	1.45309	−	2.00000i	0.100753	−	0.138675i
$209$	−3.29180	+	10.1311i	−0.227698	+	0.700783i
$210$		0			0
$211$	7.23607	+	22.2703i	0.498151	+	1.53315i	0.811987	+	0.583675i	$0.198386\pi$
$211$	7.23607	+	22.2703i	0.498151	+	1.53315i	−0.313836	+	0.949477i	$0.601614\pi$
$212$	−8.64527	−	2.80902i	−0.593759	−	0.192924i
$213$	−13.7638	−	4.47214i	−0.943081	−	0.306426i
$214$	2.89919	+	8.92278i	0.198184	+	0.609949i
$215$		0			0
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−0.983813	+	1.35410i	−0.0667856	+	0.0919224i
$218$			12.7639i			0.864483i
$219$	−10.0902	−	7.33094i	−0.681830	−	0.495379i
$220$		0			0
$221$	6.47214	−	4.70228i	0.435363	−	0.316310i
$222$	−4.70228	−	6.47214i	−0.315597	−	0.434381i
$223$	−2.93893	+	0.954915i	−0.196805	+	0.0639458i	−0.405761	−	0.913979i	$-0.632993\pi$
$223$	−2.93893	+	0.954915i	−0.196805	+	0.0639458i	0.208956	+	0.977925i	$0.432993\pi$
$224$	−0.381966			−0.0255212
$225$		0			0
$226$	−14.7639			−0.982082
$227$	10.7189	−	3.48278i	0.711438	−	0.231160i	0.0691308	−	0.997608i	$-0.477977\pi$
$227$	10.7189	−	3.48278i	0.711438	−	0.231160i	0.642307	+	0.766447i	$0.277977\pi$
$228$	4.53077	+	6.23607i	0.300057	+	0.412994i
$229$	−11.7082	+	8.50651i	−0.773700	+	0.562126i	−0.903082	−	0.429469i	$-0.858701\pi$
$229$	−11.7082	+	8.50651i	−0.773700	+	0.562126i	0.129382	+	0.991595i	$0.458701\pi$
$230$		0			0
$231$	0.427051	+	0.310271i	0.0280979	+	0.0204143i
$232$			0.472136i			0.0309972i
$233$	−7.43694	+	10.2361i	−0.487210	+	0.670587i	−0.979870	−	0.199635i	$-0.936024\pi$
$233$	−7.43694	+	10.2361i	−0.487210	+	0.670587i	0.492660	+	0.870222i	$0.336024\pi$
$234$	−0.763932	+	2.35114i	−0.0499398	+	0.153699i
$235$		0			0
$236$	−0.427051	−	1.31433i	−0.0277987	−	0.0855555i
$237$	−3.21644	−	1.04508i	−0.208930	−	0.0678856i
$238$	−1.17557	−	0.381966i	−0.0762009	−	0.0247592i
$239$	−7.94427	−	24.4500i	−0.513872	−	1.58154i	−0.785325	−	0.619084i	$-0.787504\pi$
$239$	−7.94427	−	24.4500i	−0.513872	−	1.58154i	0.271452	−	0.962452i	$-0.412496\pi$
$240$		0			0
$241$	−3.26393	+	10.0453i	−0.210248	+	0.647078i	0.789209	+	0.614125i	$0.210491\pi$
$241$	−3.26393	+	10.0453i	−0.210248	+	0.647078i	−0.999457	+	0.0329526i	$0.989509\pi$
$242$	5.34307	−	7.35410i	0.343465	−	0.472740i
$243$		−	1.00000i		−	0.0641500i
$244$	5.85410	+	4.25325i	0.374770	+	0.272287i
$245$		0			0
$246$	−6.23607	+	4.53077i	−0.397597	+	0.288871i
$247$	11.2007	+	15.4164i	0.712682	+	0.980923i
$248$	−4.16750	+	1.35410i	−0.264636	+	0.0859856i
$249$	8.85410			0.561106
$250$		0			0
$251$	−6.56231			−0.414209			−0.207105	−	0.978319i	$-0.566404\pi$
$251$	−6.56231			−0.414209			−0.207105	+	0.978319i	$0.566404\pi$
$252$	0.363271	−	0.118034i	0.0228839	−	0.00743544i
$253$	3.63271	+	5.00000i	0.228387	+	0.314347i
$254$	9.20820	−	6.69015i	0.577774	−	0.419777i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			22.0000i			1.37232i	0.727450	+	0.686161i	$0.240706\pi$
$257$			22.0000i			1.37232i	−0.727450	+	0.686161i	$0.759294\pi$
$258$	−3.35520	+	4.61803i	−0.208886	+	0.287506i
$259$	−0.944272	+	2.90617i	−0.0586742	+	0.180581i
$260$		0			0
$261$	−0.145898	−	0.449028i	−0.00903086	−	0.0277941i
$262$	−17.0130	−	5.52786i	−1.05107	−	0.341513i
$263$	1.62460	+	0.527864i	0.100177	+	0.0325495i	0.358677	−	0.933462i	$-0.383228\pi$
$263$	1.62460	+	0.527864i	0.100177	+	0.0325495i	−0.258500	+	0.966011i	$0.583228\pi$
$264$	0.427051	+	1.31433i	0.0262832	+	0.0808913i
$265$		0			0
$266$	0.909830	−	2.80017i	0.0557853	−	0.171689i
$267$	7.33094	−	10.0902i	0.448646	−	0.617508i
$268$		−	10.4721i		−	0.639688i
$269$	1.69098	+	1.22857i	0.103101	+	0.0749073i	0.638141	−	0.769919i	$-0.279704\pi$
$269$	1.69098	+	1.22857i	0.103101	+	0.0749073i	−0.535040	+	0.844827i	$0.679704\pi$
$270$		0			0
$271$	−8.92705	+	6.48588i	−0.542280	+	0.393989i	−0.824931	−	0.565233i	$-0.808786\pi$
$271$	−8.92705	+	6.48588i	−0.542280	+	0.393989i	0.282651	+	0.959223i	$0.408786\pi$
$272$	−1.90211	−	2.61803i	−0.115333	−	0.158742i
$273$	0.898056	−	0.291796i	0.0543528	−	0.0176603i
$274$	−10.1803			−0.615017
$275$		0			0
$276$	4.47214			0.269191
$277$	−0.898056	+	0.291796i	−0.0539590	+	0.0175323i	−0.335872	−	0.941908i	$-0.609031\pi$
$277$	−0.898056	+	0.291796i	−0.0539590	+	0.0175323i	0.281913	+	0.959440i	$0.409031\pi$
$278$	−0.898056	−	1.23607i	−0.0538618	−	0.0741344i
$279$	3.54508	−	2.57565i	0.212239	−	0.154200i
$280$		0			0
$281$	24.1803	+	17.5680i	1.44248	+	1.04802i	0.987517	+	0.157510i	$0.0503467\pi$
$281$	24.1803	+	17.5680i	1.44248	+	1.04802i	0.454961	+	0.890511i	$0.349653\pi$
$282$		−	11.7082i		−	0.697213i
$283$	18.4661	−	25.4164i	1.09770	−	1.51085i	0.259292	−	0.965799i	$-0.416511\pi$
$283$	18.4661	−	25.4164i	1.09770	−	1.51085i	0.838404	−	0.545050i	$-0.183489\pi$
$284$	−4.47214	+	13.7638i	−0.265372	+	0.816732i
$285$		0			0
$286$	1.05573	+	3.24920i	0.0624265	+	0.192129i
$287$	2.80017	+	0.909830i	0.165289	+	0.0537056i
$288$	0.951057	+	0.309017i	0.0560415	+	0.0182090i
$289$	2.01722	+	6.20837i	0.118660	+	0.365198i
$290$		0			0
$291$	1.73607	−	5.34307i	0.101770	−	0.313216i
$292$	−7.33094	+	10.0902i	−0.429011	+	0.590483i
$293$		−	10.9098i		−	0.637359i	−0.947863	−	0.318680i	$-0.896761\pi$
$293$		−	10.9098i		−	0.637359i	0.947863	−	0.318680i	$-0.103239\pi$
$294$	5.54508	+	4.02874i	0.323396	+	0.234961i
$295$		0			0
$296$	−6.47214	+	4.70228i	−0.376185	+	0.273315i
$297$	−0.812299	−	1.11803i	−0.0471344	−	0.0648749i
$298$	−10.3759	+	3.37132i	−0.601058	+	0.195295i
$299$	11.0557			0.639369
$300$		0			0
$301$	2.18034			0.125673
$302$	2.54290	−	0.826238i	0.146327	−	0.0475446i
$303$	3.88998	+	5.35410i	0.223474	+	0.307585i
$304$	6.23607	−	4.53077i	0.357663	−	0.259857i
$305$		0			0
$306$	2.61803	+	1.90211i	0.149663	+	0.108737i
$307$		−	10.0000i		−	0.570730i	−0.958419	−	0.285365i	$-0.907885\pi$
$307$		−	10.0000i		−	0.570730i	0.958419	−	0.285365i	$-0.0921148\pi$
$308$	0.310271	−	0.427051i	0.0176793	−	0.0243335i
$309$	−0.409830	+	1.26133i	−0.0233144	+	0.0717544i
$310$		0			0
$311$	−5.85410	−	18.0171i	−0.331956	−	1.02165i	−0.968202	−	0.250169i	$-0.919514\pi$
