LMFDB - Embedded newform 400.2.l.f.301.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(101,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("400.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			301.4
Root			$0.618969 - 1.27156i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.f.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618969 + 1.27156i) q^{2} +(-2.16859 - 2.16859i) q^{3} +(-1.23375 - 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519i q^{7} +(2.76525 - 0.594467i) q^{8} +6.40553i q^{9} +O(q^{10})$	\(q+(-0.618969 + 1.27156i) q^{2} +(-2.16859 - 2.16859i) q^{3} +(-1.23375 - 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519i q^{7} +(2.76525 - 0.594467i) q^{8} +6.40553i q^{9} +(2.01163 - 2.01163i) q^{11} +(-0.738111 + 6.08911i) q^{12} +(-0.794042 - 0.794042i) q^{13} +(4.20276 + 2.04581i) q^{14} +(-0.955702 + 3.88415i) q^{16} -4.61575 q^{17} +(-8.14504 - 3.96483i) q^{18} +(-3.48786 - 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +(1.31278 + 3.80306i) q^{22} +7.99801i q^{23} +(-7.28583 - 4.70753i) q^{24} +(1.50116 - 0.518188i) q^{26} +(7.38518 - 7.38518i) q^{27} +(-5.20276 + 4.07779i) q^{28} +(-1.95065 - 1.95065i) q^{29} -5.12695 q^{31} +(-4.34740 - 3.61941i) q^{32} -8.72480 q^{33} +(2.85701 - 5.86922i) q^{34} +(10.0831 - 7.90285i) q^{36} +(-0.448156 + 0.448156i) q^{37} +(6.59391 - 2.27616i) q^{38} +3.44390i q^{39} +4.02230i q^{41} +(-4.67754 - 13.5506i) q^{42} +(-4.97000 + 4.97000i) q^{43} +(-5.64841 - 0.684690i) q^{44} +(-10.1700 - 4.95052i) q^{46} +5.49112 q^{47} +(10.4956 - 6.35059i) q^{48} -3.92429 q^{49} +(10.0096 + 10.0096i) q^{51} +(-0.270264 + 2.22957i) q^{52} +(3.35125 - 3.35125i) q^{53} +(4.81954 + 13.9619i) q^{54} +(-1.96483 - 9.13968i) q^{56} +15.1274i q^{57} +(3.68777 - 1.27299i) q^{58} +(2.07673 - 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} +(3.17343 - 6.51925i) q^{62} +21.1715 q^{63} +(7.29322 - 3.28770i) q^{64} +(5.40038 - 11.0941i) q^{66} +(0.636094 + 0.636094i) q^{67} +(5.69470 + 7.26573i) q^{68} +(17.3444 - 17.3444i) q^{69} -6.85258i q^{71} +(3.80787 + 17.7129i) q^{72} +10.5177i q^{73} +(-0.292465 - 0.847255i) q^{74} +(-1.18714 + 9.79346i) q^{76} +(-6.64883 - 6.64883i) q^{77} +(-4.37914 - 2.13167i) q^{78} -17.3005 q^{79} -12.8142 q^{81} +(-5.11461 - 2.48968i) q^{82} +(-9.48015 - 9.48015i) q^{83} +(20.1257 + 2.43960i) q^{84} +(-3.24340 - 9.39596i) q^{86} +8.46030i q^{87} +(4.36682 - 6.75852i) q^{88} +7.62073i q^{89} +(-2.62446 + 2.62446i) q^{91} +(12.5898 - 9.86757i) q^{92} +(11.1182 + 11.1182i) q^{93} +(-3.39883 + 6.98231i) q^{94} +(1.57871 + 17.2767i) q^{96} -0.709082 q^{97} +(2.42901 - 4.98999i) q^{98} +(12.8856 + 12.8856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8	$ 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8} - 2 q^{11} - 8 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{16} + 8 q^{17} - 18 q^{18} - 14 q^{19} - 20 q^{21} - 2 q^{22} - 14 q^{24} - 16 q^{26} + 10 q^{27} - 26 q^{28} - 4 q^{31} + 16 q^{32} - 28 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} - 10 q^{38} - 10 q^{42} - 44 q^{44} - 10 q^{46} - 8 q^{47} + 28 q^{48} + 4 q^{49} + 10 q^{51} + 12 q^{52} + 16 q^{53} + 10 q^{54} + 6 q^{56} + 60 q^{58} + 20 q^{59} + 4 q^{61} + 18 q^{62} + 8 q^{63} + 38 q^{64} + 32 q^{66} - 50 q^{67} + 60 q^{68} + 14 q^{72} + 10 q^{74} + 60 q^{76} + 8 q^{77} - 4 q^{78} + 12 q^{79} - 8 q^{81} - 42 q^{82} + 2 q^{83} + 34 q^{84} + 6 q^{86} - 30 q^{88} + 2 q^{92} + 44 q^{93} + 32 q^{94} - 34 q^{96} - 64 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8 - 2 * q^11 - 8 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^16 + 8 * q^17 - 18 * q^18 - 14 * q^19 - 20 * q^21 - 2 * q^22 - 14 * q^24 - 16 * q^26 + 10 * q^27 - 26 * q^28 - 4 * q^31 + 16 * q^32 - 28 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 - 10 * q^38 - 10 * q^42 - 44 * q^44 - 10 * q^46 - 8 * q^47 + 28 * q^48 + 4 * q^49 + 10 * q^51 + 12 * q^52 + 16 * q^53 + 10 * q^54 + 6 * q^56 + 60 * q^58 + 20 * q^59 + 4 * q^61 + 18 * q^62 + 8 * q^63 + 38 * q^64 + 32 * q^66 - 50 * q^67 + 60 * q^68 + 14 * q^72 + 10 * q^74 + 60 * q^76 + 8 * q^77 - 4 * q^78 + 12 * q^79 - 8 * q^81 - 42 * q^82 + 2 * q^83 + 34 * q^84 + 6 * q^86 - 30 * q^88 + 2 * q^92 + 44 * q^93 + 32 * q^94 - 34 * q^96 - 64 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.618969	+	1.27156i	−0.437677	+	0.899132i
$2$	−0.618969	+	1.27156i	−0.437677	+	0.899132i
$3$	−2.16859	−	2.16859i	−1.25203	−	1.25203i	−0.954807	−	0.297227i	$-0.903938\pi$
$3$	−2.16859	−	2.16859i	−1.25203	−	1.25203i	−0.297227	−	0.954807i	$-0.596062\pi$
$4$	−1.23375	−	1.57412i	−0.616877	−	0.787060i
$5$		0			0
$5$		0			0
$6$	4.09979	−	1.41521i	1.67373	−	0.577757i
$7$		−	3.30519i		−	1.24924i	−0.780927	−	0.624622i	$-0.785253\pi$
$7$		−	3.30519i		−	1.24924i	0.780927	−	0.624622i	$-0.214747\pi$
$8$	2.76525	−	0.594467i	0.977664	−	0.210176i
$9$			6.40553i			2.13518i
$10$		0			0
$11$	2.01163	−	2.01163i	0.606530	−	0.606530i	−0.335507	−	0.942038i	$-0.608908\pi$
$11$	2.01163	−	2.01163i	0.606530	−	0.606530i	0.942038	+	0.335507i	$0.108908\pi$
$12$	−0.738111	+	6.08911i	−0.213074	+	1.75778i
$13$	−0.794042	−	0.794042i	−0.220228	−	0.220228i	0.588367	−	0.808594i	$-0.299771\pi$
$13$	−0.794042	−	0.794042i	−0.220228	−	0.220228i	−0.808594	+	0.588367i	$0.799771\pi$
$14$	4.20276	+	2.04581i	1.12324	+	0.546766i
$15$		0			0
$16$	−0.955702	+	3.88415i	−0.238926	+	0.971038i
$17$	−4.61575			−1.11948			−0.559741	−	0.828667i	$-0.689100\pi$
$17$	−4.61575			−1.11948			−0.559741	+	0.828667i	$0.689100\pi$
$18$	−8.14504	−	3.96483i	−1.91981	−	0.934518i
$19$	−3.48786	−	3.48786i	−0.800169	−	0.800169i	0.182953	−	0.983122i	$-0.441434\pi$
$19$	−3.48786	−	3.48786i	−0.800169	−	0.800169i	−0.983122	+	0.182953i	$0.941434\pi$
$20$		0			0
$21$	−7.16759	+	7.16759i	−1.56410	+	1.56410i
$22$	1.31278	+	3.80306i	0.279886	+	0.810815i
$23$			7.99801i			1.66770i	0.551991	+	0.833850i	$0.313868\pi$
$23$			7.99801i			1.66770i	−0.551991	+	0.833850i	$0.686132\pi$
$24$	−7.28583	−	4.70753i	−1.48721	−	0.960921i
$25$		0			0
$26$	1.50116	−	0.518188i	0.294402	−	0.101625i
$27$	7.38518	−	7.38518i	1.42128	−	1.42128i
$28$	−5.20276	+	4.07779i	−0.983230	+	0.770630i
$29$	−1.95065	−	1.95065i	−0.362227	−	0.362227i	0.502406	−	0.864632i	$-0.332448\pi$
$29$	−1.95065	−	1.95065i	−0.362227	−	0.362227i	−0.864632	+	0.502406i	$0.832448\pi$
$30$		0			0
$31$	−5.12695			−0.920828			−0.460414	−	0.887704i	$-0.652299\pi$
$31$	−5.12695			−0.920828			−0.460414	+	0.887704i	$0.652299\pi$
$32$	−4.34740	−	3.61941i	−0.768519	−	0.639827i
$33$	−8.72480			−1.51879
$34$	2.85701	−	5.86922i	0.489972	−	1.00656i
$35$		0			0
$36$	10.0831	−	7.90285i	1.68051	−	1.31714i
$37$	−0.448156	+	0.448156i	−0.0736764	+	0.0736764i	−0.742985	−	0.669308i	$-0.766591\pi$
$37$	−0.448156	+	0.448156i	−0.0736764	+	0.0736764i	0.669308	+	0.742985i	$0.266591\pi$
$38$	6.59391	−	2.27616i	1.06967	−	0.369242i
$39$			3.44390i			0.551465i
$40$		0			0
$41$			4.02230i			0.628177i	0.949394	+	0.314089i	$0.101699\pi$
$41$			4.02230i			0.628177i	−0.949394	+	0.314089i	$0.898301\pi$
$42$	−4.67754	−	13.5506i	−0.721760	−	2.09090i
$43$	−4.97000	+	4.97000i	−0.757918	+	0.757918i	−0.975943	−	0.218025i	$-0.930039\pi$
$43$	−4.97000	+	4.97000i	−0.757918	+	0.757918i	0.218025	+	0.975943i	$0.430039\pi$
$44$	−5.64841	−	0.684690i	−0.851530	−	0.103221i
$45$		0			0
$46$	−10.1700	−	4.95052i	−1.49948	−	0.729915i
$47$	5.49112			0.800962			0.400481	−	0.916305i	$-0.368843\pi$
$47$	5.49112			0.800962			0.400481	+	0.916305i	$0.368843\pi$
$48$	10.4956	−	6.35059i	1.51491	−	0.916629i
$49$	−3.92429			−0.560612
$50$		0			0
$51$	10.0096	+	10.0096i	1.40163	+	1.40163i
$52$	−0.270264	+	2.22957i	−0.0374789	+	0.309186i
$53$	3.35125	−	3.35125i	0.460330	−	0.460330i	−0.438434	−	0.898763i	$-0.644467\pi$
$53$	3.35125	−	3.35125i	0.460330	−	0.460330i	0.898763	+	0.438434i	$0.144467\pi$
$54$	4.81954	+	13.9619i	0.655856	+	1.89998i
$55$		0			0
$56$	−1.96483	−	9.13968i	−0.262561	−	1.22134i
$57$			15.1274i			2.00368i
$58$	3.68777	−	1.27299i	0.484228	−	0.167151i
$59$	2.07673	−	2.07673i	0.270367	−	0.270367i	−0.558881	−	0.829248i	$-0.688769\pi$