$311$	−5.85410	−	18.0171i	−0.331956	−	1.02165i	0.636247	−	0.771486i	$-0.280486\pi$
$312$	2.35114	+	0.763932i	0.133107	+	0.0432491i
$313$	16.4252	+	5.33688i	0.928409	+	0.301658i	0.733912	−	0.679245i	$-0.237693\pi$
$313$	16.4252	+	5.33688i	0.928409	+	0.301658i	0.194497	+	0.980903i	$0.437693\pi$
$314$	7.00000	+	21.5438i	0.395033	+	1.21579i
$315$		0			0
$316$	−1.04508	+	3.21644i	−0.0587906	+	0.180939i
$317$	0.257270	−	0.354102i	0.0144497	−	0.0198883i	−0.801731	−	0.597685i	$-0.796087\pi$
$317$	0.257270	−	0.354102i	0.0144497	−	0.0198883i	0.816181	+	0.577797i	$0.196087\pi$
$318$		−	9.09017i		−	0.509751i
$319$	−0.527864	−	0.383516i	−0.0295547	−	0.0214728i
$320$		0			0
$321$	−7.59017	+	5.51458i	−0.423642	+	0.307794i
$322$	−1.00406	−	1.38197i	−0.0559539	−	0.0770140i
$323$	23.7234	−	7.70820i	1.32001	−	0.428896i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	8.47214			0.469228
$327$	−12.1392	+	3.94427i	−0.671300	+	0.218119i
$328$	4.53077	+	6.23607i	0.250170	+	0.344329i
$329$	−3.61803	+	2.62866i	−0.199469	+	0.144922i
$330$		0			0
$331$	14.5623	+	10.5801i	0.800417	+	0.581537i	0.911036	−	0.412326i	$-0.135284\pi$
$331$	14.5623	+	10.5801i	0.800417	+	0.581537i	−0.110620	+	0.993863i	$0.535284\pi$
$332$		−	8.85410i		−	0.485932i
$333$	4.70228	−	6.47214i	0.257683	−	0.354671i
$334$	0.527864	−	1.62460i	0.0288834	−	0.0888941i
$335$		0			0
$336$	−0.118034	−	0.363271i	−0.00643928	−	0.0198181i
$337$	−11.4984	−	3.73607i	−0.626360	−	0.203517i	−0.0213978	−	0.999771i	$-0.506812\pi$
$337$	−11.4984	−	3.73607i	−0.626360	−	0.203517i	−0.604962	+	0.796254i	$0.706812\pi$
$338$	−6.55139	−	2.12868i	−0.356349	−	0.115785i
$339$	−4.56231	−	14.0413i	−0.247790	−	0.762621i
$340$		0			0
$341$	1.87132	−	5.75934i	0.101338	−	0.311886i
$342$	−4.53077	+	6.23607i	−0.244996	+	0.337208i
$343$		−	5.29180i		−	0.285730i
$344$	4.61803	+	3.35520i	0.248988	+	0.180900i
$345$		0			0
$346$	4.92705	−	3.57971i	0.264880	−	0.192447i
$347$	0.257270	+	0.354102i	0.0138110	+	0.0190092i	0.815867	−	0.578240i	$-0.196260\pi$
$347$	0.257270	+	0.354102i	0.0138110	+	0.0190092i	−0.802056	+	0.597249i	$0.796260\pi$
$348$	−0.449028	+	0.145898i	−0.0240704	+	0.00782096i
$349$	−7.88854			−0.422264			−0.211132	−	0.977458i	$-0.567715\pi$
$349$	−7.88854			−0.422264			−0.211132	+	0.977458i	$0.567715\pi$
$350$		0			0
$351$	−2.47214			−0.131953
$352$	1.31433	−	0.427051i	0.0700539	−	0.0227619i
$353$	5.15131	+	7.09017i	0.274177	+	0.377372i	0.923794	−	0.382889i	$-0.125071\pi$
$353$	5.15131	+	7.09017i	0.274177	+	0.377372i	−0.649618	+	0.760261i	$0.725071\pi$
$354$	1.11803	−	0.812299i	0.0594228	−	0.0431732i
$355$		0			0
$356$	−10.0902	−	7.33094i	−0.534778	−	0.388539i
$357$		−	1.23607i		−	0.0654197i
$358$	1.84911	−	2.54508i	0.0977286	−	0.134512i
$359$	0.0557281	−	0.171513i	0.00294122	−	0.00905213i	−0.949575	−	0.313540i	$-0.898485\pi$
$359$	0.0557281	−	0.171513i	0.00294122	−	0.00905213i	0.952516	+	0.304487i	$0.0984852\pi$
$360$		0			0
$361$	12.4894	+	38.4383i	0.657335	+	2.02307i
$362$	−23.4459	−	7.61803i	−1.23229	−	0.400395i
$363$	8.64527	+	2.80902i	0.453759	+	0.147435i
$364$	−0.291796	−	0.898056i	−0.0152943	−	0.0470709i
$365$		0			0
$366$	−2.23607	+	6.88191i	−0.116881	+	0.359723i
$367$	16.6825	−	22.9615i	0.870819	−	1.19858i	−0.108060	−	0.994144i	$-0.534464\pi$
$367$	16.6825	−	22.9615i	0.870819	−	1.19858i	0.978880	−	0.204436i	$-0.0655360\pi$
$368$		−	4.47214i		−	0.233126i
$369$	−6.23607	−	4.53077i	−0.324637	−	0.235862i
$370$		0			0
$371$	−2.80902	+	2.04087i	−0.145837	+	0.105957i
$372$	−2.57565	−	3.54508i	−0.133541	−	0.183804i
$373$	19.4702	−	6.32624i	1.00813	−	0.327560i	0.242018	−	0.970272i	$-0.422191\pi$
$373$	19.4702	−	6.32624i	1.00813	−	0.327560i	0.766108	+	0.642712i	$0.222191\pi$
$374$	4.47214			0.231249
$375$		0			0
$376$	−11.7082			−0.603805
$377$	−1.11006	+	0.360680i	−0.0571709	+	0.0185760i
$378$	0.224514	+	0.309017i	0.0115478	+	0.0158941i
$379$	1.76393	−	1.28157i	0.0906071	−	0.0658299i	−0.541559	−	0.840662i	$-0.682166\pi$
$379$	1.76393	−	1.28157i	0.0906071	−	0.0658299i	0.632166	+	0.774833i	$0.282166\pi$
$380$		0			0
$381$	9.20820	+	6.69015i	0.471751	+	0.342747i
$382$		−	17.7082i		−	0.906031i
$383$	−11.7557	+	16.1803i	−0.600688	+	0.826777i	−0.995771	−	0.0918688i	$-0.970716\pi$
$383$	−11.7557	+	16.1803i	−0.600688	+	0.826777i	0.395083	+	0.918646i	$0.370716\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$		0			0
$386$	3.44427	+	10.6004i	0.175309	+	0.539545i
$387$	−5.42882	−	1.76393i	−0.275963	−	0.0896657i
$388$	−5.34307	−	1.73607i	−0.271253	−	0.0881355i
$389$	4.51722	+	13.9026i	0.229032	+	0.704889i	0.997857	+	0.0654294i	$0.0208417\pi$
$389$	4.51722	+	13.9026i	0.229032	+	0.704889i	−0.768825	+	0.639459i	$0.779158\pi$
$390$		0			0
$391$	4.47214	−	13.7638i	0.226166	−	0.696066i
$392$	4.02874	−	5.54508i	0.203482	−	0.280069i
$393$		−	17.8885i		−	0.902358i
$394$	−4.78115	−	3.47371i	−0.240871	−	0.175003i
$395$		0			0
$396$	−1.11803	+	0.812299i	−0.0561833	+	0.0408196i
$397$	−20.7112	−	28.5066i	−1.03947	−	1.43070i	−0.897596	−	0.440819i	$-0.854688\pi$
$397$	−20.7112	−	28.5066i	−1.03947	−	1.43070i	−0.141871	−	0.989885i	$-0.545312\pi$
$398$	17.6008	−	5.71885i	0.882248	−	0.286660i
$399$	2.94427			0.147398
$400$		0			0
$401$	12.2918			0.613823			0.306912	−	0.951738i	$-0.400704\pi$
$401$	12.2918			0.613823			0.306912	+	0.951738i	$0.400704\pi$
$402$	9.95959	−	3.23607i	0.496739	−	0.161400i
$403$	−6.36737	−	8.76393i	−0.317181	−	0.436563i
$404$	5.35410	−	3.88998i	0.266377	−	0.193534i
$405$		0			0
$406$	0.145898	+	0.106001i	0.00724080	+	0.00526075i
$407$		−	11.0557i		−	0.548012i
$408$	1.90211	−	2.61803i	0.0941686	−	0.129612i
$409$	5.80902	−	17.8783i	0.287237	−	0.884026i	−0.698482	−	0.715628i	$-0.746141\pi$
$409$	5.80902	−	17.8783i	0.287237	−	0.884026i	0.985719	−	0.168398i	$-0.0538594\pi$
$410$		0			0
$411$	−3.14590	−	9.68208i	−0.155176	−	0.477582i
$412$	1.26133	+	0.409830i	0.0621411	+	0.0201909i
$413$	−0.502029	−	0.163119i	−0.0247032	−	0.00802656i
$414$	1.38197	+	4.25325i	0.0679199	+	0.209036i
$415$		0			0
$416$	0.763932	−	2.35114i	0.0374548	−	0.115274i
$417$	0.898056	−	1.23607i	0.0439780	−	0.0605305i
$418$			10.6525i			0.521030i
$419$	6.54508	+	4.75528i	0.319748	+	0.232311i	0.736068	−	0.676908i	$-0.236680\pi$
$419$	6.54508	+	4.75528i	0.319748	+	0.232311i	−0.416320	+	0.909218i	$0.636680\pi$
$420$		0			0
$421$	22.0344	−	16.0090i	1.07389	−	0.780229i	0.0972850	−	0.995257i	$-0.468984\pi$
$421$	22.0344	−	16.0090i	1.07389	−	0.780229i	0.976608	+	0.215028i	$0.0689842\pi$
$422$	13.7638	+	18.9443i	0.670012	+	0.922193i
$423$	11.1352	−	3.61803i	0.541410	−	0.175915i
$424$	−9.09017			−0.441458
$425$		0			0
$426$	−14.4721			−0.701177
$427$	2.62866	−	0.854102i	0.127210	−	0.0413329i
$428$	5.51458	+	7.59017i	0.266557	+	0.366885i
$429$	−2.76393	+	2.00811i	−0.133444	+	0.0969527i
$430$		0			0
$431$	29.7984	+	21.6498i	1.43534	+	1.04283i	0.988991	+	0.147973i	$0.0472748\pi$
$431$	29.7984	+	21.6498i	1.43534	+	1.04283i	0.446346	+	0.894861i	$0.352725\pi$
$432$			1.00000i			0.0481125i
$433$	−13.2290	+	18.2082i	−0.635747	+	0.875030i	−0.998380	−	0.0569016i	$-0.981878\pi$
$433$	−13.2290	+	18.2082i	−0.635747	+	0.875030i	0.362633	+	0.931932i	$0.381878\pi$
$434$	−0.517221	+	1.59184i	−0.0248274	+	0.0764109i
$435$		0			0
$436$	3.94427	+	12.1392i	0.188896	+	0.581363i
$437$	32.7849	+	10.6525i	1.56832	+	0.509577i
$438$	−11.8617	−	3.85410i	−0.566774	−	0.184156i
$439$	−4.48278	−	13.7966i	−0.213951	−	0.658475i	−0.999226	−	0.0393275i	$-0.987478\pi$
$439$	−4.48278	−	13.7966i	−0.213951	−	0.658475i	0.785275	−	0.619147i	$-0.212522\pi$
$440$		0			0
$441$	−2.11803	+	6.51864i	−0.100859	+	0.310411i
$442$	4.70228	−	6.47214i	0.223665	−	0.307848i
$443$			14.3820i			0.683308i	0.939826	+	0.341654i	$0.110987\pi$
$443$			14.3820i			0.683308i	−0.939826	+	0.341654i	$0.889013\pi$
$444$	−6.47214	−	4.70228i	−0.307154	−	0.223160i
$445$		0			0
$446$	−2.50000	+	1.81636i	−0.118378	+	0.0860070i
$447$	−6.41264	−	8.82624i	−0.303307	−	0.417467i
$448$	−0.363271	+	0.118034i	−0.0171630	+	0.00557658i
$449$	14.2918			0.674472			0.337236	−	0.941420i	$-0.390508\pi$
$449$	14.2918			0.674472			0.337236	+	0.941420i	$0.390508\pi$
$450$		0			0
$451$	−10.6525			−0.501605
$452$	−14.0413	+	4.56231i	−0.660449	+	0.214593i
$453$	1.57160	+	2.16312i	0.0738401	+	0.101632i
$454$	9.11803	−	6.62464i	0.427931	−	0.310910i
$455$		0			0
$456$	6.23607	+	4.53077i	0.292031	+	0.212173i
$457$		−	7.09017i		−	0.331664i	−0.986154	−	0.165832i	$-0.946969\pi$
$457$		−	7.09017i		−	0.331664i	0.986154	−	0.165832i	$-0.0530310\pi$
$458$	−8.50651	+	11.7082i	−0.397483	+	0.547088i
$459$	−1.00000	+	3.07768i	−0.0466760	+	0.143654i
$460$		0			0
$461$	−3.88197	−	11.9475i	−0.180801	−	0.556449i	0.819050	−	0.573723i	$-0.194501\pi$
$461$	−3.88197	−	11.9475i	−0.180801	−	0.556449i	−0.999851	+	0.0172739i	$0.994501\pi$
$462$	0.502029	+	0.163119i	0.0233565	+	0.00758898i
$463$	29.3238	+	9.52786i	1.36279	+	0.442797i	0.896974	−	0.442084i	$-0.145761\pi$
$463$	29.3238	+	9.52786i	1.36279	+	0.442797i	0.465817	+	0.884881i	$0.345761\pi$
$464$	0.145898	+	0.449028i	0.00677315	+	0.0208456i
$465$		0			0
$466$	−3.90983	+	12.0332i	−0.181119	+	0.557428i
$467$	−15.4742	+	21.2984i	−0.716059	+	0.985571i	0.283586	+	0.958947i	$0.408476\pi$
$467$	−15.4742	+	21.2984i	−0.716059	+	0.985571i	−0.999646	+	0.0266244i	$0.991524\pi$
$468$			2.47214i			0.114275i
$469$	−3.23607	−	2.35114i	−0.149428	−	0.108566i
$470$		0			0
$471$	−18.3262	+	13.3148i	−0.844428	+	0.613513i
$472$	−0.812299	−	1.11803i	−0.0373891	−	0.0514617i
$473$	−7.50245	+	2.43769i	−0.344963	+	0.112085i
$474$	−3.38197			−0.155339
$475$		0			0
$476$	−1.23607			−0.0566551
$477$	8.64527	−	2.80902i	0.395840	−	0.128616i
$478$	−15.1109	−	20.7984i	−0.691157	−	0.951295i
$479$	9.00000	−	6.53888i	0.411220	−	0.298769i	−0.362875	−	0.931838i	$-0.618205\pi$
$479$	9.00000	−	6.53888i	0.411220	−	0.298769i	0.774096	+	0.633069i	$0.218205\pi$
$480$		0			0
$481$	−16.0000	−	11.6247i	−0.729537	−	0.530040i
$482$			10.5623i			0.481100i
$483$	1.00406	−	1.38197i	0.0456862	−	0.0628816i
$484$	2.80902	−	8.64527i	0.127683	−	0.392967i
$485$		0			0
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	6.46564	+	2.10081i	0.292986	+	0.0951969i	0.451822	−	0.892108i	$-0.350774\pi$
$487$	6.46564	+	2.10081i	0.292986	+	0.0951969i	−0.158836	+	0.987305i	$0.550774\pi$
$488$	6.88191	+	2.23607i	0.311529	+	0.101222i
$489$	2.61803	+	8.05748i	0.118392	+	0.364372i
$490$		0			0
$491$	2.55573	−	7.86572i	0.115338	−	0.354975i	−0.876679	−	0.481076i	$-0.840246\pi$
$491$	2.55573	−	7.86572i	0.115338	−	0.354975i	0.992017	+	0.126101i	$0.0402462\pi$
$492$	−4.53077	+	6.23607i	−0.204263	+	0.281144i
$493$			1.52786i			0.0688115i
$494$	15.4164	+	11.2007i	0.693617	+	0.503942i
$495$		0			0
$496$	−3.54508	+	2.57565i	−0.159179	+	0.115650i
$497$	3.24920	+	4.47214i	0.145746	+	0.200603i
$498$	8.42075	−	2.73607i	0.377343	−	0.122606i
$499$	13.5967			0.608674			0.304337	−	0.952564i	$-0.401565\pi$
$499$	13.5967			0.608674			0.304337	+	0.952564i	$0.401565\pi$
$500$		0			0
$501$	1.70820			0.0763169
$502$	−6.24112	+	2.02786i	−0.278555	+	0.0905080i
$503$	6.98791	+	9.61803i	0.311576	+	0.428847i	0.935872	−	0.352341i	$-0.114614\pi$
$503$	6.98791	+	9.61803i	0.311576	+	0.428847i	−0.624296	+	0.781188i	$0.714614\pi$
$504$	0.309017	−	0.224514i	0.0137647	−	0.0100006i
$505$		0			0
$506$	5.00000	+	3.63271i	0.222277	+	0.161494i
$507$		−	6.88854i		−	0.305931i
$508$	6.69015	−	9.20820i	0.296827	−	0.408548i
$509$	−6.33688	+	19.5029i	−0.280877	+	0.864451i	0.706727	+	0.707487i	$0.250171\pi$
$509$	−6.33688	+	19.5029i	−0.280877	+	0.864451i	−0.987604	+	0.156965i	$0.949829\pi$
$510$		0			0
$511$	1.47214	+	4.53077i	0.0651235	+	0.200429i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−7.33094	−	2.38197i	−0.323669	−	0.105166i
$514$	6.79837	+	20.9232i	0.299863	+	0.922885i
$515$		0			0
$516$	−1.76393	+	5.42882i	−0.0776528	+	0.238991i
$517$	9.51057	−	13.0902i	0.418274	−	0.575705i
$518$			3.05573i			0.134261i
$519$	4.92705	+	3.57971i	0.216274	+	0.157132i
$520$		0			0
$521$	6.61803	−	4.80828i	0.289941	−	0.210655i	−0.433301	−	0.901249i	$-0.642651\pi$