$59$	2.07673	−	2.07673i	0.270367	−	0.270367i	0.829248	+	0.558881i	$0.188769\pi$
$60$		0			0
$61$	−0.557208	−	0.557208i	−0.0713432	−	0.0713432i	0.670535	−	0.741878i	$-0.266065\pi$
$61$	−0.557208	−	0.557208i	−0.0713432	−	0.0713432i	−0.741878	+	0.670535i	$0.766065\pi$
$62$	3.17343	−	6.51925i	0.403026	−	0.827946i
$63$	21.1715			2.66736
$64$	7.29322	−	3.28770i	0.911652	−	0.410962i
$65$		0			0
$66$	5.40038	−	11.0941i	0.664741	−	1.36560i
$67$	0.636094	+	0.636094i	0.0777112	+	0.0777112i	0.744894	−	0.667183i	$-0.232500\pi$
$67$	0.636094	+	0.636094i	0.0777112	+	0.0777112i	−0.667183	+	0.744894i	$0.732500\pi$
$68$	5.69470	+	7.26573i	0.690583	+	0.881100i
$69$	17.3444	−	17.3444i	2.08802	−	2.08802i
$70$		0			0
$71$		−	6.85258i		−	0.813252i	−0.913595	−	0.406626i	$-0.866705\pi$
$71$		−	6.85258i		−	0.813252i	0.913595	−	0.406626i	$-0.133295\pi$
$72$	3.80787	+	17.7129i	0.448762	+	2.08748i
$73$			10.5177i			1.23101i	0.788134	+	0.615504i	$0.211047\pi$
$73$			10.5177i			1.23101i	−0.788134	+	0.615504i	$0.788953\pi$
$74$	−0.292465	−	0.847255i	−0.0339983	−	0.0984913i
$75$		0			0
$76$	−1.18714	+	9.79346i	−0.136175	+	1.12339i
$77$	−6.64883	−	6.64883i	−0.757705	−	0.757705i
$78$	−4.37914	−	2.13167i	−0.495840	−	0.241364i
$79$	−17.3005			−1.94646			−0.973230	−	0.229833i	$-0.926182\pi$
$79$	−17.3005			−1.94646			−0.973230	+	0.229833i	$0.926182\pi$
$80$		0			0
$81$	−12.8142			−1.42380
$82$	−5.11461	−	2.48968i	−0.564814	−	0.274939i
$83$	−9.48015	−	9.48015i	−1.04058	−	1.04058i	−0.999141	−	0.0414412i	$-0.986805\pi$
$83$	−9.48015	−	9.48015i	−1.04058	−	1.04058i	−0.0414412	−	0.999141i	$-0.513195\pi$
$84$	20.1257	+	2.43960i	2.19589	+	0.266182i
$85$		0			0
$86$	−3.24340	−	9.39596i	−0.349745	−	1.01319i
$87$			8.46030i			0.907040i
$88$	4.36682	−	6.75852i	0.465505	−	0.720460i
$89$			7.62073i			0.807796i	0.914804	+	0.403898i	$0.132345\pi$
$89$			7.62073i			0.807796i	−0.914804	+	0.403898i	$0.867655\pi$
$90$		0			0
$91$	−2.62446	+	2.62446i	−0.275118	+	0.275118i
$92$	12.5898	−	9.86757i	1.31258	−	1.02877i
$93$	11.1182	+	11.1182i	1.15291	+	1.15291i
$94$	−3.39883	+	6.98231i	−0.350563	+	0.720171i
$95$		0			0
$96$	1.57871	+	17.2767i	0.161127	+	1.76330i
$97$	−0.709082			−0.0719964			−0.0359982	−	0.999352i	$-0.511461\pi$
$97$	−0.709082			−0.0719964			−0.0359982	+	0.999352i	$0.511461\pi$
$98$	2.42901	−	4.98999i	0.245367	−	0.504065i
$99$	12.8856	+	12.8856i	1.29505	+	1.29505i
$100$		0			0
$101$	6.16223	−	6.16223i	0.613164	−	0.613164i	−0.330605	−	0.943769i	$-0.607253\pi$
$101$	6.16223	−	6.16223i	0.613164	−	0.613164i	0.943769	+	0.330605i	$0.107253\pi$
$102$	−18.9236	+	6.53225i	−1.87371	+	0.646789i
$103$		−	15.9410i		−	1.57072i	−0.619040	−	0.785359i	$-0.712478\pi$
$103$		−	15.9410i		−	1.57072i	0.619040	−	0.785359i	$-0.287522\pi$
$104$	−2.66776	−	1.72369i	−0.261595	−	0.169022i
$105$		0			0
$106$	2.18701	+	6.33565i	0.212421	+	0.615373i
$107$	3.38717	−	3.38717i	0.327450	−	0.327450i	−0.524166	−	0.851616i	$-0.675623\pi$
$107$	3.38717	−	3.38717i	0.327450	−	0.327450i	0.851616	+	0.524166i	$0.175623\pi$
$108$	−20.7367	−	2.51366i	−1.99539	−	0.241877i
$109$	−2.43964	−	2.43964i	−0.233675	−	0.233675i	0.580550	−	0.814225i	$-0.302838\pi$
$109$	−2.43964	−	2.43964i	−0.233675	−	0.233675i	−0.814225	+	0.580550i	$0.802838\pi$
$110$		0			0
$111$	1.94373			0.184491
$112$	12.8379	+	3.15878i	1.21306	+	0.298477i
$113$	−1.09801			−0.103292			−0.0516461	−	0.998665i	$-0.516447\pi$
$113$	−1.09801			−0.103292			−0.0516461	+	0.998665i	$0.516447\pi$
$114$	−19.2355	−	9.36341i	−1.80157	−	0.876964i
$115$		0			0
$116$	−0.663933	+	5.47718i	−0.0616447	+	0.508543i
$117$	5.08626	−	5.08626i	0.470225	−	0.470225i
$118$	1.35526	+	3.92612i	0.124762	+	0.361429i
$119$			15.2559i			1.39851i
$120$		0			0
$121$			2.90666i			0.264242i
$122$	1.05342	−	0.363632i	0.0953723	−	0.0329217i
$123$	8.72270	−	8.72270i	0.786499	−	0.786499i
$124$	6.32540	+	8.07044i	0.568038	+	0.724747i
$125$		0			0
$126$	−13.1045	+	26.9209i	−1.16744	+	2.39831i
$127$	1.51159			0.134131			0.0670657	−	0.997749i	$-0.478636\pi$
$127$	1.51159			0.134131			0.0670657	+	0.997749i	$0.478636\pi$
$128$	−0.333758	+	11.3088i	−0.0295003	+	0.999565i
$129$	21.5557			1.89788
$130$		0			0
$131$	−9.21660	−	9.21660i	−0.805258	−	0.805258i	0.178654	−	0.983912i	$-0.442826\pi$
$131$	−9.21660	−	9.21660i	−0.805258	−	0.805258i	−0.983912	+	0.178654i	$0.942826\pi$
$132$	10.7643	+	13.7339i	0.936908	+	1.19538i
$133$	−11.5280	+	11.5280i	−0.999607	+	0.999607i
$134$	−1.20256	+	0.415112i	−0.103885	+	0.0358602i
$135$		0			0
$136$	−12.7637	+	2.74391i	−1.09448	+	0.235288i
$137$		−	3.38639i		−	0.289318i	−0.989482	−	0.144659i	$-0.953791\pi$
$137$		−	3.38639i		−	0.289318i	0.989482	−	0.144659i	$-0.0462086\pi$
$138$	11.3189	+	32.7901i	0.963525	+	2.79128i
$139$	−2.09626	+	2.09626i	−0.177802	+	0.177802i	−0.790397	−	0.612595i	$-0.790126\pi$
$139$	−2.09626	+	2.09626i	−0.177802	+	0.177802i	0.612595	+	0.790397i	$0.290126\pi$
$140$		0			0
$141$	−11.9080	−	11.9080i	−1.00283	−	1.00283i
$142$	8.71350	+	4.24154i	0.731221	+	0.355942i
$143$	−3.19464			−0.267149
$144$	−24.8800	−	6.12178i	−2.07334	−	0.510148i
$145$		0			0
$146$	−13.3740	−	6.51016i	−1.10684	−	0.538784i
$147$	8.51015	+	8.51015i	0.701906	+	0.701906i
$148$	1.25837	+	0.152537i	0.103437	+	0.0125384i
$149$	−2.45247	+	2.45247i	−0.200915	+	0.200915i	−0.800392	−	0.599477i	$-0.795375\pi$
$149$	−2.45247	+	2.45247i	−0.200915	+	0.200915i	0.599477	+	0.800392i	$0.295375\pi$
$150$		0			0
$151$		−	1.11727i		−	0.0909222i	−0.998966	−	0.0454611i	$-0.985524\pi$
$151$		−	1.11727i		−	0.0909222i	0.998966	−	0.0454611i	$-0.0144757\pi$
$152$	−11.7182	−	7.57138i	−0.950472	−	0.614120i
$153$		−	29.5663i		−	2.39029i
$154$	12.5698	−	4.33900i	1.01291	−	0.349646i
$155$		0			0
$156$	5.42110	−	4.24892i	0.434036	−	0.340186i
$157$	−15.8377	−	15.8377i	−1.26398	−	1.26398i	−0.949145	−	0.314839i	$-0.898050\pi$
$157$	−15.8377	−	15.8377i	−1.26398	−	1.26398i	−0.314839	−	0.949145i	$-0.601950\pi$
$158$	10.7085	−	21.9987i	0.851922	−	1.75012i
$159$	−14.5349			−1.15270
$160$		0			0
$161$	26.4349			2.08337
$162$	7.93160	−	16.2941i	0.623166	−	1.28019i
$163$	7.22102	+	7.22102i	0.565594	+	0.565594i	0.930891	−	0.365297i	$-0.119033\pi$
$163$	7.22102	+	7.22102i	0.565594	+	0.565594i	−0.365297	+	0.930891i	$0.619033\pi$
$164$	6.33158	−	4.96253i	0.494413	−	0.387508i
$165$		0			0
$166$	17.9226	−	6.18671i	1.39106	−	0.480182i
$167$		−	13.2304i		−	1.02380i	−0.859044	−	0.511901i	$-0.828941\pi$
$167$		−	13.2304i		−	1.02380i	0.859044	−	0.511901i	$-0.171059\pi$
$168$	−15.5593	+	24.0811i	−1.20043	+	1.85790i
$169$		−	11.7390i		−	0.903000i
$170$		0			0
$171$	22.3416	−	22.3416i	1.70850	−	1.70850i
$172$	13.9551	+	1.69162i	1.06407	+	0.128984i
$173$	−11.7503	−	11.7503i	−0.893355	−	0.893355i	0.101482	−	0.994837i	$-0.467641\pi$
$173$	−11.7503	−	11.7503i	−0.893355	−	0.893355i	−0.994837	+	0.101482i	$0.967641\pi$
$174$	−10.7578	−	5.23667i	−0.815548	−	0.396991i
$175$		0			0
$176$	5.89097	+	9.73601i	0.444048	+	0.733879i
$177$	−9.00712			−0.677017
$178$	−9.69026	−	4.71700i	−0.726315	−	0.353554i
$179$	4.84732	+	4.84732i	0.362306	+	0.362306i	0.864661	−	0.502355i	$-0.167533\pi$
$179$	4.84732	+	4.84732i	0.362306	+	0.362306i	−0.502355	+	0.864661i	$0.667533\pi$
$180$		0			0
$181$	10.5742	−	10.5742i	0.785976	−	0.785976i	−0.194856	−	0.980832i	$-0.562424\pi$
$181$	10.5742	−	10.5742i	0.785976	−	0.785976i	0.980832	+	0.194856i	$0.0624240\pi$
$182$	−1.71271	−	4.96163i	−0.126955	−	0.367781i
$183$			2.41671i			0.178648i
$184$	4.75455	+	22.1165i	0.350510	+	1.63045i
$185$		0			0
$186$	−21.0194	+	7.25571i	−1.54122	+	0.532015i
$187$	−9.28519	+	9.28519i	−0.679000	+	0.679000i
$188$	−6.77469	−	8.64368i	−0.494095	−	0.630405i
$189$	−24.4094	−	24.4094i	−1.77553	−	1.77553i
$190$		0			0
$191$	7.94268			0.574712			0.287356	−	0.957824i	$-0.407224\pi$
$191$	7.94268			0.574712			0.287356	+	0.957824i	$0.407224\pi$
$192$	−22.9456	−	8.68632i	−1.65596	−	0.626881i
$193$	20.8617			1.50166			0.750829	−	0.660496i	$-0.229654\pi$
$193$	20.8617			1.50166			0.750829	+	0.660496i	$0.229654\pi$
$194$	0.438900	−	0.901644i	0.0315112	−	0.0647343i