$521$	6.61803	−	4.80828i	0.289941	−	0.210655i	0.723242	+	0.690595i	$0.242651\pi$
$522$	−0.277515	−	0.381966i	−0.0121465	−	0.0167182i
$523$	−27.5276	+	8.94427i	−1.20370	+	0.391106i	−0.841121	−	0.540847i	$-0.818104\pi$
$523$	−27.5276	+	8.94427i	−1.20370	+	0.391106i	−0.362579	+	0.931953i	$0.618104\pi$
$524$	−17.8885			−0.781465
$525$		0			0
$526$	1.70820			0.0744812
$527$	−13.4863	+	4.38197i	−0.587473	+	0.190881i
$528$	0.812299	+	1.11803i	0.0353508	+	0.0486562i
$529$	−2.42705	+	1.76336i	−0.105524	+	0.0766676i
$530$		0			0
$531$	1.11803	+	0.812299i	0.0485185	+	0.0352508i
$532$		−	2.94427i		−	0.127650i
$533$	−11.2007	+	15.4164i	−0.485155	+	0.667759i
$534$	3.85410	−	11.8617i	0.166783	−	0.513306i
$535$		0			0
$536$	−3.23607	−	9.95959i	−0.139777	−	0.430189i
$537$	2.99193	+	0.972136i	0.129111	+	0.0419508i
$538$	1.98787	+	0.645898i	0.0857032	+	0.0278466i
$539$	2.92705	+	9.00854i	0.126077	+	0.388025i
$540$		0			0
$541$	−1.18034	+	3.63271i	−0.0507468	+	0.156183i	−0.973218	−	0.229882i	$-0.926166\pi$
$541$	−1.18034	+	3.63271i	−0.0507468	+	0.156183i	0.922472	+	0.386065i	$0.126166\pi$
$542$	−6.48588	+	8.92705i	−0.278592	+	0.383450i
$543$		−	24.6525i		−	1.05794i
$544$	−2.61803	−	1.90211i	−0.112247	−	0.0815524i
$545$		0			0
$546$	0.763932	−	0.555029i	0.0326933	−	0.0237531i
$547$	−2.17963	−	3.00000i	−0.0931941	−	0.128271i	0.759874	−	0.650071i	$-0.225261\pi$
$547$	−2.17963	−	3.00000i	−0.0931941	−	0.128271i	−0.853068	+	0.521800i	$0.825261\pi$
$548$	−9.68208	+	3.14590i	−0.413598	+	0.134386i
$549$	−7.23607			−0.308828
$550$		0			0
$551$	−3.63932			−0.155040
$552$	4.25325	−	1.38197i	0.181031	−	0.0588204i
$553$	0.759299	+	1.04508i	0.0322887	+	0.0444415i
$554$	−0.763932	+	0.555029i	−0.0324564	+	0.0235809i
$555$		0			0
$556$	−1.23607	−	0.898056i	−0.0524210	−	0.0380861i
$557$			2.67376i			0.113291i	0.998394	+	0.0566455i	$0.0180405\pi$
$557$			2.67376i			0.113291i	−0.998394	+	0.0566455i	$0.981960\pi$
$558$	2.57565	−	3.54508i	0.109036	−	0.150075i
$559$	−4.36068	+	13.4208i	−0.184437	+	0.567639i
$560$		0			0
$561$	1.38197	+	4.25325i	0.0583467	+	0.179573i
$562$	28.4257	+	9.23607i	1.19907	+	0.389600i
$563$	−11.6699	−	3.79180i	−0.491830	−	0.159805i	0.0525933	−	0.998616i	$-0.483251\pi$
$563$	−11.6699	−	3.79180i	−0.491830	−	0.159805i	−0.544423	+	0.838811i	$0.683251\pi$
$564$	−3.61803	−	11.1352i	−0.152347	−	0.468875i
$565$		0			0
$566$	9.70820	−	29.8788i	0.408066	−	1.25590i
$567$	−0.224514	+	0.309017i	−0.00942870	+	0.0129775i
$568$			14.4721i			0.607237i
$569$	35.4164	+	25.7315i	1.48473	+	1.07872i	0.975993	+	0.217801i	$0.0698885\pi$
$569$	35.4164	+	25.7315i	1.48473	+	1.07872i	0.508740	+	0.860920i	$0.330111\pi$
$570$		0			0
$571$	22.5623	−	16.3925i	0.944203	−	0.686004i	−0.00522561	−	0.999986i	$-0.501663\pi$
$571$	22.5623	−	16.3925i	0.944203	−	0.686004i	0.949429	+	0.313983i	$0.101663\pi$
$572$	2.00811	+	2.76393i	0.0839635	+	0.115566i
$573$	16.8415	−	5.47214i	0.703564	−	0.228602i
$574$	2.94427			0.122892
$575$		0			0
$576$	1.00000			0.0416667
$577$	−36.1199	+	11.7361i	−1.50369	+	0.488579i	−0.941092	−	0.338151i	$-0.890199\pi$
$577$	−36.1199	+	11.7361i	−1.50369	+	0.488579i	−0.562599	+	0.826730i	$0.690199\pi$
$578$	3.83698	+	5.28115i	0.159597	+	0.219667i
$579$	−9.01722	+	6.55139i	−0.374743	+	0.272267i
$580$		0			0
$581$	−2.73607	−	1.98787i	−0.113511	−	0.0824707i
$582$		−	5.61803i		−	0.232875i
$583$	7.38394	−	10.1631i	0.305811	−	0.420913i
$584$	−3.85410	+	11.8617i	−0.159484	+	0.490841i
$585$		0			0
$586$	−3.37132	−	10.3759i	−0.139268	−	0.428623i
$587$	28.5645	+	9.28115i	1.17898	+	0.383074i	0.831988	−	0.554794i	$-0.187203\pi$
$587$	28.5645	+	9.28115i	1.17898	+	0.383074i	0.346993	+	0.937868i	$0.387203\pi$
$588$	6.51864	+	2.11803i	0.268824	+	0.0873462i
$589$	−10.4377	−	32.1239i	−0.430078	−	1.32364i
$590$		0			0
$591$	1.82624	−	5.62058i	0.0751214	−	0.231200i
$592$	−4.70228	+	6.47214i	−0.193263	+	0.266003i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−1.11803	−	0.812299i	−0.0458735	−	0.0333290i
$595$		0			0
$596$	−8.82624	+	6.41264i	−0.361537	+	0.262672i
$597$	10.8779	+	14.9721i	0.445203	+	0.612769i
$598$	10.5146	−	3.41641i	0.429975	−	0.139707i
$599$	8.47214			0.346162			0.173081	−	0.984908i	$-0.444628\pi$
$599$	8.47214			0.346162			0.173081	+	0.984908i	$0.444628\pi$
$600$		0			0
$601$	−41.2705			−1.68346			−0.841730	−	0.539899i	$-0.818462\pi$
$601$	−41.2705			−1.68346			−0.841730	+	0.539899i	$0.818462\pi$
$602$	2.07363	−	0.673762i	0.0845147	−	0.0274605i
$603$	6.15537	+	8.47214i	0.250666	+	0.345012i
$604$	2.16312	−	1.57160i	0.0880161	−	0.0639474i
$605$		0			0
$606$	5.35410	+	3.88998i	0.217496	+	0.158020i
$607$			13.5623i			0.550477i	0.961376	+	0.275239i	$0.0887568\pi$
$607$			13.5623i			0.550477i	−0.961376	+	0.275239i	$0.911243\pi$
$608$	4.53077	−	6.23607i	0.183747	−	0.252906i
$609$	−0.0557281	+	0.171513i	−0.00225822	+	0.00695007i
$610$		0			0
$611$	−8.94427	−	27.5276i	−0.361847	−	1.11365i
$612$	3.07768	+	1.00000i	0.124408	+	0.0404226i
$613$	−30.6708	−	9.96556i	−1.23878	−	0.402505i	−0.384895	−	0.922961i	$-0.625762\pi$
$613$	−30.6708	−	9.96556i	−1.23878	−	0.402505i	−0.853889	+	0.520455i	$0.825762\pi$
$614$	−3.09017	−	9.51057i	−0.124709	−	0.383815i
$615$		0			0
$616$	0.163119	−	0.502029i	0.00657225	−	0.0202273i
$617$	−22.2703	+	30.6525i	−0.896570	+	1.23402i	0.0749797	+	0.997185i	$0.476111\pi$
$617$	−22.2703	+	30.6525i	−0.896570	+	1.23402i	−0.971549	+	0.236837i	$0.923889\pi$
$618$			1.32624i			0.0533491i
$619$	14.0902	+	10.2371i	0.566332	+	0.411464i	0.833771	−	0.552111i	$-0.186177\pi$
$619$	14.0902	+	10.2371i	0.566332	+	0.411464i	−0.267439	+	0.963575i	$0.586177\pi$
$620$		0			0
$621$	−3.61803	+	2.62866i	−0.145187	+	0.105484i
$622$	−11.1352	−	15.3262i	−0.446479	−	0.614526i
$623$	−4.53077	+	1.47214i	−0.181521	+	0.0589799i
$624$	2.47214			0.0989646
$625$		0			0
$626$	17.2705			0.690268
$627$	−10.1311	+	3.29180i	−0.404597	+	0.131462i
$628$	13.3148	+	18.3262i	0.531318	+	0.731297i
$629$	−20.9443	+	15.2169i	−0.835103	+	0.606738i
$630$		0			0
$631$	−30.3607	−	22.0583i	−1.20864	−	0.878128i	−0.213533	−	0.976936i	$-0.568497\pi$
$631$	−30.3607	−	22.0583i	−1.20864	−	0.878128i	−0.995107	+	0.0988078i	$0.968497\pi$
$632$			3.38197i			0.134527i
$633$	−13.7638	+	18.9443i	−0.547063	+	0.752967i
$634$	0.135255	−	0.416272i	0.00537166	−	0.0165323i
$635$		0			0
$636$	−2.80902	−	8.64527i	−0.111385	−	0.342807i
$637$	16.1150	+	5.23607i	0.638498	+	0.207461i
$638$	−0.620541	−	0.201626i	−0.0245675	−	0.00798245i
$639$	−4.47214	−	13.7638i	−0.176915	−	0.544488i
$640$		0			0
$641$	−11.1803	+	34.4095i	−0.441597	+	1.35910i	0.444576	+	0.895741i	$0.353354\pi$
$641$	−11.1803	+	34.4095i	−0.441597	+	1.35910i	−0.886173	+	0.463354i	$0.846646\pi$
$642$	−5.51458	+	7.59017i	−0.217643	+	0.299560i
$643$		−	13.8885i		−	0.547711i	−0.961771	−	0.273855i	$-0.911701\pi$
$643$		−	13.8885i		−	0.547711i	0.961771	−	0.273855i	$-0.0882990\pi$
$644$	−1.38197	−	1.00406i	−0.0544571	−	0.0395654i
$645$		0			0
$646$	20.1803	−	14.6619i	0.793985	−	0.576864i
$647$	−2.97168	−	4.09017i	−0.116829	−	0.160801i	0.746598	−	0.665276i	$-0.231686\pi$
$647$	−2.97168	−	4.09017i	−0.116829	−	0.160801i	−0.863426	+	0.504475i	$0.831686\pi$
$648$	−0.951057	+	0.309017i	−0.0373610	+	0.0121393i
$649$	1.90983			0.0749674
$650$		0			0
$651$	−1.67376			−0.0655999
$652$	8.05748	−	2.61803i	0.315555	−	0.102530i
$653$	−1.67760	−	2.30902i	−0.0656495	−	0.0903588i	0.774930	−	0.632047i	$-0.217785\pi$
$653$	−1.67760	−	2.30902i	−0.0656495	−	0.0903588i	−0.840579	+	0.541689i	$0.817785\pi$
$654$	−10.3262	+	7.50245i	−0.403788	+	0.293369i
$655$		0			0
$656$	6.23607	+	4.53077i	0.243478	+	0.176897i
$657$		−	12.4721i		−	0.486584i
$658$	−2.62866	+	3.61803i	−0.102476	+	0.141046i
$659$	5.68034	−	17.4823i	0.221275	−	0.681013i	−0.777374	−	0.629039i	$-0.783449\pi$
$659$	5.68034	−	17.4823i	0.221275	−	0.681013i	0.998648	−	0.0519743i	$-0.0165514\pi$
$660$		0			0
$661$	−6.65248	−	20.4742i	−0.258751	−	0.796355i	−0.993067	−	0.117547i	$-0.962497\pi$
$661$	−6.65248	−	20.4742i	−0.258751	−	0.796355i	0.734316	−	0.678808i	$-0.237503\pi$
$662$	17.1190	+	5.56231i	0.665350	+	0.216185i
$663$	7.60845	+	2.47214i	0.295488	+	0.0960098i
$664$	−2.73607	−	8.42075i	−0.106180	−	0.326789i
$665$		0			0
$666$	2.47214	−	7.60845i	0.0957933	−	0.294822i
$667$	−1.24108	+	1.70820i	−0.0480549	+	0.0661419i
$668$		−	1.70820i		−	0.0660924i
$669$	−2.50000	−	1.81636i	−0.0966556	−	0.0702244i
$670$		0			0
$671$	−8.09017	+	5.87785i	−0.312318	+	0.226912i
$672$	−0.224514	−	0.309017i	−0.00866082	−	0.0119206i
$673$	−23.2541	+	7.55573i	−0.896381	+	0.291252i	−0.720743	−	0.693203i	$-0.756199\pi$
$673$	−23.2541	+	7.55573i	−0.896381	+	0.291252i	−0.175639	+	0.984455i	$0.556199\pi$
$674$	−12.0902			−0.465696
$675$		0			0
$676$	−6.88854			−0.264944
$677$	17.0333	−	5.53444i	0.654641	−	0.212706i	0.0371818	−	0.999309i	$-0.488162\pi$
$677$	17.0333	−	5.53444i	0.654641	−	0.212706i	0.617460	+	0.786603i	$0.288162\pi$
$678$	−8.67802	−	11.9443i	−0.333277	−	0.458717i
$679$	−1.73607	+	1.26133i	−0.0666242	+	0.0484053i
$680$		0			0
$681$	9.11803	+	6.62464i	0.349404	+	0.253857i
$682$		−	6.05573i		−	0.231886i
$683$	−2.64890	+	3.64590i	−0.101357	+	0.139506i	−0.856683	−	0.515843i	$-0.827479\pi$
$683$	−2.64890	+	3.64590i	−0.101357	+	0.139506i	0.755326	+	0.655350i	$0.227479\pi$
$684$	−2.38197	+	7.33094i	−0.0910767	+	0.280305i
$685$		0			0
$686$	−1.63525	−	5.03280i	−0.0624343	−	0.192153i
$687$	−13.7638	−	4.47214i	−0.525122	−	0.170623i
$688$	5.42882	+	1.76393i	0.206972	+	0.0672493i
$689$	−6.94427	−	21.3723i	−0.264556	−	0.814219i
$690$		0			0
$691$	2.09017	−	6.43288i	0.0795138	−	0.244718i	−0.903396	−	0.428808i	$-0.858934\pi$
$691$	2.09017	−	6.43288i	0.0795138	−	0.244718i	0.982909	+	0.184090i	$0.0589337\pi$
$692$	3.57971	−	4.92705i	0.136080	−	0.187298i
$693$			0.527864i			0.0200519i
$694$	0.354102	+	0.257270i	0.0134415	+	0.00976584i
$695$		0			0
$696$	−0.381966	+	0.277515i	−0.0144784	+	0.0105192i
$697$	14.6619	+	20.1803i	0.555358	+	0.764385i
$698$	−7.50245	+	2.43769i	−0.283972	+	0.0922681i
$699$	−12.6525			−0.478561
$700$		0			0
$701$	−12.8328			−0.484689			−0.242344	−	0.970190i	$-0.577916\pi$
$701$	−12.8328			−0.484689			−0.242344	+	0.970190i	$0.577916\pi$
$702$	−2.35114	+	0.763932i	−0.0887381	+	0.0288328i
$703$	−36.2461	−	49.8885i	−1.36705	−	1.88158i
$704$	1.11803	−	0.812299i	0.0421375	−	0.0306147i
$705$		0			0
$706$	7.09017	+	5.15131i	0.266842	+	0.193872i
$707$		−	2.52786i		−	0.0950701i
$708$	0.812299	−	1.11803i	0.0305281	−	0.0420183i
$709$	9.36068	−	28.8092i	0.351548	−	1.08195i	−0.606437	−	0.795132i	$-0.707402\pi$
$709$	9.36068	−	28.8092i	0.351548	−	1.08195i	0.957984	−	0.286821i	$-0.0925984\pi$
$710$		0			0
$711$	−1.04508	−	3.21644i	−0.0391937	−	0.120626i
$712$	−11.8617	−	3.85410i	−0.444536	−	0.144439i
$713$	−18.6376	−	6.05573i	−0.697984	−	0.226789i
$714$	−0.381966	−	1.17557i	−0.0142947	−	0.0439946i
$715$		0			0
$716$	0.972136	−	2.99193i	0.0363304	−	0.111814i
$717$	15.1109	−	20.7984i	0.564327	−	0.776730i
$718$		−	0.180340i		−	0.00673022i
$719$	−35.1246	−	25.5195i	−1.30993	−	0.951718i	−1.00000		0.000957448i	$-0.999695\pi$
$719$	−35.1246	−	25.5195i	−1.30993	−	0.951718i	−0.309927	−	0.950760i	$-0.600305\pi$
$720$		0			0
$721$	0.409830	−	0.297759i	0.0152629	−	0.0110891i
$722$	23.7562	+	32.6976i	0.884113	+	1.21688i
$723$	−10.0453	+	3.26393i	−0.373591	+	0.121387i
$724$	−24.6525			−0.916202
$725$		0			0
$726$	9.09017			0.337368
$727$	−33.6830	+	10.9443i	−1.24923	+	0.405901i	−0.857646	−	0.514240i	$-0.828074\pi$
$727$	−33.6830	+	10.9443i	−1.24923	+	0.405901i	−0.391587	+	0.920141i	$0.628074\pi$
$728$	−0.555029	−	0.763932i	−0.0205707	−	0.0283132i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	14.9443	+	10.8576i	0.552734	+	0.401585i
$732$			7.23607i			0.267453i
$733$	−0.0655123	+	0.0901699i	−0.00241975	+	0.00333050i	−0.810225	−	0.586119i	$-0.800655\pi$
$733$	−0.0655123	+	0.0901699i	−0.00241975	+	0.00333050i	0.807805	+	0.589449i	$0.200655\pi$
$734$	8.77051	−	26.9929i	0.323725	−	0.996324i
$735$		0			0
$736$	−1.38197	−	4.25325i	−0.0509399	−	0.156777i