$195$		0			0
$196$	4.84160	+	6.17730i	0.345829	+	0.441235i
$197$	−2.07707	+	2.07707i	−0.147985	+	0.147985i	−0.777217	−	0.629232i	$-0.783369\pi$
$197$	−2.07707	+	2.07707i	−0.147985	+	0.147985i	0.629232	+	0.777217i	$0.283369\pi$
$198$	−24.3606	+	8.40907i	−1.73123	+	0.597606i
$199$		−	23.2807i		−	1.65033i	−0.564893	−	0.825164i	$-0.691083\pi$
$199$		−	23.2807i		−	1.65033i	0.564893	−	0.825164i	$-0.308917\pi$
$200$		0			0
$201$		−	2.75885i		−	0.194594i
$202$	4.02144	+	11.6499i	0.282948	+	0.819684i
$203$	−6.44727	+	6.44727i	−0.452510	+	0.452510i
$204$	3.40693	−	28.1058i	0.238533	−	1.96780i
$205$		0			0
$206$	20.2701	+	9.86702i	1.41228	+	0.687468i
$207$	−51.2315			−3.56083
$208$	3.84305	−	2.32531i	0.266467	−	0.161231i
$209$	−14.0326			−0.970653
$210$		0			0
$211$	−2.51586	−	2.51586i	−0.173199	−	0.173199i	0.615184	−	0.788383i	$-0.289082\pi$
$211$	−2.51586	−	2.51586i	−0.173199	−	0.173199i	−0.788383	+	0.615184i	$0.789082\pi$
$212$	−9.40989	−	1.14065i	−0.646274	−	0.0783401i
$213$	−14.8604	+	14.8604i	−1.01822	+	1.01822i
$214$	2.21045	+	6.40357i	0.151103	+	0.437739i
$215$		0			0
$216$	16.0316	−	24.8121i	1.09081	−	1.68825i
$217$			16.9456i			1.15034i
$218$	4.61222	−	1.59210i	0.312379	−	0.107830i
$219$	22.8086	−	22.8086i	1.54126	−	1.54126i
$220$		0			0
$221$	3.66510	+	3.66510i	0.246541	+	0.246541i
$222$	−1.20311	+	2.47158i	−0.0807474	+	0.165882i
$223$	−10.9088			−0.730507			−0.365253	−	0.930908i	$-0.619018\pi$
$223$	−10.9088			−0.730507			−0.365253	+	0.930908i	$0.619018\pi$
$224$	−11.9628	+	14.3690i	−0.799300	+	0.960068i
$225$		0			0
$226$	0.679635	−	1.39619i	0.0452086	−	0.0928733i
$227$	11.6347	+	11.6347i	0.772220	+	0.772220i	0.978494	−	0.206275i	$-0.0661340\pi$
$227$	11.6347	+	11.6347i	0.772220	+	0.772220i	−0.206275	+	0.978494i	$0.566134\pi$
$228$	23.8124	−	18.6635i	1.57701	−	1.23602i
$229$	−1.60760	+	1.60760i	−0.106233	+	0.106233i	−0.758226	−	0.651992i	$-0.773933\pi$
$229$	−1.60760	+	1.60760i	−0.106233	+	0.106233i	0.651992	+	0.758226i	$0.273933\pi$
$230$		0			0
$231$			28.8371i			1.89734i
$232$	−6.55363	−	4.23444i	−0.430267	−	0.278005i
$233$		−	23.8100i		−	1.55985i	−0.625875	−	0.779924i	$-0.715258\pi$
$233$		−	23.8100i		−	1.55985i	0.625875	−	0.779924i	$-0.284742\pi$
$234$	3.31927	+	9.61575i	0.216987	+	0.628601i
$235$		0			0
$236$	−5.83118	−	0.706845i	−0.379578	−	0.0460117i
$237$	37.5177	+	37.5177i	2.43703	+	2.43703i
$238$	−19.3989	−	9.44295i	−1.25744	−	0.612095i
$239$	−0.199630			−0.0129130			−0.00645649	−	0.999979i	$-0.502055\pi$
$239$	−0.199630			−0.0129130			−0.00645649	+	0.999979i	$0.502055\pi$
$240$		0			0
$241$	−16.8755			−1.08705			−0.543525	−	0.839393i	$-0.682911\pi$
$241$	−16.8755			−1.08705			−0.543525	+	0.839393i	$0.682911\pi$
$242$	−3.69601	−	1.79914i	−0.237589	−	0.115653i
$243$	5.63317	+	5.63317i	0.361368	+	0.361368i
$244$	−0.189654	+	1.56457i	−0.0121414	+	0.100161i
$245$		0			0
$246$	5.69239	+	16.4906i	0.362934	+	1.05140i
$247$			5.53901i			0.352439i
$248$	−14.1773	+	3.04780i	−0.900260	+	0.193536i
$249$			41.1171i			2.60569i
$250$		0			0
$251$	−6.10023	+	6.10023i	−0.385043	+	0.385043i	−0.872915	−	0.487872i	$-0.837773\pi$
$251$	−6.10023	+	6.10023i	−0.385043	+	0.385043i	0.487872	+	0.872915i	$0.337773\pi$
$252$	−26.1204	−	33.3265i	−1.64543	−	2.09937i
$253$	16.0891	+	16.0891i	1.01151	+	1.01151i
$254$	−0.935625	+	1.92208i	−0.0587063	+	0.120602i
$255$		0			0
$256$	−14.1733	−	7.42418i	−0.885829	−	0.464012i
$257$	19.8360			1.23733			0.618667	−	0.785653i	$-0.287673\pi$
$257$	19.8360			1.23733			0.618667	+	0.785653i	$0.287673\pi$
$258$	−13.3423	+	27.4095i	−0.830658	+	1.70644i
$259$	1.48124	+	1.48124i	0.0920399	+	0.0920399i
$260$		0			0
$261$	12.4949	−	12.4949i	0.773418	−	0.773418i
$262$	17.4243	−	6.01471i	1.07648	−	0.371590i
$263$		−	7.14438i		−	0.440542i	−0.975439	−	0.220271i	$-0.929306\pi$
$263$		−	7.14438i		−	0.440542i	0.975439	−	0.220271i	$-0.0706941\pi$
$264$	−24.1263	+	5.18660i	−1.48487	+	0.319213i
$265$		0			0
$266$	−7.52314	−	21.7941i	−0.461273	−	1.33628i
$267$	16.5262	−	16.5262i	1.01139	−	1.01139i
$268$	0.216504	−	1.78607i	0.0132251	−	0.109102i
$269$	21.7716	+	21.7716i	1.32744	+	1.32744i	0.907596	+	0.419844i	$0.137915\pi$
$269$	21.7716	+	21.7716i	1.32744	+	1.32744i	0.419844	+	0.907596i	$0.362085\pi$
$270$		0			0
$271$	−4.71328			−0.286312			−0.143156	−	0.989700i	$-0.545725\pi$
$271$	−4.71328			−0.286312			−0.143156	+	0.989700i	$0.545725\pi$
$272$	4.41128	−	17.9283i	0.267473	−	1.08706i
$273$	11.3827			0.688915
$274$	4.30601	+	2.09607i	0.260136	+	0.126628i
$275$		0			0
$276$	−48.7008	−	5.90342i	−2.93144	−	0.355344i
$277$	−20.4588	+	20.4588i	−1.22925	+	1.22925i	−0.265006	+	0.964247i	$0.585374\pi$
$277$	−20.4588	+	20.4588i	−1.22925	+	1.22925i	−0.964247	+	0.265006i	$0.914626\pi$
$278$	−1.36801	−	3.96304i	−0.0820476	−	0.237687i
$279$		−	32.8409i		−	1.96613i
$280$		0			0
$281$			17.6481i			1.05280i	0.850239	+	0.526398i	$0.176458\pi$
$281$			17.6481i			1.05280i	−0.850239	+	0.526398i	$0.823542\pi$
$282$	22.5124	−	7.77108i	1.34059	−	0.462761i
$283$	−18.1525	+	18.1525i	−1.07906	+	1.07906i	−0.0824607	+	0.996594i	$0.526278\pi$
$283$	−18.1525	+	18.1525i	−1.07906	+	1.07906i	−0.996594	+	0.0824607i	$0.973722\pi$
$284$	−10.7868	+	8.45440i	−0.640077	+	0.501676i
$285$		0			0
$286$	1.97739	−	4.06220i	0.116925	−	0.240203i
$287$	13.2945			0.784747
$288$	23.1842	−	27.8474i	1.36614	−	1.64092i
$289$	4.30511			0.253242
$290$		0			0
$291$	1.53771	+	1.53771i	0.0901419	+	0.0901419i
$292$	16.5562	−	12.9763i	0.968877	−	0.759380i
$293$	0.638480	−	0.638480i	0.0373004	−	0.0373004i	−0.688211	−	0.725511i	$-0.741603\pi$
$293$	0.638480	−	0.638480i	0.0373004	−	0.0373004i	0.725511	+	0.688211i	$0.241603\pi$
$294$	−16.0887	+	5.55369i	−0.938314	+	0.323898i
$295$		0			0
$296$	−0.972850	+	1.50568i	−0.0565458	+	0.0875157i
$297$		−	29.7126i		−	1.72410i
$298$	−1.60047	−	4.63649i	−0.0927130	−	0.268584i
$299$	6.35076	−	6.35076i	0.367274	−	0.367274i
$300$		0			0
$301$	16.4268	+	16.4268i	0.946825	+	0.946825i
$302$	1.42068	+	0.691557i	0.0817511	+	0.0397946i
$303$	−26.7266			−1.53540
$304$	16.8807	−	10.2140i	0.968175	−	0.585814i
$305$		0			0
$306$	37.5955	+	18.3006i	2.14919	+	1.04618i
$307$	−4.52224	−	4.52224i	−0.258098	−	0.258098i	0.566182	−	0.824280i	$-0.308420\pi$
$307$	−4.52224	−	4.52224i	−0.258098	−	0.258098i	−0.824280	+	0.566182i	$0.808420\pi$
$308$	−2.26303	+	18.6691i	−0.128948	+	1.06377i
$309$	−34.5695	+	34.5695i	−1.96659	+	1.96659i
$310$		0			0
$311$		−	14.1014i		−	0.799620i	−0.916598	−	0.399810i	$-0.869076\pi$
$311$		−	14.1014i		−	0.799620i	0.916598	−	0.399810i	$-0.130924\pi$
$312$	2.04728	+	9.52324i	0.115904	+	0.539147i
$313$		−	11.9204i		−	0.673779i	−0.941544	−	0.336889i	$-0.890625\pi$
$313$		−	11.9204i		−	0.673779i	0.941544	−	0.336889i	$-0.109375\pi$
$314$	29.9417	−	10.3356i	1.68971	−	0.583271i
$315$		0			0
$316$	21.3446	+	27.2331i	1.20073	+	1.53198i
$317$	−17.6516	−	17.6516i	−0.991410	−	0.991410i	0.00855359	−	0.999963i	$-0.497277\pi$
$317$	−17.6516	−	17.6516i	−0.991410	−	0.991410i	−0.999963	+	0.00855359i	$0.997277\pi$
$318$	8.99669	−	18.4821i	0.504509	−	1.03643i
$319$	−7.84798			−0.439403
$320$		0			0
$321$	−14.6907			−0.819958
$322$	−16.3624	+	33.6137i	−0.911842	+	1.87322i
$323$	16.0991	+	16.0991i	0.895775	+	0.895775i
$324$	15.8096	+	20.1711i	0.878310	+	1.12062i
$325$		0			0
$326$	−13.6516	+	4.71241i	−0.756092	+	0.260996i
$327$			10.5811i			0.585138i
$328$	2.39112	+	11.1227i	0.132028	+	0.614146i
$329$		−	18.1492i		−	1.00060i
$330$		0			0
$331$	−24.9785	+	24.9785i	−1.37294	+	1.37294i	−0.516888	+	0.856053i	$0.672910\pi$
$331$	−24.9785	+	24.9785i	−1.37294	+	1.37294i	−0.856053	+	0.516888i	$0.827090\pi$
$332$	−3.22671	+	26.6191i	−0.177089	+	1.46091i
$333$	−2.87068	−	2.87068i	−0.157312	−	0.157312i
$334$	16.8234	+	8.18924i	0.920534	+	0.448095i
$335$		0			0
$336$	−20.9899	−	34.6901i	−1.14509	−	1.89250i
$337$	24.3167			1.32462			0.662308	−	0.749231i	$-0.269577\pi$
$337$	24.3167			1.32462			0.662308	+	0.749231i	$0.269577\pi$
$338$	14.9269	+	7.26608i	0.811916	+	0.395223i
$339$	2.38113	+	2.38113i	0.129325	+	0.129325i
$340$		0			0
$341$	−10.3136	+	10.3136i	−0.558510	+	0.558510i
$342$	14.5800	+	42.2375i	0.788396	+	2.28394i
$343$		−	10.1658i		−	0.548903i
$344$	−10.7888	+	16.6978i	−0.581693	+	0.900285i
$345$		0			0
$346$	22.2142	−	7.66816i	1.19425	−	0.412243i
$347$	−17.3818	+	17.3818i	−0.933106	+	0.933106i	−0.997899	−	0.0647931i	$-0.979361\pi$
$347$	−17.3818	+	17.3818i	−0.933106	+	0.933106i	0.0647931	+	0.997899i	$0.479361\pi$
$348$	13.3175	−	10.4379i	0.713894	−	0.559532i
$349$	−0.773103	−	0.773103i	−0.0413832	−	0.0413832i	0.686112	−	0.727496i	$-0.259316\pi$
$349$	−0.773103	−	0.773103i	−0.0413832	−	0.0413832i	−0.727496	+	0.686112i	$0.759316\pi$
$350$		0			0
$351$	−11.7283			−0.626010
$352$	−16.0263	+	1.46445i	−0.854204	+	0.0780556i
$353$	−13.3720			−0.711720			−0.355860	−	0.934539i	$-0.615812\pi$
$353$	−13.3720			−0.711720			−0.355860	+	0.934539i	$0.615812\pi$
$354$	5.57513	−	11.4531i	0.296315	−	0.608727i
$355$		0			0
$356$	11.9959	−	9.40211i	0.635784	−	0.498311i
$357$	33.0838	−	33.0838i	1.75098	−	1.75098i
$358$	−9.16403	+	3.16334i	−0.484334	+	0.167188i
$359$			28.5413i			1.50635i	0.657818	+	0.753177i	$0.271480\pi$
$359$			28.5413i			1.50635i	−0.657818	+	0.753177i	$0.728520\pi$
$360$		0			0
$361$			5.33027i			0.280541i
$362$	6.90069	+	19.9909i	0.362692	+	1.05070i
$363$	6.30335	−	6.30335i	0.330840	−	0.330840i
$364$	7.36915	+	0.893275i	0.386249	+	0.0468203i
$365$		0			0
$366$	−3.07300	−	1.49587i	−0.160628	−	0.0781903i
$367$	0.909186			0.0474591			0.0237296	−	0.999718i	$-0.492446\pi$
$367$	0.909186			0.0474591			0.0237296	+	0.999718i	$0.492446\pi$
$368$	−31.0655	−	7.64371i	−1.61940	−	0.398456i
$369$	−25.7649			−1.34127
$370$		0			0
$371$	−11.0765	−	11.0765i	−0.575064	−	0.575064i
$372$	3.78426	−	31.2186i	0.196205	−	1.61861i
$373$	26.5010	−	26.5010i	1.37217	−	1.37217i	0.514946	−	0.857223i	$-0.327812\pi$
$373$	26.5010	−	26.5010i	1.37217	−	1.37217i	0.857223	−	0.514946i	$-0.172188\pi$
$374$	−6.05947	−	17.5540i	−0.313328	−	0.907694i
$375$		0			0
$376$	15.1843	−	3.26429i	0.783071	−	0.168343i
$377$			3.09780i			0.159545i
$378$	46.1469	−	15.9295i	2.37354	−	0.819324i
$379$	1.23724	−	1.23724i	0.0635529	−	0.0635529i	−0.674616	−	0.738169i	$-0.735691\pi$
$379$	1.23724	−	1.23724i	0.0635529	−	0.0635529i	0.738169	+	0.674616i	$0.235691\pi$
$380$		0			0
$381$	−3.27800	−	3.27800i	−0.167937	−	0.167937i
$382$	−4.91628	+	10.0996i	−0.251539	+	0.516742i
$383$	15.7161			0.803057			0.401529	−	0.915846i	$-0.368479\pi$
$383$	15.7161			0.803057			0.401529	+	0.915846i	$0.368479\pi$
$384$	25.2479	−	23.8003i	1.28842	−	1.21455i
$385$		0			0
$386$	−12.9128	+	26.5270i	−0.657242	+	1.35019i
$387$	−31.8355	−	31.8355i	−1.61829	−	1.61829i
$388$	0.874833	+	1.11618i	0.0444129	+	0.0566655i
$389$	16.2799	−	16.2799i	0.825423	−	0.825423i	−0.161457	−	0.986880i	$-0.551619\pi$
$389$	16.2799	−	16.2799i	0.825423	−	0.825423i	0.986880	+	0.161457i	$0.0516193\pi$
$390$		0			0
$391$		−	36.9168i		−	1.86696i
$392$	−10.8516	+	2.33286i	−0.548090	+	0.117827i
$393$			39.9740i			2.01642i
$394$	−1.35549	−	3.92677i	−0.0682885	−	0.197828i
$395$		0			0
$396$	4.38580	−	36.1811i	0.220395	−	1.81817i
$397$	−22.8944	−	22.8944i	−1.14903	−	1.14903i	−0.986743	−	0.162292i	$-0.948111\pi$
$397$	−22.8944	−	22.8944i	−1.14903	−	1.14903i	−0.162292	−	0.986743i	$-0.551889\pi$
$398$	29.6030	+	14.4101i	1.48386	+	0.722311i
$399$	49.9990			2.50308
$400$		0			0
$401$	15.8553			0.791778			0.395889	−	0.918298i	$-0.370437\pi$
$401$	15.8553			0.791778			0.395889	+	0.918298i	$0.370437\pi$
$402$	3.50805	+	1.70764i	0.174966	+	0.0851694i
$403$	4.07102	+	4.07102i	0.202792	+	0.202792i
$404$	−17.3027	−	2.09741i	−0.860844	−	0.104350i
$405$		0			0
$406$	−4.20746	−	12.1888i	−0.208813	−	0.604919i
$407$			1.80305i			0.0893740i
$408$	33.6296	+	21.7288i	1.66491	+	1.07573i
$409$			10.0220i			0.495557i	0.968817	+	0.247779i	$0.0797006\pi$
$409$			10.0220i			0.495557i	−0.968817	+	0.247779i	$0.920299\pi$
$410$		0			0
$411$	−7.34367	+	7.34367i	−0.362236	+	0.362236i
$412$	−25.0931	+	19.6673i	−1.23625	+	0.968940i
$413$	−6.86398	−	6.86398i	−0.337754	−	0.337754i
$414$	31.7107	−	65.1441i	1.55850	−	3.20166i
$415$		0			0
$416$	0.578056	+	6.32598i	0.0283415	+	0.310157i
$417$	9.09182			0.445228
$418$	8.68573	−	17.8433i	0.424833	−	0.872745i
$419$	14.4998	+	14.4998i	0.708362	+	0.708362i	0.966191	−	0.257829i	$-0.0830071\pi$
$419$	14.4998	+	14.4998i	0.708362	+	0.708362i	−0.257829	+	0.966191i	$0.583007\pi$
$420$		0			0
$421$	12.9983	−	12.9983i	0.633498	−	0.633498i	−0.315446	−	0.948944i	$-0.602154\pi$
$421$	12.9983	−	12.9983i	0.633498	−	0.633498i	0.948944	+	0.315446i	$0.102154\pi$
$422$	4.75632	−	1.64184i	0.231534	−	0.0799235i
$423$			35.1735i			1.71020i
$424$	7.27484	−	11.2593i	0.353297	−	0.546798i
$425$		0			0
$426$	−9.69783	−	28.0941i	−0.469862	−	1.36116i
$427$	−1.84168	+	1.84168i	−0.0891251	+	0.0891251i
$428$	−9.51075	−	1.15288i	−0.459720	−	0.0557263i
$429$	6.92786	+	6.92786i	0.334480	+	0.334480i
$430$		0			0
$431$	−34.4404			−1.65894			−0.829469	−	0.558553i	$-0.811357\pi$
$431$	−34.4404			−1.65894			−0.829469	+	0.558553i	$0.811357\pi$
$432$	21.6271	+	35.7432i	1.04054	+	1.71970i
$433$	14.5895			0.701128			0.350564	−	0.936539i	$-0.385990\pi$
$433$	14.5895			0.701128			0.350564	+	0.936539i	$0.385990\pi$
$434$	−21.5474	−	10.4888i	−1.03431	−	0.503478i
$435$		0			0
$436$	−0.830368	+	6.85019i	−0.0397674	+	0.328065i
$437$	27.8959	−	27.8959i	1.33444	−	1.33444i
$438$	14.8848	+	43.1205i	0.711223	+	2.06038i
$439$		−	5.70179i		−	0.272131i	−0.990700	−	0.136066i	$-0.956554\pi$
$439$		−	5.70179i		−	0.272131i	0.990700	−	0.136066i	$-0.0434458\pi$
$440$		0			0
$441$		−	25.1371i		−	1.19701i
$442$	−6.92899	+	2.39183i	−0.329578	+	0.113768i
$443$	−5.03375	+	5.03375i	−0.239161	+	0.239161i	−0.816503	−	0.577342i	$-0.804090\pi$
$443$	−5.03375	+	5.03375i	−0.239161	+	0.239161i	0.577342	+	0.816503i	$0.304090\pi$
$444$	−2.39808	−	3.05966i	−0.113808	−	0.145205i
$445$		0			0
$446$	6.75221	−	13.8712i	0.319726	−	0.656822i
$447$	10.6368			0.503104
$448$	−10.8665	−	24.1055i	−0.513392	−	1.13888i
$449$	22.2502			1.05005			0.525025	−	0.851087i	$-0.324056\pi$
$449$	22.2502			1.05005			0.525025	+	0.851087i	$0.324056\pi$
$450$		0			0
$451$	8.09139	+	8.09139i	0.381009	+	0.381009i
$452$	1.35468	+	1.72840i	0.0637186	+	0.0812971i
$453$	−2.42290	+	2.42290i	−0.113838	+	0.113838i
$454$	−21.9957	+	7.59273i	−1.03231	+	0.356344i
$455$		0			0
$456$	8.99275	+	41.8311i	0.421124	+	1.95892i
$457$		−	8.92927i		−	0.417694i	−0.977948	−	0.208847i	$-0.933029\pi$
$457$		−	8.92927i		−	0.417694i	0.977948	−	0.208847i	$-0.0669710\pi$
$458$	−1.04912	−	3.03923i	−0.0490219	−	0.142014i
$459$	−34.0881	+	34.0881i	−1.59110	+	1.59110i
$460$		0			0
$461$	−8.14776	−	8.14776i	−0.379479	−	0.379479i	0.491435	−	0.870914i	$-0.336472\pi$
$461$	−8.14776	−	8.14776i	−0.379479	−	0.379479i	−0.870914	+	0.491435i	$0.836472\pi$
$462$	−36.6683	−	17.8493i	−1.70596	−	0.830424i
$463$	31.7058			1.47349			0.736747	−	0.676168i	$-0.236361\pi$
$463$	31.7058			1.47349			0.736747	+	0.676168i	$0.236361\pi$
$464$	9.44086	−	5.71238i	0.438281	−	0.265191i
$465$		0			0
$466$	30.2760	+	14.7377i	1.40251	+	0.682710i
$467$	17.7683	+	17.7683i	0.822219	+	0.822219i	0.986426	−	0.164207i	$-0.0525065\pi$
$467$	17.7683	+	17.7683i	0.822219	+	0.822219i	−0.164207	+	0.986426i	$0.552506\pi$
$468$	−14.2816	−	1.73119i	−0.660166	−	0.0800241i
$469$	2.10241	−	2.10241i	0.0970803	−	0.0970803i
$470$		0			0
$471$			68.6907i			3.16510i
$472$	4.50812	−	6.97721i	0.207503	−	0.321152i
$473$			19.9956i			0.919401i
$474$	−70.9284	+	24.4839i	−3.25785	+	1.12458i
$475$		0			0
$476$	24.0146	−	18.8221i	1.10071	−	0.862707i
$477$	21.4665	+	21.4665i	0.982885	+	0.982885i
$478$	0.123565	−	0.253842i	0.00565172	−	0.0116105i
$479$	−7.80806			−0.356759			−0.178380	−	0.983962i	$-0.557086\pi$
$479$	−7.80806			−0.356759			−0.178380	+	0.983962i	$0.557086\pi$
$480$		0			0
$481$	0.711710			0.0324512
$482$	10.4454	−	21.4584i	0.475777	−	0.977401i
$483$	−57.3264	−	57.3264i	−2.60844	−	2.60844i
$484$	4.57544	−	3.58611i	0.207974	−	0.163005i
$485$		0			0
$486$	−10.6497	+	3.67618i	−0.483081	+	0.166755i