$737$	13.7638	+	4.47214i	0.506997	+	0.164733i
$738$	−7.33094	−	2.38197i	−0.269856	−	0.0876814i
$739$	7.97871	+	24.5560i	0.293502	+	0.903305i	0.983721	+	0.179705i	$0.0575142\pi$
$739$	7.97871	+	24.5560i	0.293502	+	0.903305i	−0.690219	+	0.723601i	$0.742486\pi$
$740$		0			0
$741$	−5.88854	+	18.1231i	−0.216321	+	0.665768i
$742$	−2.04087	+	2.80902i	−0.0749227	+	0.103122i
$743$			37.0132i			1.35788i	0.734193	+	0.678940i	$0.237561\pi$
$743$			37.0132i			1.35788i	−0.734193	+	0.678940i	$0.762439\pi$
$744$	−3.54508	−	2.57565i	−0.129969	−	0.0944281i
$745$		0			0
$746$	16.5623	−	12.0332i	0.606389	−	0.440567i
$747$	5.20431	+	7.16312i	0.190416	+	0.262085i
$748$	4.25325	−	1.38197i	0.155514	−	0.0505297i
$749$	3.58359			0.130942
$750$		0			0
$751$	0.201626			0.00735744			0.00367872	−	0.999993i	$-0.498829\pi$
$751$	0.201626			0.00735744			0.00367872	+	0.999993i	$0.498829\pi$
$752$	−11.1352	+	3.61803i	−0.406058	+	0.131936i
$753$	−3.85723	−	5.30902i	−0.140565	−	0.193471i
$754$	−0.944272	+	0.686054i	−0.0343884	+	0.0249846i
$755$		0			0
$756$	0.309017	+	0.224514i	0.0112388	+	0.00816549i
$757$		−	23.1246i		−	0.840478i	−0.907413	−	0.420239i	$-0.861946\pi$
$757$		−	23.1246i		−	0.840478i	0.907413	−	0.420239i	$-0.138054\pi$
$758$	1.28157	−	1.76393i	0.0465488	−	0.0640689i
$759$	−1.90983	+	5.87785i	−0.0693224	+	0.213353i
$760$		0			0
$761$	−7.85410	−	24.1724i	−0.284711	−	0.876250i	−0.986485	−	0.163851i	$-0.947608\pi$
$761$	−7.85410	−	24.1724i	−0.284711	−	0.876250i	0.701774	−	0.712399i	$-0.252392\pi$
$762$	10.8249	+	3.51722i	0.392144	+	0.127415i
$763$	4.63677	+	1.50658i	0.167862	+	0.0545418i
$764$	−5.47214	−	16.8415i	−0.197975	−	0.609304i
$765$		0			0
$766$	−6.18034	+	19.0211i	−0.223305	+	0.687261i
$767$	2.00811	−	2.76393i	0.0725088	−	0.0997998i
$768$		−	1.00000i		−	0.0360844i
$769$	−28.8713	−	20.9762i	−1.04113	−	0.756423i	−0.0706214	−	0.997503i	$-0.522498\pi$
$769$	−28.8713	−	20.9762i	−1.04113	−	0.756423i	−0.970505	+	0.241080i	$0.922498\pi$
$770$		0			0
$771$	−17.7984	+	12.9313i	−0.640993	+	0.465709i
$772$	6.55139	+	9.01722i	0.235790	+	0.324537i
$773$	7.46969	−	2.42705i	0.268666	−	0.0872950i	−0.171586	−	0.985169i	$-0.554889\pi$
$773$	7.46969	−	2.42705i	0.268666	−	0.0872950i	0.440252	+	0.897874i	$0.354889\pi$
$774$	−5.70820			−0.205177
$775$		0			0
$776$	−5.61803			−0.201676
$777$	−2.90617	+	0.944272i	−0.104258	+	0.0338756i
$778$	8.59226	+	11.8262i	0.308048	+	0.423991i
$779$	−48.0689	+	34.9241i	−1.72225	+	1.25129i
$780$		0			0
$781$	−16.1803	−	11.7557i	−0.578978	−	0.420652i
$782$		−	14.4721i		−	0.517523i
$783$	0.277515	−	0.381966i	0.00991756	−	0.0136504i
$784$	2.11803	−	6.51864i	0.0756441	−	0.232809i
$785$		0			0
$786$	−5.52786	−	17.0130i	−0.197172	−	0.606834i
$787$	28.5972	+	9.29180i	1.01938	+	0.331217i	0.770584	−	0.637339i	$-0.219965\pi$
$787$	28.5972	+	9.29180i	1.01938	+	0.331217i	0.248797	+	0.968556i	$0.419965\pi$
$788$	−5.62058	−	1.82624i	−0.200225	−	0.0650570i
$789$	0.527864	+	1.62460i	0.0187925	+	0.0578372i
$790$		0			0
$791$	−1.74265	+	5.36331i	−0.0619614	+	0.190697i
$792$	−0.812299	+	1.11803i	−0.0288638	+	0.0397276i
$793$			17.8885i			0.635241i
$794$	−28.5066	−	20.7112i	−1.01166	−	0.735014i
$795$		0			0
$796$	14.9721	−	10.8779i	0.530673	−	0.385557i
$797$	−21.4580	−	29.5344i	−0.760082	−	1.04616i	−0.997207	−	0.0746844i	$-0.976205\pi$
$797$	−21.4580	−	29.5344i	−0.760082	−	1.04616i	0.237125	−	0.971479i	$-0.423795\pi$
$798$	2.80017	−	0.909830i	0.0991249	−	0.0322076i
$799$	−37.8885			−1.34040
$800$		0			0
$801$	12.4721			0.440681
$802$	11.6902	−	3.79837i	0.412795	−	0.134125i
$803$	−10.1311	−	13.9443i	−0.357519	−	0.492083i
$804$	8.47214	−	6.15537i	0.298789	−	0.217083i
$805$		0			0
$806$	−8.76393	−	6.36737i	−0.308696	−	0.224281i
$807$			2.09017i			0.0735775i
$808$	3.88998	−	5.35410i	0.136849	−	0.188357i
$809$	−7.05573	+	21.7153i	−0.248066	+	0.763469i	0.747051	+	0.664767i	$0.231469\pi$
$809$	−7.05573	+	21.7153i	−0.248066	+	0.763469i	−0.995117	+	0.0987023i	$0.968531\pi$
$810$		0			0
$811$	2.38197	+	7.33094i	0.0836421	+	0.257424i	0.984128	−	0.177462i	$-0.0567887\pi$
$811$	2.38197	+	7.33094i	0.0836421	+	0.257424i	−0.900486	+	0.434886i	$0.856789\pi$
$812$	0.171513	+	0.0557281i	0.00601894	+	0.00195567i
$813$	−10.4944	−	3.40983i	−0.368054	−	0.119588i
$814$	−3.41641	−	10.5146i	−0.119745	−	0.368537i
$815$		0			0
$816$	1.00000	−	3.07768i	0.0350070	−	0.107740i
$817$	−25.8626	+	35.5967i	−0.904816	+	1.24537i
$818$		−	18.7984i		−	0.657270i
$819$	0.763932	+	0.555029i	0.0266939	+	0.0193943i
$820$		0			0
$821$	27.4336	−	19.9317i	0.957440	−	0.695621i	0.00488541	−	0.999988i	$-0.498445\pi$
$821$	27.4336	−	19.9317i	0.957440	−	0.695621i	0.952555	+	0.304367i	$0.0984449\pi$
$822$	−5.98385	−	8.23607i	−0.208711	−	0.287266i
$823$	−30.4666	+	9.89919i	−1.06200	+	0.345064i	−0.787366	−	0.616486i	$-0.788556\pi$
$823$	−30.4666	+	9.89919i	−1.06200	+	0.345064i	−0.274631	+	0.961550i	$0.588556\pi$
$824$	1.32624			0.0462017
$825$		0			0
$826$	−0.527864			−0.0183667
$827$	−40.9937	+	13.3197i	−1.42549	+	0.463170i	−0.917342	−	0.398100i	$-0.869670\pi$
$827$	−40.9937	+	13.3197i	−1.42549	+	0.463170i	−0.508148	+	0.861270i	$0.669670\pi$
$828$	2.62866	+	3.61803i	0.0913521	+	0.125735i
$829$	−8.00000	+	5.81234i	−0.277851	+	0.201871i	−0.717980	−	0.696064i	$-0.754933\pi$
$829$	−8.00000	+	5.81234i	−0.277851	+	0.201871i	0.440128	+	0.897935i	$0.354933\pi$
$830$		0			0
$831$	−0.763932	−	0.555029i	−0.0265005	−	0.0192537i
$832$		−	2.47214i		−	0.0857059i
$833$	13.0373	−	17.9443i	0.451715	−	0.621732i
$834$	0.472136	−	1.45309i	0.0163487	−	0.0503162i
$835$		0			0
$836$	3.29180	+	10.1311i	0.113849	+	0.350392i
$837$	4.16750	+	1.35410i	0.144050	+	0.0468046i
$838$	7.69421	+	2.50000i	0.265792	+	0.0863611i
$839$	11.8541	+	36.4832i	0.409249	+	1.25954i	0.917295	+	0.398209i	$0.130368\pi$
$839$	11.8541	+	36.4832i	0.409249	+	1.25954i	−0.508046	+	0.861330i	$0.669632\pi$
$840$		0			0
$841$	−8.89261	+	27.3686i	−0.306642	+	0.943746i
$842$	16.0090	−	22.0344i	0.551705	−	0.759357i