$487$		−	27.6753i		−	1.25409i	−0.778984	−	0.627044i	$-0.784265\pi$
$487$		−	27.6753i		−	1.25409i	0.778984	−	0.627044i	$-0.215735\pi$
$488$	−1.87206	−	1.20958i	−0.0847443	−	0.0547551i
$489$		−	31.3188i		−	1.41629i
$490$		0			0
$491$	−11.7995	+	11.7995i	−0.532505	+	0.532505i	−0.921317	−	0.388812i	$-0.872886\pi$
$491$	−11.7995	+	11.7995i	−0.532505	+	0.532505i	0.388812	+	0.921317i	$0.372886\pi$
$492$	−24.4922	−	2.96890i	−1.10419	−	0.133848i
$493$	9.00370	+	9.00370i	0.405506	+	0.405506i
$494$	−7.04321	−	3.42848i	−0.316889	−	0.154254i
$495$		0			0
$496$	4.89984	−	19.9139i	0.220009	−	0.894159i
$497$	−22.6491			−1.01595
$498$	−52.2830	−	25.4502i	−2.34286	−	1.14045i
$499$	−25.0477	−	25.0477i	−1.12129	−	1.12129i	−0.991548	−	0.129743i	$-0.958585\pi$
$499$	−25.0477	−	25.0477i	−1.12129	−	1.12129i	−0.129743	−	0.991548i	$-0.541415\pi$
$500$		0			0
$501$	−28.6914	+	28.6914i	−1.28184	+	1.28184i
$502$	−3.98098	−	11.5327i	−0.177680	−	0.514729i
$503$			22.8644i			1.01947i	0.860331	+	0.509736i	$0.170257\pi$
$503$			22.8644i			1.01947i	−0.860331	+	0.509736i	$0.829743\pi$
$504$	58.5445	−	12.5857i	2.60778	−	0.560614i
$505$		0			0
$506$	−30.4169	+	10.4996i	−1.35220	+	0.466766i
$507$	−25.4570	+	25.4570i	−1.13059	+	1.13059i
$508$	−1.86492	−	2.37942i	−0.0827426	−	0.105569i
$509$	−17.1633	−	17.1633i	−0.760748	−	0.760748i	0.215710	−	0.976458i	$-0.430794\pi$
$509$	−17.1633	−	17.1633i	−0.760748	−	0.760748i	−0.976458	+	0.215710i	$0.930794\pi$
$510$		0			0
$511$	34.7631			1.53783
$512$	18.2131	−	13.4269i	0.804915	−	0.593390i
$513$	−51.5169			−2.27453
$514$	−12.2779	+	25.2227i	−0.541553	+	1.11253i
$515$		0			0
$516$	−26.5945	−	33.9313i	−1.17076	−	1.49374i
$517$	11.0461	−	11.0461i	0.485808	−	0.485808i
$518$	−2.80034	+	0.966652i	−0.123040	+	0.0424722i
$519$			50.9629i			2.23702i
$520$		0			0
$521$		−	11.5206i		−	0.504726i	−0.967633	−	0.252363i	$-0.918792\pi$
$521$		−	11.5206i		−	0.504726i	0.967633	−	0.252363i	$-0.0812077\pi$
$522$	8.15414	+	23.6221i	0.356897	+	1.03391i
$523$	25.4249	−	25.4249i	1.11175	−	1.11175i	0.118841	−	0.992913i	$-0.462082\pi$
$523$	25.4249	−	25.4249i	1.11175	−	1.11175i	0.992913	−	0.118841i	$-0.0379180\pi$
$524$	−3.13701	+	25.8790i	−0.137041	+	1.13053i
$525$		0			0
$526$	9.08455	+	4.42215i	0.396105	+	0.192815i
$527$	23.6647			1.03085
$528$	8.33831	−	33.8884i	0.362878	−	1.47481i
$529$	−40.9681			−1.78122
$530$		0			0
$531$	13.3025	+	13.3025i	0.577281	+	0.577281i
$532$	32.3692	+	3.92374i	1.40338	+	0.170116i
$533$	3.19387	−	3.19387i	0.138342	−	0.138342i
$534$	10.7849	+	31.2434i	0.466710	+	1.35203i
$535$		0			0
$536$	2.13709	+	1.38082i	0.0923084	+	0.0596424i
$537$		−	21.0237i		−	0.907239i
$538$	−41.1600	+	14.2081i	−1.77454	+	0.612554i
$539$	−7.89423	+	7.89423i	−0.340028	+	0.340028i
$540$		0			0
$541$	−29.7997	−	29.7997i	−1.28119	−	1.28119i	−0.939992	−	0.341196i	$-0.889168\pi$
$541$	−29.7997	−	29.7997i	−1.28119	−	1.28119i	−0.341196	−	0.939992i	$-0.610832\pi$
$542$	2.91738	−	5.99325i	0.125312	−	0.257432i
$543$	−45.8622			−1.96814
$544$	20.0665	+	16.7063i	0.860344	+	0.716275i
$545$		0			0
$546$	−7.04556	+	14.4739i	−0.301522	+	0.619425i
$547$	−28.3699	−	28.3699i	−1.21301	−	1.21301i	−0.970032	−	0.242979i	$-0.921875\pi$
$547$	−28.3699	−	28.3699i	−1.21301	−	1.21301i	−0.242979	−	0.970032i	$-0.578125\pi$
$548$	−5.33057	+	4.17797i	−0.227711	+	0.178474i
$549$	3.56921	−	3.56921i	0.152330	−	0.152330i
$550$		0			0
$551$			13.6072i			0.579685i
$552$	37.6509	−	58.2722i	1.60253	−	2.48023i
$553$			57.1815i			2.43161i
$554$	−13.3513	−	38.6781i	−0.567244	−	1.64328i
$555$		0			0
$556$	5.88602	+	0.713492i	0.249623	+	0.0302588i
$557$	21.7769	+	21.7769i	0.922718	+	0.922718i	0.997221	−	0.0745028i	$-0.0237370\pi$
$557$	21.7769	+	21.7769i	0.922718	+	0.922718i	−0.0745028	+	0.997221i	$0.523737\pi$
$558$	41.7593	+	20.3275i	1.76781	+	0.860531i
$559$	7.89278			0.333829
$560$		0			0
$561$	40.2715			1.70026
$562$	−22.4407	−	10.9236i	−0.946602	−	0.460785i
$563$	10.9022	+	10.9022i	0.459473	+	0.459473i	0.898482	−	0.439010i	$-0.144671\pi$
$563$	10.9022	+	10.9022i	0.459473	+	0.459473i	−0.439010	+	0.898482i	$0.644671\pi$
$564$	−4.05306	+	33.4361i	−0.170664	+	1.40791i
$565$		0			0
$566$	−11.8462	−	34.3179i	−0.497935	−	1.44249i
$567$			42.3534i			1.77868i
$568$	−4.07363	−	18.9491i	−0.170926	−	0.795087i
$569$		−	31.1881i		−	1.30747i	−0.756723	−	0.653736i	$-0.773201\pi$
$569$		−	31.1881i		−	1.30747i	0.756723	−	0.653736i	$-0.226799\pi$
$570$		0			0
$571$	−2.20354	+	2.20354i	−0.0922153	+	0.0922153i	−0.751710	−	0.659494i	$-0.770770\pi$
$571$	−2.20354	+	2.20354i	−0.0922153	+	0.0922153i	0.659494	+	0.751710i	$0.270770\pi$
$572$	3.94140	+	5.02875i	0.164798	+	0.210263i
$573$	−17.2244	−	17.2244i	−0.719559	−	0.719559i
$574$	−8.22886	+	16.9048i	−0.343466	+	0.705591i
$575$		0			0
$576$	21.0594	+	46.7169i	0.877477	+	1.94654i
$577$	8.42524			0.350747			0.175374	−	0.984502i	$-0.443887\pi$
$577$	8.42524			0.350747			0.175374	+	0.984502i	$0.443887\pi$
$578$	−2.66473	+	5.47423i	−0.110838	+	0.227698i
$579$	−45.2404	−	45.2404i	−1.88013	−	1.88013i
$580$		0			0
$581$	−31.3337	+	31.3337i	−1.29994	+	1.29994i
$582$	−2.90709	+	1.00350i	−0.120503	+	0.0415964i
$583$		−	13.4830i		−	0.558408i
$584$	6.25244	+	29.0842i	0.258728	+	1.20351i
$585$		0			0
$586$	0.416669	+	1.20707i	0.0172125	+	0.0498636i
$587$	−19.3370	+	19.3370i	−0.798125	+	0.798125i	−0.982800	−	0.184675i	$-0.940877\pi$
$587$	−19.3370	+	19.3370i	−0.798125	+	0.798125i	0.184675	+	0.982800i	$0.440877\pi$
$588$	2.89656	−	23.8954i	0.119452	−	0.985431i
$589$	17.8821	+	17.8821i	0.736818	+	0.736818i
$590$		0			0
$591$	9.00862			0.370565
$592$	−1.31240	−	2.16901i	−0.0539394	−	0.0891458i
$593$	18.1804			0.746580			0.373290	−	0.927715i	$-0.378230\pi$
$593$	18.1804			0.746580			0.373290	+	0.927715i	$0.378230\pi$
$594$	37.7814	+	18.3912i	1.55019	+	0.754598i
$595$		0			0
$596$	6.88624	+	0.834737i	0.282071	+	0.0341922i
$597$	−50.4863	+	50.4863i	−2.06627	+	2.06627i
$598$	4.14447	+	12.0063i	0.169480	+	0.490975i
$599$			1.64695i			0.0672927i	0.999434	+	0.0336463i	$0.0107120\pi$
$599$			1.64695i			0.0672927i	−0.999434	+	0.0336463i	$0.989288\pi$
$600$		0			0
$601$		−	12.7485i		−	0.520021i	−0.965606	−	0.260011i	$-0.916274\pi$
$601$		−	12.7485i		−	0.520021i	0.965606	−	0.260011i	$-0.0837261\pi$
$602$	−31.0554	+	10.7201i	−1.26572	+	0.436917i
$603$	−4.07452	+	4.07452i	−0.165927	+	0.165927i
$604$	−1.75872	+	1.37844i	−0.0715612	+	0.0560878i
$605$		0			0
$606$	16.5430	−	33.9846i	0.672012	−	1.38053i
$607$	15.6773			0.636322			0.318161	−	0.948037i	$-0.396935\pi$
$607$	15.6773			0.636322			0.318161	+	0.948037i	$0.396935\pi$
$608$	2.53913	+	27.7871i	0.102975	+	1.12691i
$609$	27.9629			1.13311
$610$		0			0
$611$	−4.36018	−	4.36018i	−0.176394	−	0.176394i
$612$	−46.5409	+	36.4775i	−1.88130	+	1.47452i
$613$	8.29399	−	8.29399i	0.334991	−	0.334991i	−0.519487	−	0.854478i	$-0.673877\pi$
$613$	8.29399	−	8.29399i	0.334991	−	0.334991i	0.854478	+	0.519487i	$0.173877\pi$
$614$	8.54945	−	2.95119i	0.345028	−	0.119100i
$615$		0			0
$616$	−22.3382	−	14.4332i	−0.900031	−	0.581529i
$617$			20.3330i			0.818575i	0.912406	+	0.409287i	$0.134223\pi$
$617$			20.3330i			0.818575i	−0.912406	+	0.409287i	$0.865777\pi$
$618$	−22.5599	−	65.3549i	−0.907493	−	2.62896i
$619$	12.5878	−	12.5878i	0.505946	−	0.505946i	−0.407333	−	0.913280i	$-0.633541\pi$
$619$	12.5878	−	12.5878i	0.505946	−	0.505946i	0.913280	+	0.407333i	$0.133541\pi$
$620$		0			0
$621$	59.0667	+	59.0667i	2.37027	+	2.37027i
$622$	17.9309	+	8.72836i	0.718964	+	0.349975i
$623$	25.1880			1.00914
$624$	−13.3766	−	3.29134i	−0.535493	−	0.131759i
$625$		0			0
$626$	15.1575	+	7.37834i	0.605816	+	0.294898i
$627$	30.4308	+	30.4308i	1.21529	+	1.21529i
$628$	−5.39059	+	44.4702i	−0.215108	+	1.77455i
$629$	2.06858	−	2.06858i	0.0824795	−	0.0824795i
$630$		0			0
$631$		−	21.4887i		−	0.855453i	−0.903908	−	0.427726i	$-0.859315\pi$
$631$		−	21.4887i		−	0.855453i	0.903908	−	0.427726i	$-0.140685\pi$
$632$	−47.8403	+	10.2846i	−1.90298	+	0.409099i
$633$			10.9117i			0.433702i
$634$	33.3709	−	11.5193i	1.32533	−	0.457491i
$635$		0			0
$636$	17.9325	+	22.8797i	0.711072	+	0.907241i
$637$	3.11605	+	3.11605i	0.123462	+	0.123462i
$638$	4.85766	−	9.97922i	0.192317	−	0.395081i
$639$	43.8944			1.73644
$640$		0			0
$641$	26.1687			1.03360			0.516800	−	0.856106i	$-0.327123\pi$
$641$	26.1687			1.03360			0.516800	+	0.856106i	$0.327123\pi$
$642$	9.09312	−	18.6802i	0.358877	−	0.737250i
$643$	−14.6501	−	14.6501i	−0.577743	−	0.577743i	0.356538	−	0.934281i	$-0.383957\pi$
$643$	−14.6501	−	14.6501i	−0.577743	−	0.577743i	−0.934281	+	0.356538i	$0.883957\pi$
$644$	−32.6142	−	41.6118i	−1.28518	−	1.63973i
$645$		0			0
$646$	−30.4358	+	10.5062i	−1.19748	+	0.413360i
$647$			16.2623i			0.639337i	0.947530	+	0.319668i	$0.103571\pi$
$647$			16.2623i			0.639337i	−0.947530	+	0.319668i	$0.896429\pi$
$648$	−35.4345	+	7.61762i	−1.39200	+	0.299248i
$649$		−	8.35522i		−	0.327971i
$650$		0			0
$651$	36.7479	−	36.7479i	1.44026	−	1.44026i
$652$	2.45778	−	20.2757i	0.0962543	−	0.794058i
$653$	−32.0639	−	32.0639i	−1.25476	−	1.25476i	−0.953563	−	0.301194i	$-0.902615\pi$
$653$	−32.0639	−	32.0639i	−1.25476	−	1.25476i	−0.301194	−	0.953563i	$-0.597385\pi$
$654$	−13.4546	−	6.54939i	−0.526116	−	0.256101i
$655$		0			0
$656$	−15.6232	−	3.84412i	−0.609984	−	0.150088i
$657$	−67.3717			−2.62842
$658$	23.0779	+	11.2338i	0.899669	+	0.437939i
$659$	−7.04696	−	7.04696i	−0.274511	−	0.274511i	0.556402	−	0.830913i	$-0.312181\pi$
$659$	−7.04696	−	7.04696i	−0.274511	−	0.274511i	−0.830913	+	0.556402i	$0.812181\pi$
$660$		0			0
$661$	5.78655	−	5.78655i	0.225071	−	0.225071i	−0.585559	−	0.810630i	$-0.699125\pi$
$661$	5.78655	−	5.78655i	0.225071	−	0.225071i	0.810630	+	0.585559i	$0.199125\pi$
$662$	−16.3008	−	47.2226i	−0.633550	−	1.83536i
$663$		−	15.8962i		−	0.617355i
$664$	−31.8506	−	20.5794i	−1.23604	−	0.798634i
$665$		0			0
$666$	5.42711	−	1.87339i	0.210296	−	0.0725924i
$667$	15.6013	−	15.6013i	0.604085	−	0.604085i
$668$	−20.8263	+	16.3231i	−0.805794	+	0.631560i
$669$	23.6567	+	23.6567i	0.914619	+	0.914619i
$670$		0			0
$671$	−2.24180			−0.0865436
$672$	57.1028	−	5.21795i	2.20279	−	0.201287i
$673$	−35.3380			−1.36218			−0.681090	−	0.732200i	$-0.738494\pi$
$673$	−35.3380			−1.36218			−0.681090	+	0.732200i	$0.738494\pi$
$674$	−15.0513	+	30.9203i	−0.579755	+	1.19101i
$675$		0			0
$676$	−18.4786	+	14.4830i	−0.710714	+	0.557040i
$677$	−7.72259	+	7.72259i	−0.296803	+	0.296803i	−0.839760	−	0.542957i	$-0.817305\pi$
$677$	−7.72259	+	7.72259i	−0.296803	+	0.296803i	0.542957	+	0.839760i	$0.317305\pi$
$678$	−4.50161	+	1.55391i	−0.172883	+	0.0596777i
$679$			2.34365i			0.0899411i
$680$		0			0
$681$		−	50.4615i		−	1.93369i
$682$	−6.73058	−	19.4981i	−0.257727	−	0.746622i
$683$	15.6011	−	15.6011i	0.596958	−	0.596958i	−0.342544	−	0.939502i	$-0.611289\pi$
$683$	15.6011	−	15.6011i	0.596958	−	0.596958i	0.939502	+	0.342544i	$0.111289\pi$
$684$	−62.7323	−	7.60429i	−2.39863	−	0.290757i
$685$		0			0
$686$	12.9265	+	6.29233i	0.493536	+	0.240242i
$687$	6.97246			0.266016
$688$	−14.5544	−	24.0541i	−0.554881	−	0.917053i
$689$	−5.32207			−0.202755
$690$		0			0
$691$	30.0975	+	30.0975i	1.14496	+	1.14496i	0.987530	+	0.157433i	$0.0503218\pi$
$691$	30.0975	+	30.0975i	1.14496	+	1.14496i	0.157433	+	0.987530i	$0.449678\pi$
$692$	−3.99938	+	32.9932i	−0.152033	+	1.25421i
$693$	42.5893	−	42.5893i	1.61783	−	1.61783i
$694$	−11.3433	−	32.8609i	−0.430586	−	1.24738i
$695$		0			0
$696$	5.02937	+	23.3949i	0.190638	+	0.886780i
$697$		−	18.5659i		−	0.703234i
$698$	1.46158	−	0.504523i	0.0553215	−	0.0190965i
$699$	−51.6341	+	51.6341i	−1.95298	+	1.95298i
$700$		0			0
$701$	14.8151	+	14.8151i	0.559559	+	0.559559i	0.929182	−	0.369623i	$-0.120513\pi$
$701$	14.8151	+	14.8151i	0.559559	+	0.559559i	−0.369623	+	0.929182i	$0.620513\pi$
$702$	7.25945	−	14.9133i	0.273990	−	0.562865i
$703$	3.12621			0.117907
$704$	8.05764	−	21.2849i	0.303684	−	0.802206i
$705$		0			0
$706$	8.27686	−	17.0034i	0.311504	−	0.639930i
$707$	−20.3673	−	20.3673i	−0.765992	−	0.765992i
$708$	11.1126	+	14.1783i	0.417636	+	0.532852i
$709$	9.26566	−	9.26566i	0.347979	−	0.347979i	−0.511377	−	0.859356i	$-0.670864\pi$
$709$	9.26566	−	9.26566i	0.347979	−	0.347979i	0.859356	+	0.511377i	$0.170864\pi$
$710$		0			0
$711$		−	110.819i		−	4.15604i
$712$	4.53027	+	21.0732i	0.169779	+	0.789753i
$713$		−	41.0054i		−	1.53567i
$714$	21.5903	+	62.5460i	0.807998	+	2.34073i
$715$		0			0
$716$	1.64986	−	13.6107i	0.0616582	−	0.508655i
$717$	0.432914	+	0.432914i	0.0161675	+	0.0161675i
$718$	−36.2922	−	17.6662i	−1.35441	−	0.659297i
$719$	40.8143			1.52212			0.761058	−	0.648684i	$-0.224680\pi$
$719$	40.8143			1.52212			0.761058	+	0.648684i	$0.224680\pi$
$720$		0			0
$721$	−52.6882			−1.96221
$722$	−6.77778	−	3.29927i	−0.252243	−	0.122786i
$723$	36.5961	+	36.5961i	1.36102	+	1.36102i
$724$	−29.6911	−	3.59910i	−1.10346	−	0.133759i
$725$		0			0
$726$	4.11354	+	11.9167i	0.152668	+	0.442270i
$727$			5.20944i			0.193208i	0.995323	+	0.0966038i	$0.0307980\pi$
$727$			5.20944i			0.193208i	−0.995323	+	0.0966038i	$0.969202\pi$
$728$	−5.69714	+	8.81744i	−0.211150	+	0.326796i
$729$			14.0106i			0.518911i
$730$		0			0
$731$	22.9403	−	22.9403i	0.848476	−	0.848476i
$732$	3.80419	−	2.98162i	0.140607	−	0.110204i
$733$	14.7039	+	14.7039i	0.543099	+	0.543099i	0.924436	−	0.381337i	$-0.124536\pi$
$733$	14.7039	+	14.7039i	0.543099	+	0.543099i	−0.381337	+	0.924436i	$0.624536\pi$
$734$	−0.562758	+	1.15609i	−0.0207718	+	0.0426720i
$735$		0			0
$736$	28.9481	−	34.7705i	1.06704	−	1.28166i
$737$	2.55917			0.0942684
$738$	15.9477	−	32.7618i	0.587043	−	1.20598i
$739$	7.68017	+	7.68017i	0.282520	+	0.282520i	0.834113	−	0.551594i	$-0.185980\pi$
$739$	7.68017	+	7.68017i	0.282520	+	0.282520i	−0.551594	+	0.834113i	$0.685980\pi$
$740$		0			0
$741$	12.0118	−	12.0118i	0.441265	−	0.441265i
$742$	20.9405	−	7.22849i	0.768752	−	0.265366i
$743$			34.9882i			1.28359i	0.766876	+	0.641796i	$0.221810\pi$
$743$			34.9882i			1.28359i	−0.766876	+	0.641796i	$0.778190\pi$
$744$	37.3541	+	24.1353i	1.36947	+	0.884843i
$745$		0			0
$746$	17.2944	+	50.1010i	0.633194	+	1.83433i
$747$	60.7254	−	60.7254i	2.22183	−	2.22183i
$748$	26.0716	+	3.16035i	0.953273	+	0.115554i
$749$	−11.1953	−	11.1953i	−0.409066	−	0.409066i
$750$		0			0
$751$	−33.1447			−1.20947			−0.604733	−	0.796428i	$-0.706720\pi$
$751$	−33.1447			−1.20947			−0.604733	+	0.796428i	$0.706720\pi$
$752$	−5.24788	+	21.3283i	−0.191370	+	0.777765i
$753$	26.4577			0.964174
$754$	−3.93905	−	1.91744i	−0.143452	−	0.0698291i
$755$		0			0
$756$	−8.30812	+	68.5386i	−0.302163	+	2.49272i
$757$	−22.1553	+	22.1553i	−0.805248	+	0.805248i	−0.983910	−	0.178663i	$-0.942823\pi$
$757$	−22.1553	+	22.1553i	−0.805248	+	0.805248i	0.178663	+	0.983910i	$0.442823\pi$
$758$	0.807419	+	2.33905i	0.0293268	+	0.0849581i
$759$		−	69.7810i		−	2.53289i
$760$		0			0
$761$			48.1426i			1.74517i	0.488466	+	0.872583i	$0.337557\pi$
$761$			48.1426i			1.74517i	−0.488466	+	0.872583i	$0.662443\pi$
$762$	6.19717	−	2.13921i	0.224500	−	0.0774954i
$763$	−8.06347	+	8.06347i	−0.291917	+	0.291917i
$764$	−9.79932	−	12.5027i	−0.354527	−	0.452333i
$765$		0			0
$766$	−9.72781	+	19.9841i	−0.351480	+	0.722055i
$767$	−3.29802			−0.119084
$768$	14.6360	+	46.8359i	0.528130	+	1.69005i
$769$	−41.1054			−1.48230			−0.741150	−	0.671339i	$-0.765719\pi$
$769$	−41.1054			−1.48230			−0.741150	+	0.671339i	$0.765719\pi$
$770$		0			0
$771$	−43.0160	−	43.0160i	−1.54918	−	1.54918i
$772$	−25.7382	−	32.8388i	−0.926339	−	1.18189i
$773$	−10.8044	+	10.8044i	−0.388607	+	0.388607i	−0.874190	−	0.485583i	$-0.838607\pi$
$773$	−10.8044	+	10.8044i	−0.388607	+	0.388607i	0.485583	+	0.874190i	$0.338607\pi$
$774$	60.1861	−	20.7757i	2.16334	−	0.746767i
$775$		0			0
$776$	−1.96079	+	0.421526i	−0.0703883	+	0.0151319i
$777$		−	6.42440i		−	0.230474i
$778$	10.6242	+	30.7777i	0.380895	+	1.10343i
$779$	14.0292	−	14.0292i	0.502648	−	0.502648i
$780$		0			0
$781$	−13.7849	−	13.7849i	−0.493262	−	0.493262i
$782$	46.9421	+	22.8504i	1.67865	+	0.817127i
$783$	−28.8118			−1.02965
$784$	3.75045	−	15.2425i	0.133945	−	0.544376i
$785$		0			0
$786$	−50.8295	−	24.7427i	−1.81303	−	0.882541i
$787$	−11.7496	−	11.7496i	−0.418826	−	0.418826i	0.465973	−	0.884799i	$-0.345704\pi$