$843$			29.8885i			1.02942i
$844$	18.9443	+	13.7638i	0.652089	+	0.473770i
$845$		0			0
$846$	9.47214	−	6.88191i	0.325659	−	0.236605i
$847$	−2.04087	−	2.80902i	−0.0701251	−	0.0965190i
$848$	−8.64527	+	2.80902i	−0.296880	+	0.0964620i
$849$	31.4164			1.07821
$850$		0			0
$851$	−35.7771			−1.22642
$852$	−13.7638	+	4.47214i	−0.471541	+	0.153213i
$853$	−3.28969	−	4.52786i	−0.112637	−	0.155031i	0.748977	−	0.662597i	$-0.230546\pi$
$853$	−3.28969	−	4.52786i	−0.112637	−	0.155031i	−0.861613	+	0.507565i	$0.830546\pi$
$854$	2.23607	−	1.62460i	0.0765167	−	0.0555926i
$855$		0			0
$856$	7.59017	+	5.51458i	0.259427	+	0.188485i
$857$		−	42.0689i		−	1.43705i	−0.695503	−	0.718523i	$-0.744819\pi$
$857$		−	42.0689i		−	1.43705i	0.695503	−	0.718523i	$-0.255181\pi$
$858$	−2.00811	+	2.76393i	−0.0685559	+	0.0943591i
$859$	4.85410	−	14.9394i	0.165620	−	0.509725i	−0.833462	−	0.552577i	$-0.813644\pi$
$859$	4.85410	−	14.9394i	0.165620	−	0.509725i	0.999081	+	0.0428520i	$0.0136444\pi$
$860$		0			0
$861$	0.909830	+	2.80017i	0.0310069	+	0.0954295i
$862$	35.0301	+	11.3820i	1.19313	+	0.387671i
$863$	11.5842	+	3.76393i	0.394330	+	0.128126i	0.499469	−	0.866332i	$-0.333529\pi$
$863$	11.5842	+	3.76393i	0.394330	+	0.128126i	−0.105138	+	0.994458i	$0.533529\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$		0			0
$866$	−6.95492	+	21.4050i	−0.236338	+	0.727372i
$867$	−3.83698	+	5.28115i	−0.130311	+	0.179357i
$868$			1.67376i			0.0568112i
$869$	−3.78115	−	2.74717i	−0.128267	−	0.0931913i
$870$		0			0
$871$	20.9443	−	15.2169i	0.709670	−	0.515605i
$872$	7.50245	+	10.3262i	0.254065	+	0.349691i
$873$	5.34307	−	1.73607i	0.180835	−	0.0587570i
$874$	34.4721			1.16604
$875$		0			0
$876$	−12.4721			−0.421394
$877$	2.97168	−	0.965558i	0.100347	−	0.0326046i	−0.258413	−	0.966034i	$-0.583200\pi$
$877$	2.97168	−	0.965558i	0.100347	−	0.0326046i	0.358760	+	0.933430i	$0.383200\pi$
$878$	−8.52675	−	11.7361i	−0.287764	−	0.396073i
$879$	8.82624	−	6.41264i	0.297702	−	0.216293i
$880$		0			0
$881$	−20.7082	−	15.0454i	−0.697677	−	0.506892i	0.181498	−	0.983391i	$-0.441905\pi$
$881$	−20.7082	−	15.0454i	−0.697677	−	0.506892i	−0.879175	+	0.476499i	$0.841905\pi$
$882$			6.85410i			0.230790i
$883$	16.4985	−	22.7082i	0.555218	−	0.764192i	−0.435491	−	0.900193i	$-0.643425\pi$
$883$	16.4985	−	22.7082i	0.555218	−	0.764192i	0.990709	+	0.136001i	$0.0434251\pi$
$884$	2.47214	−	7.60845i	0.0831469	−	0.255900i
$885$		0			0
$886$	4.44427	+	13.6781i	0.149308	+	0.459523i
$887$	3.24920	+	1.05573i	0.109097	+	0.0354479i	0.363057	−	0.931767i	$-0.381733\pi$
$887$	3.24920	+	1.05573i	0.109097	+	0.0354479i	−0.253960	+	0.967215i	$0.581733\pi$
$888$	−7.60845	−	2.47214i	−0.255323	−	0.0829595i
$889$	−1.34346	−	4.13474i	−0.0450582	−	0.138675i
$890$		0			0
$891$	0.427051	−	1.31433i	0.0143067	−	0.0440316i
$892$	−1.81636	+	2.50000i	−0.0608161	+	0.0837062i
$893$		−	90.2492i		−	3.02008i
$894$	−8.82624	−	6.41264i	−0.295194	−	0.214471i
$895$		0			0
$896$	−0.309017	+	0.224514i	−0.0103235	+	0.00750049i
$897$	6.49839	+	8.94427i	0.216975	+	0.298641i
$898$	13.5923	−	4.41641i	0.453581	−	0.147377i
$899$	2.06888			0.0690011
$900$		0			0
$901$	−29.4164			−0.980003
$902$	−10.1311	+	3.29180i	−0.337329	+	0.109605i
$903$	1.28157	+	1.76393i	0.0426480	+	0.0587000i
$904$	−11.9443	+	8.67802i	−0.397261	+	0.288627i
$905$		0			0
$906$	2.16312	+	1.57160i	0.0718648	+	0.0522128i
$907$		−	21.5279i		−	0.714821i	−0.933947	−	0.357410i	$-0.883660\pi$
$907$		−	21.5279i		−	0.714821i	0.933947	−	0.357410i	$-0.116340\pi$
$908$	6.62464	−	9.11803i	0.219846	−	0.302593i
$909$	−2.04508	+	6.29412i	−0.0678312	+	0.208763i
$910$		0			0
$911$	−1.29180	−	3.97574i	−0.0427991	−	0.131722i	0.927374	−	0.374136i	$-0.122061\pi$
$911$	−1.29180	−	3.97574i	−0.0427991	−	0.131722i	−0.970173	+	0.242414i	$0.922061\pi$
$912$	7.33094	+	2.38197i	0.242752	+	0.0788748i
$913$	11.6372	+	3.78115i	0.385135	+	0.125138i
$914$	−2.19098	−	6.74315i	−0.0724713	−	0.223044i
$915$		0			0
$916$	−4.47214	+	13.7638i	−0.147764	+	0.454769i
$917$	−4.01623	+	5.52786i	−0.132628	+	0.182546i
$918$			3.23607i			0.106806i
$919$	39.4164	+	28.6377i	1.30023	+	0.944670i	0.999958	−	0.00918396i	$-0.00292339\pi$
$919$	39.4164	+	28.6377i	1.30023	+	0.944670i	0.300269	+	0.953854i	$0.402923\pi$
$920$		0			0
$921$	8.09017	−	5.87785i	0.266580	−	0.193682i
$922$	−7.38394	−	10.1631i	−0.243177	−	0.334704i
$923$	−34.0260	+	11.0557i	−1.11998	+	0.363904i
$924$	0.527864			0.0173655
$925$		0			0
$926$	30.8328			1.01323
$927$	−1.26133	+	0.409830i	−0.0414274	+	0.0134606i
$928$	0.277515	+	0.381966i	0.00910986	+	0.0125386i
$929$	46.1246	−	33.5115i	1.51330	−	1.09948i	0.548613	−	0.836077i	$-0.315156\pi$
$929$	46.1246	−	33.5115i	1.51330	−	1.09948i	0.964687	−	0.263400i	$-0.0848438\pi$
$930$		0			0
$931$	42.7426	+	31.0543i	1.40083	+	1.01777i
$932$			12.6525i			0.414446i
$933$	11.1352	−	15.3262i	0.364549	−	0.501759i
$934$	−8.13525	+	25.0377i	−0.266194	+	0.819260i
$935$		0			0
$936$	0.763932	+	2.35114i	0.0249699	+	0.0768494i
$937$	−49.1572	−	15.9721i	−1.60590	−	0.521787i	−0.637339	−	0.770583i	$-0.719965\pi$
$937$	−49.1572	−	15.9721i	−1.60590	−	0.521787i	−0.968556	+	0.248796i	$0.919965\pi$
$938$	−3.80423	−	1.23607i	−0.124212	−	0.0403591i
$939$	5.33688	+	16.4252i	0.174163	+	0.536017i
$940$		0			0
$941$	−7.59017	+	23.3601i	−0.247432	+	0.761519i	0.747794	+	0.663930i	$0.231113\pi$
$941$	−7.59017	+	23.3601i	−0.247432	+	0.761519i	−0.995227	+	0.0975885i	$0.968887\pi$
$942$	−13.3148	+	18.3262i	−0.433819	+	0.597101i
$943$			34.4721i			1.12257i
$944$	−1.11803	−	0.812299i	−0.0363889	−	0.0264381i
$945$		0			0
$946$	−6.38197	+	4.63677i	−0.207496	+	0.150754i
$947$	−7.89848	−	10.8713i	−0.256666	−	0.353271i	0.661166	−	0.750240i	$-0.270062\pi$
$947$	−7.89848	−	10.8713i	−0.256666	−	0.353271i	−0.917832	+	0.396969i	$0.870062\pi$
$948$	−3.21644	+	1.04508i	−0.104465	+	0.0339428i
$949$	−30.8328			−1.00088
$950$		0			0
$951$	0.437694			0.0141932
$952$	−1.17557	+	0.381966i	−0.0381005	+	0.0123796i
$953$	33.6830	+	46.3607i	1.09110	+	1.50177i	0.846682	+	0.532100i	$0.178597\pi$