$787$	−11.7496	−	11.7496i	−0.418826	−	0.418826i	−0.884799	+	0.465973i	$0.845704\pi$
$788$	5.83215	+	0.706963i	0.207762	+	0.0251845i
$789$	−15.4932	+	15.4932i	−0.551573	+	0.551573i
$790$		0			0
$791$			3.62914i			0.129037i
$792$	43.2919	+	27.9718i	1.53831	+	0.993934i
$793$			0.884894i			0.0314235i
$794$	43.2826	−	14.9408i	1.53604	−	0.530227i
$795$		0			0
$796$	−36.6467	+	28.7227i	−1.29891	+	1.01805i
$797$	−15.9126	−	15.9126i	−0.563652	−	0.563652i	0.366691	−	0.930343i	$-0.380491\pi$
$797$	−15.9126	−	15.9126i	−0.563652	−	0.563652i	−0.930343	+	0.366691i	$0.880491\pi$
$798$	−30.9479	+	63.5770i	−1.09554	+	2.25060i
$799$	−25.3456			−0.896663
$800$		0			0
$801$	−48.8148			−1.72479
$802$	−9.81397	+	20.1611i	−0.346543	+	0.711913i
$803$	21.1578	+	21.1578i	0.746643	+	0.746643i
$804$	−4.34276	+	3.40374i	−0.153157	+	0.120041i
$805$		0			0
$806$	−7.69640	+	2.65673i	−0.271094	+	0.0935792i
$807$		−	94.4274i		−	3.32400i
$808$	13.3769	−	20.7033i	0.470596	−	0.728341i
$809$		−	9.06814i		−	0.318819i	−0.987213	−	0.159409i	$-0.949041\pi$
$809$		−	9.06814i		−	0.318819i	0.987213	−	0.159409i	$-0.0509590\pi$
$810$		0			0
$811$	−17.0825	+	17.0825i	−0.599849	+	0.599849i	−0.940272	−	0.340424i	$-0.889430\pi$
$811$	−17.0825	+	17.0825i	−0.599849	+	0.599849i	0.340424	+	0.940272i	$0.389430\pi$
$812$	18.1031	+	2.19443i	0.635295	+	0.0770093i
$813$	10.2212	+	10.2212i	0.358472	+	0.358472i
$814$	−2.29270	−	1.11603i	−0.0803590	−	0.0391170i
$815$		0			0
$816$	−48.4452	+	29.3127i	−1.69592	+	1.02615i
$817$	34.6693			1.21293
$818$	−12.7437	−	6.20333i	−0.445571	−	0.216894i
$819$	−16.8111	−	16.8111i	−0.587426	−	0.587426i
$820$		0			0
$821$	18.0531	−	18.0531i	0.630057	−	0.630057i	−0.318026	−	0.948082i	$-0.603020\pi$
$821$	18.0531	−	18.0531i	0.630057	−	0.630057i	0.948082	+	0.318026i	$0.103020\pi$
$822$	−4.79244	−	13.8835i	−0.167156	−	0.484241i
$823$		−	25.3535i		−	0.883767i	−0.897072	−	0.441884i	$-0.854310\pi$
$823$		−	25.3535i		−	0.883767i	0.897072	−	0.441884i	$-0.145690\pi$
$824$	−9.47642	−	44.0810i	−0.330127	−	1.53563i
$825$		0			0
$826$	12.9766	−	4.47940i	0.451513	−	0.155858i
$827$	−15.3396	+	15.3396i	−0.533410	+	0.533410i	−0.921585	−	0.388176i	$-0.873105\pi$
$827$	−15.3396	+	15.3396i	−0.533410	+	0.533410i	0.388176	+	0.921585i	$0.373105\pi$
$828$	63.2070	+	80.6444i	2.19660	+	2.80259i
$829$	37.2546	+	37.2546i	1.29391	+	1.29391i	0.932351	+	0.361555i	$0.117754\pi$
$829$	37.2546	+	37.2546i	1.29391	+	1.29391i	0.361555	+	0.932351i	$0.382246\pi$
$830$		0			0
$831$	88.7335			3.07813
$832$	−8.40169	−	3.18055i	−0.291276	−	0.110266i
$833$	18.1135			0.627596
$834$	−5.62756	+	11.5608i	−0.194866	+	0.400319i
$835$		0			0
$836$	17.3127	+	22.0889i	0.598774	+	0.763962i
$837$	−37.8635	+	37.8635i	−1.30875	+	1.30875i
$838$	−27.4124	+	9.46250i	−0.946945	+	0.326877i
$839$		−	17.9621i		−	0.620120i	−0.950717	−	0.310060i	$-0.899651\pi$
$839$		−	17.9621i		−	0.620120i	0.950717	−	0.310060i	$-0.100349\pi$
$840$		0			0
$841$		−	21.3899i		−	0.737584i
$842$	8.48262	+	24.5737i	0.292331	+	0.846866i
$843$	38.2713	−	38.2713i	1.31813	−	1.31813i
$844$	−0.856312	+	7.06422i	−0.0294755	+	0.243161i
$845$		0			0
$846$	−44.7254	−	21.7713i	−1.53769	−	0.748514i
$847$	9.60708			0.330103
$848$	9.81397	+	16.2196i	0.337013	+	0.556982i
$849$	78.7306			2.70203
$850$		0			0
$851$	−3.58436	−	3.58436i	−0.122870	−	0.122870i
$852$	41.7261	+	5.05797i	1.42951	+	0.173283i
$853$	9.29007	−	9.29007i	0.318086	−	0.318086i	−0.529946	−	0.848032i	$-0.677788\pi$
$853$	9.29007	−	9.29007i	0.318086	−	0.318086i	0.848032	+	0.529946i	$0.177788\pi$
$854$	−1.20187	−	3.48176i	−0.0411272	−	0.119143i
$855$		0			0
$856$	7.35282	−	11.3799i	0.251314	−	0.388958i
$857$			10.3997i			0.355246i	0.984099	+	0.177623i	$0.0568407\pi$
$857$			10.3997i			0.355246i	−0.984099	+	0.177623i	$0.943159\pi$
$858$	−13.0973	+	4.52109i	−0.447136	+	0.154347i
$859$	15.3452	−	15.3452i	0.523571	−	0.523571i	−0.395077	−	0.918648i	$-0.629282\pi$
$859$	15.3452	−	15.3452i	0.523571	−	0.523571i	0.918648	+	0.395077i	$0.129282\pi$
$860$		0			0
$861$	−28.8302	−	28.8302i	−0.982530	−	0.982530i
$862$	21.3176	−	43.7932i	0.726079	−	1.49160i
$863$	−8.81329			−0.300008			−0.150004	−	0.988685i	$-0.547929\pi$
$863$	−8.81329			−0.300008			−0.150004	+	0.988685i	$0.547929\pi$
$864$	−58.8363	+	5.37635i	−2.00165	+	0.182907i
$865$		0			0
$866$	−9.03047	+	18.5515i	−0.306868	+	0.630407i
$867$	−9.33601	−	9.33601i	−0.317067	−	0.317067i
$868$	26.6743	−	20.9067i	0.905386	−	0.709618i
$869$	−34.8023	+	34.8023i	−1.18059	+	1.18059i
$870$		0			0
$871$		−	1.01017i		−	0.0342283i
$872$	−8.19649	−	5.29592i	−0.277568	−	0.179343i
$873$		−	4.54205i		−	0.153725i
$874$	18.2047	+	52.7381i	0.615784	+	1.78389i
$875$		0			0
$876$	−64.0437	−	7.76326i	−2.16384	−	0.262296i
$877$	5.68862	+	5.68862i	0.192091	+	0.192091i	0.796599	−	0.604508i	$-0.206630\pi$
$877$	5.68862	+	5.68862i	0.192091	+	0.192091i	−0.604508	+	0.796599i	$0.706630\pi$
$878$	7.25019	+	3.52923i	0.244682	+	0.119106i
$879$	−2.76920			−0.0934028
$880$		0			0
$881$	−20.3573			−0.685856			−0.342928	−	0.939362i	$-0.611419\pi$
$881$	−20.3573			−0.685856			−0.342928	+	0.939362i	$0.611419\pi$
$882$	31.9635	+	15.5591i	1.07627	+	0.523903i
$883$	19.3524	+	19.3524i	0.651262	+	0.651262i	0.953297	−	0.302035i	$-0.0976660\pi$
$883$	19.3524	+	19.3524i	0.651262	+	0.651262i	−0.302035	+	0.953297i	$0.597666\pi$
$884$	1.24747	−	10.2911i	0.0419570	−	0.346128i
$885$		0			0
$886$	−3.28500	−	9.51647i	−0.110362	−	0.319712i
$887$		−	12.7863i		−	0.429323i	−0.976689	−	0.214661i	$-0.931135\pi$
$887$		−	12.7863i		−	0.429323i	0.976689	−	0.214661i	$-0.0688648\pi$
$888$	5.37490	−	1.15548i	0.180370	−	0.0387755i
$889$		−	4.99608i		−	0.167563i
$890$		0			0
$891$	−25.7775	+	25.7775i	−0.863579	+	0.863579i
$892$	13.4588	+	17.1717i	0.450633	+	0.574953i
$893$	−19.1522	−	19.1522i	−0.640905	−	0.640905i
$894$	−6.58385	+	13.5254i	−0.220197	+	0.452357i
$895$		0			0
$896$	37.3777	+	1.10313i	1.24870	+	0.0368531i
$897$	−27.5443			−0.919678
$898$	−13.7722	+	28.2925i	−0.459584	+	0.944134i
$899$	10.0009	+	10.0009i	0.333548	+	0.333548i
$900$		0			0
$901$	−15.4685	+	15.4685i	−0.515331	+	0.515331i
$902$	−15.2970	+	5.28040i	−0.509336	+	0.175818i
$903$		−	71.2459i		−	2.37091i
$904$	−3.03627	+	0.652731i	−0.100985	+	0.0217095i
$905$		0			0
$906$	−1.58117	−	4.58057i	−0.0525309	−	0.152179i
$907$	2.88449	−	2.88449i	0.0957780	−	0.0957780i	−0.657594	−	0.753372i	$-0.728426\pi$
$907$	2.88449	−	2.88449i	0.0957780	−	0.0957780i	0.753372	+	0.657594i	$0.228426\pi$
$908$	3.96003	−	32.6687i	0.131418	−	1.08415i
$909$	39.4723	+	39.4723i	1.30921	+	1.30921i
$910$		0			0
$911$	59.0271			1.95565			0.977827	−	0.209412i	$-0.0671550\pi$
$911$	59.0271			1.95565			0.977827	+	0.209412i	$0.0671550\pi$
$912$	−58.7572	−	14.4573i	−1.94565	−	0.478730i
$913$	−38.1412			−1.26229
$914$	11.3542	+	5.52695i	0.375562	+	0.182815i
$915$		0			0
$916$	4.51395	+	0.547173i	0.149145	+	0.0180791i
$917$	−30.4626	+	30.4626i	−1.00596	+	1.00596i
$918$	−22.2458	−	64.4448i	−0.734219	−	2.12699i
$919$			24.0062i			0.791893i	0.918274	+	0.395946i	$0.129583\pi$
$919$			24.0062i			0.791893i	−0.918274	+	0.395946i	$0.870417\pi$
$920$		0			0
$921$			19.6137i			0.646294i
$922$	15.4036	−	5.31719i	0.507291	−	0.175112i
$923$	−5.44124	+	5.44124i	−0.179100	+	0.179100i
$924$	45.3931	−	35.5779i	1.49332	−	1.17043i
$925$		0			0
$926$	−19.6249	+	40.3160i	−0.644915	+	1.32487i
$927$	102.111			3.35376
$928$	1.42006	+	15.5405i	0.0466157	+	0.510140i
$929$	15.1568			0.497279			0.248639	−	0.968596i	$-0.420017\pi$
$929$	15.1568			0.497279			0.248639	+	0.968596i	$0.420017\pi$
$930$		0			0
$931$	13.6873	+	13.6873i	0.448585	+	0.448585i
$932$	−37.4798	+	29.3757i	−1.22769	+	0.962234i
$933$	−30.5802	+	30.5802i	−1.00115	+	1.00115i
$934$	−33.5916	+	11.5955i	−1.09915	+	0.379417i
$935$		0			0
$936$	11.0412	−	17.0884i	0.360892	−	0.558552i
$937$			39.9323i			1.30453i	0.757991	+	0.652266i	$0.226181\pi$
$937$			39.9323i			1.30453i	−0.757991	+	0.652266i	$0.773819\pi$
$938$	1.37202	+	3.97468i	0.0447982	+	0.129778i
$939$	−25.8503	+	25.8503i	−0.843594	+	0.843594i
$940$		0			0