$953$	33.6830	+	46.3607i	1.09110	+	1.50177i	0.244418	+	0.969670i	$0.421403\pi$
$954$	7.35410	−	5.34307i	0.238098	−	0.172988i
$955$		0			0
$956$	−20.7984	−	15.1109i	−0.672667	−	0.488722i
$957$		−	0.652476i		−	0.0210915i
$958$	6.53888	−	9.00000i	0.211262	−	0.290777i
$959$	−1.20163	+	3.69822i	−0.0388025	+	0.119422i
$960$		0			0
$961$	−3.64590	−	11.2209i	−0.117610	−	0.361965i
$962$	−18.8091	−	6.11146i	−0.606431	−	0.197041i
$963$	−8.92278	−	2.89919i	−0.287533	−	0.0934250i
$964$	3.26393	+	10.0453i	0.105124	+	0.323539i
$965$		0			0
$966$	0.527864	−	1.62460i	0.0169837	−	0.0522706i
$967$	−12.9843	+	17.8713i	−0.417546	+	0.574703i	−0.965039	−	0.262108i	$-0.915582\pi$
$967$	−12.9843	+	17.8713i	−0.417546	+	0.574703i	0.547492	+	0.836811i	$0.315582\pi$
$968$		−	9.09017i		−	0.292169i
$969$	20.1803	+	14.6619i	0.648286	+	0.471007i
$970$		0			0
$971$	−30.1074	+	21.8743i	−0.966192	+	0.701980i	−0.954581	−	0.297953i	$-0.903696\pi$
$971$	−30.1074	+	21.8743i	−0.966192	+	0.701980i	−0.0116116	+	0.999933i	$0.503696\pi$
$972$	−0.587785	−	0.809017i	−0.0188532	−	0.0259492i
$973$	−0.555029	+	0.180340i	−0.0177934	+	0.00578143i
$974$	6.79837			0.217834
$975$		0			0
$976$	7.23607			0.231621
$977$	−4.97980	+	1.61803i	−0.159318	+	0.0517655i	−0.387590	−	0.921832i	$-0.626692\pi$
$977$	−4.97980	+	1.61803i	−0.159318	+	0.0517655i	0.228272	+	0.973597i	$0.426692\pi$
$978$	4.97980	+	6.85410i	0.159236	+	0.219170i
$979$	13.9443	−	10.1311i	0.445661	−	0.323792i
$980$		0			0
$981$	−10.3262	−	7.50245i	−0.329691	−	0.239535i
$982$		−	8.27051i		−	0.263923i
$983$	10.4741	−	14.4164i	0.334073	−	0.459812i	−0.608626	−	0.793458i	$-0.708279\pi$
$983$	10.4741	−	14.4164i	0.334073	−	0.459812i	0.942699	+	0.333646i	$0.108279\pi$
$984$	−2.38197	+	7.33094i	−0.0759343	+	0.233702i
$985$		0			0
$986$	0.472136	+	1.45309i	0.0150359	+	0.0462757i
$987$	−4.25325	−	1.38197i	−0.135383	−	0.0439885i
$988$	18.1231	+	5.88854i	0.576572	+	0.187340i
$989$	7.88854	+	24.2784i	0.250841	+	0.772010i
$990$		0			0
$991$	−8.17376	+	25.1563i	−0.259648	+	0.799115i	0.733230	+	0.679981i	$0.238012\pi$
$991$	−8.17376	+	25.1563i	−0.259648	+	0.799115i	−0.992878	+	0.119134i	$0.961988\pi$
$992$	−2.57565	+	3.54508i	−0.0817771	+	0.112557i
$993$			18.0000i			0.571213i
$994$	4.47214	+	3.24920i	0.141848	+	0.103058i
$995$		0			0
$996$	7.16312	−	5.20431i	0.226972	−	0.164905i
$997$	25.6255	+	35.2705i	0.811569	+	1.11703i	0.991079	+	0.133272i	$0.0425485\pi$
$997$	25.6255	+	35.2705i	0.811569	+	1.11703i	−0.179511	+	0.983756i	$0.557452\pi$
$998$	12.9313	−	4.20163i	0.409332	−	0.133000i
$999$	8.00000			0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.h.b.349.2		8
5.2	odd	4		150.2.g.a.31.1	✓	4
5.3	odd	4		750.2.g.b.151.1		4
5.4	even	2	inner	750.2.h.b.349.1		8
15.2	even	4		450.2.h.c.181.1		4
25.2	odd	20		3750.2.a.f.1.1		2
25.3	odd	20		750.2.g.b.601.1		4
25.4	even	10	inner	750.2.h.b.649.2		8
25.11	even	5		3750.2.c.b.1249.2		4
25.14	even	10		3750.2.c.b.1249.3		4
25.21	even	5	inner	750.2.h.b.649.1		8
25.22	odd	20		150.2.g.a.121.1	yes	4
25.23	odd	20		3750.2.a.d.1.2		2
75.47	even	20		450.2.h.c.271.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.31.1	✓	4	5.2	odd	4
150.2.g.a.121.1	yes	4	25.22	odd	20
450.2.h.c.181.1		4	15.2	even	4
450.2.h.c.271.1		4	75.47	even	20
750.2.g.b.151.1		4	5.3	odd	4
750.2.g.b.601.1		4	25.3	odd	20
750.2.h.b.349.1		8	5.4	even	2	inner
750.2.h.b.349.2		8	1.1	even	1	trivial
750.2.h.b.649.1		8	25.21	even	5	inner
750.2.h.b.649.2		8	25.4	even	10	inner
3750.2.a.d.1.2		2	25.23	odd	20
3750.2.a.f.1.1		2	25.2	odd	20
3750.2.c.b.1249.2		4	25.11	even	5
3750.2.c.b.1249.3		4	25.14	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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} -0.381966i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} -0.381966i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(0.427051 + 1.31433i) q^{11} +(0.951057 + 0.309017i) q^{12} +(2.35114 + 0.763932i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(0.309017 - 0.951057i) q^{16} +(1.90211 - 2.61803i) q^{17} +1.00000i q^{18} +(6.23607 + 4.53077i) q^{19} +(0.309017 - 0.224514i) q^{21} +(0.812299 + 1.11803i) q^{22} +(4.25325 - 1.38197i) q^{23} +1.00000 q^{24} +2.47214 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.224514 - 0.309017i) q^{28} +(-0.381966 + 0.277515i) q^{29} +(-3.54508 - 2.57565i) q^{31} -1.00000i q^{32} +(-0.812299 + 1.11803i) q^{33} +(1.00000 - 3.07768i) q^{34} +(0.309017 + 0.951057i) q^{36} +(-7.60845 - 2.47214i) q^{37} +(7.33094 + 2.38197i) q^{38} +(0.763932 + 2.35114i) q^{39} +(-2.38197 + 7.33094i) q^{41} +(0.224514 - 0.309017i) q^{42} +5.70820i q^{43} +(1.11803 + 0.812299i) q^{44} +(3.61803 - 2.62866i) q^{46} +(-6.88191 - 9.47214i) q^{47} +(0.951057 - 0.309017i) q^{48} +6.85410 q^{49} +3.23607 q^{51} +(2.35114 - 0.763932i) q^{52} +(-5.34307 - 7.35410i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.309017 - 0.224514i) q^{56} +7.70820i q^{57} +(-0.277515 + 0.381966i) q^{58} +(0.427051 - 1.31433i) q^{59} +(2.23607 + 6.88191i) q^{61} +(-4.16750 - 1.35410i) q^{62} +(0.363271 + 0.118034i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.427051 + 1.31433i) q^{66} +(6.15537 - 8.47214i) q^{67} -3.23607i q^{68} +(3.61803 + 2.62866i) q^{69} +(-11.7082 + 8.50651i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-11.8617 + 3.85410i) q^{73} -8.00000 q^{74} +7.70820 q^{76} +(0.502029 - 0.163119i) q^{77} +(1.45309 + 2.00000i) q^{78} +(-2.73607 + 1.98787i) q^{79} +(-0.809017 - 0.587785i) q^{81} +7.70820i q^{82} +(5.20431 - 7.16312i) q^{83} +(0.118034 - 0.363271i) q^{84} +(1.76393 + 5.42882i) q^{86} +(-0.449028 - 0.145898i) q^{87} +(1.31433 + 0.427051i) q^{88} +(-3.85410 - 11.8617i) q^{89} +(0.291796 - 0.898056i) q^{91} +(2.62866 - 3.61803i) q^{92} -4.38197i q^{93} +(-9.47214 - 6.88191i) q^{94} +(0.809017 - 0.587785i) q^{96} +(-3.30220 - 4.54508i) q^{97} +(6.51864 - 2.11803i) q^{98} -1.38197 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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