$941$	−21.6002	−	21.6002i	−0.704145	−	0.704145i	0.261153	−	0.965298i	$-0.415897\pi$
$941$	−21.6002	−	21.6002i	−0.704145	−	0.704145i	−0.965298	+	0.261153i	$0.915897\pi$
$942$	−87.3447	−	42.5174i	−2.84584	−	1.38529i
$943$	−32.1704			−1.04761
$944$	6.08159	+	10.0511i	0.197939	+	0.327134i
$945$		0			0
$946$	−25.4258	−	12.3767i	−0.826662	−	0.402401i
$947$	16.2944	+	16.2944i	0.529498	+	0.529498i	0.920423	−	0.390925i	$-0.127845\pi$
$947$	16.2944	+	16.2944i	0.529498	+	0.529498i	−0.390925	+	0.920423i	$0.627845\pi$
$948$	12.7697	−	105.345i	0.414741	−	3.42144i
$949$	8.35152	−	8.35152i	0.271102	−	0.271102i
$950$		0			0
$951$			76.5578i			2.48256i
$952$	9.06914	+	42.1864i	0.293932	+	1.36727i
$953$		−	12.0232i		−	0.389468i	−0.980856	−	0.194734i	$-0.937616\pi$
$953$		−	12.0232i		−	0.389468i	0.980856	−	0.194734i	$-0.0623844\pi$
$954$	−40.5832	+	14.0090i	−1.31393	+	0.453557i
$955$		0			0
$956$	0.246294	+	0.314241i	0.00796571	+	0.0101633i
$957$	17.0190	+	17.0190i	0.550147	+	0.550147i
$958$	4.83295	−	9.92846i	0.156146	−	0.320774i
$959$	−11.1927			−0.361430
$960$		0			0
$961$	−4.71434			−0.152076
$962$	−0.440526	+	0.904985i	−0.0142031	+	0.0291779i
$963$	21.6966	+	21.6966i	0.699164	+	0.699164i
$964$	20.8203	+	26.5641i	0.670576	+	0.855573i
$965$		0			0
$966$	108.378	−	37.4110i	3.48699	−	1.20368i
$967$			43.8237i			1.40927i	0.709568	+	0.704637i	$0.248890\pi$
$967$			43.8237i			1.40927i	−0.709568	+	0.704637i	$0.751110\pi$
$968$	1.72791	+	8.03765i	0.0555373	+	0.258340i
$969$		−	69.8244i		−	2.24308i
$970$		0			0
$971$	35.9986	−	35.9986i	1.15525	−	1.15525i	0.169766	−	0.985484i	$-0.445699\pi$
$971$	35.9986	−	35.9986i	1.15525	−	1.15525i	0.985484	−	0.169766i	$-0.0543011\pi$
$972$	1.91734	−	15.8172i	0.0614986	−	0.507338i
$973$	6.92852	+	6.92852i	0.222118	+	0.222118i
$974$	35.1910	+	17.1302i	1.12759	+	0.548886i
$975$		0			0
$976$	2.69681	−	1.63176i	0.0863227	−	0.0522312i
$977$	−0.204913			−0.00655576			−0.00327788	−	0.999995i	$-0.501043\pi$
$977$	−0.204913			−0.00655576			−0.00327788	+	0.999995i	$0.501043\pi$
$978$	39.8239	+	19.3854i	1.27343	+	0.619876i
$979$	15.3301	+	15.3301i	0.489953	+	0.489953i
$980$		0			0
$981$	15.6272	−	15.6272i	0.498937	−	0.498937i
$982$	−7.70032	−	22.3074i	−0.245727	−	0.711858i
$983$			34.0060i			1.08462i	0.840177	+	0.542312i	$0.182451\pi$
$983$			34.0060i			1.08462i	−0.840177	+	0.542312i	$0.817549\pi$
$984$	18.9351	−	29.3058i	0.603629	−	0.934235i
$985$		0			0
$986$	−17.0218	+	5.87578i	−0.542085	+	0.187123i
$987$	−39.3581	+	39.3581i	−1.25278	+	1.25278i
$988$	8.71906	−	6.83377i	0.277390	−	0.217411i
$989$	−39.7501	−	39.7501i	−1.26398	−	1.26398i
$990$		0			0
$991$	13.8223			0.439079			0.219539	−	0.975604i	$-0.429545\pi$
$991$	13.8223			0.439079			0.219539	+	0.975604i	$0.429545\pi$
$992$	22.2889	+	18.5565i	0.707674	+	0.589171i
$993$	108.336			3.43794
$994$	14.0191	−	28.7998i	0.444658	−	0.913474i
$995$		0			0
$996$	64.7231	−	50.7283i	2.05083	−	1.60739i
$997$	6.37875	−	6.37875i	0.202017	−	0.202017i	−0.598847	−	0.800864i	$-0.704374\pi$
$997$	6.37875	−	6.37875i	0.202017	−	0.202017i	0.800864	+	0.598847i	$0.204374\pi$
$998$	47.3536	−	16.3460i	1.49895	−	0.517425i
$999$			6.61943i			0.209429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.f.301.4	yes	12
4.3	odd	2		1600.2.l.g.401.6		12
5.2	odd	4		400.2.q.f.349.1		12
5.3	odd	4		400.2.q.e.349.6		12
5.4	even	2		400.2.l.g.301.3	yes	12
16.5	even	4	inner	400.2.l.f.101.4	✓	12
16.11	odd	4		1600.2.l.g.1201.6		12
20.3	even	4		1600.2.q.e.849.1		12
20.7	even	4		1600.2.q.f.849.6		12
20.19	odd	2		1600.2.l.f.401.1		12
80.27	even	4		1600.2.q.e.49.1		12
80.37	odd	4		400.2.q.e.149.6		12
80.43	even	4		1600.2.q.f.49.6		12
80.53	odd	4		400.2.q.f.149.1		12
80.59	odd	4		1600.2.l.f.1201.1		12
80.69	even	4		400.2.l.g.101.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.4	✓	12	16.5	even	4	inner
400.2.l.f.301.4	yes	12	1.1	even	1	trivial
400.2.l.g.101.3	yes	12	80.69	even	4
400.2.l.g.301.3	yes	12	5.4	even	2
400.2.q.e.149.6		12	80.37	odd	4
400.2.q.e.349.6		12	5.3	odd	4
400.2.q.f.149.1		12	80.53	odd	4
400.2.q.f.349.1		12	5.2	odd	4
1600.2.l.f.401.1		12	20.19	odd	2
1600.2.l.f.1201.1		12	80.59	odd	4
1600.2.l.g.401.6		12	4.3	odd	2
1600.2.l.g.1201.6		12	16.11	odd	4
1600.2.q.e.49.1		12	80.27	even	4
1600.2.q.e.849.1		12	20.3	even	4
1600.2.q.f.49.6		12	80.43	even	4
1600.2.q.f.849.6		12	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.618969 + 1.27156i) q^{2} +(-2.16859 - 2.16859i) q^{3} +(-1.23375 - 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519i q^{7} +(2.76525 - 0.594467i) q^{8} +6.40553i q^{9} +O(q^{10})\)	\(q+(-0.618969 + 1.27156i) q^{2} +(-2.16859 - 2.16859i) q^{3} +(-1.23375 - 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519i q^{7} +(2.76525 - 0.594467i) q^{8} +6.40553i q^{9} +(2.01163 - 2.01163i) q^{11} +(-0.738111 + 6.08911i) q^{12} +(-0.794042 - 0.794042i) q^{13} +(4.20276 + 2.04581i) q^{14} +(-0.955702 + 3.88415i) q^{16} -4.61575 q^{17} +(-8.14504 - 3.96483i) q^{18} +(-3.48786 - 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +(1.31278 + 3.80306i) q^{22} +7.99801i q^{23} +(-7.28583 - 4.70753i) q^{24} +(1.50116 - 0.518188i) q^{26} +(7.38518 - 7.38518i) q^{27} +(-5.20276 + 4.07779i) q^{28} +(-1.95065 - 1.95065i) q^{29} -5.12695 q^{31} +(-4.34740 - 3.61941i) q^{32} -8.72480 q^{33} +(2.85701 - 5.86922i) q^{34} +(10.0831 - 7.90285i) q^{36} +(-0.448156 + 0.448156i) q^{37} +(6.59391 - 2.27616i) q^{38} +3.44390i q^{39} +4.02230i q^{41} +(-4.67754 - 13.5506i) q^{42} +(-4.97000 + 4.97000i) q^{43} +(-5.64841 - 0.684690i) q^{44} +(-10.1700 - 4.95052i) q^{46} +5.49112 q^{47} +(10.4956 - 6.35059i) q^{48} -3.92429 q^{49} +(10.0096 + 10.0096i) q^{51} +(-0.270264 + 2.22957i) q^{52} +(3.35125 - 3.35125i) q^{53} +(4.81954 + 13.9619i) q^{54} +(-1.96483 - 9.13968i) q^{56} +15.1274i q^{57} +(3.68777 - 1.27299i) q^{58} +(2.07673 - 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} +(3.17343 - 6.51925i) q^{62} +21.1715 q^{63} +(7.29322 - 3.28770i) q^{64} +(5.40038 - 11.0941i) q^{66} +(0.636094 + 0.636094i) q^{67} +(5.69470 + 7.26573i) q^{68} +(17.3444 - 17.3444i) q^{69} -6.85258i q^{71} +(3.80787 + 17.7129i) q^{72} +10.5177i q^{73} +(-0.292465 - 0.847255i) q^{74} +(-1.18714 + 9.79346i) q^{76} +(-6.64883 - 6.64883i) q^{77} +(-4.37914 - 2.13167i) q^{78} -17.3005 q^{79} -12.8142 q^{81} +(-5.11461 - 2.48968i) q^{82} +(-9.48015 - 9.48015i) q^{83} +(20.1257 + 2.43960i) q^{84} +(-3.24340 - 9.39596i) q^{86} +8.46030i q^{87} +(4.36682 - 6.75852i) q^{88} +7.62073i q^{89} +(-2.62446 + 2.62446i) q^{91} +(12.5898 - 9.86757i) q^{92} +(11.1182 + 11.1182i) q^{93} +(-3.39883 + 6.98231i) q^{94} +(1.57871 + 17.2767i) q^{96} -0.709082 q^{97} +(2.42901 - 4.98999i) q^{98} +(12.8856 + 12.8856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8	\( 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8} - 2 q^{11} - 8 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{16} + 8 q^{17} - 18 q^{18} - 14 q^{19} - 20 q^{21} - 2 q^{22} - 14 q^{24} - 16 q^{26} + 10 q^{27} - 26 q^{28} - 4 q^{31} + 16 q^{32} - 28 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} - 10 q^{38} - 10 q^{42} - 44 q^{44} - 10 q^{46} - 8 q^{47} + 28 q^{48} + 4 q^{49} + 10 q^{51} + 12 q^{52} + 16 q^{53} + 10 q^{54} + 6 q^{56} + 60 q^{58} + 20 q^{59} + 4 q^{61} + 18 q^{62} + 8 q^{63} + 38 q^{64} + 32 q^{66} - 50 q^{67} + 60 q^{68} + 14 q^{72} + 10 q^{74} + 60 q^{76} + 8 q^{77} - 4 q^{78} + 12 q^{79} - 8 q^{81} - 42 q^{82} + 2 q^{83} + 34 q^{84} + 6 q^{86} - 30 q^{88} + 2 q^{92} + 44 q^{93} + 32 q^{94} - 34 q^{96} - 64 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8 - 2 * q^11 - 8 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^16 + 8 * q^17 - 18 * q^18 - 14 * q^19 - 20 * q^21 - 2 * q^22 - 14 * q^24 - 16 * q^26 + 10 * q^27 - 26 * q^28 - 4 * q^31 + 16 * q^32 - 28 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 - 10 * q^38 - 10 * q^42 - 44 * q^44 - 10 * q^46 - 8 * q^47 + 28 * q^48 + 4 * q^49 + 10 * q^51 + 12 * q^52 + 16 * q^53 + 10 * q^54 + 6 * q^56 + 60 * q^58 + 20 * q^59 + 4 * q^61 + 18 * q^62 + 8 * q^63 + 38 * q^64 + 32 * q^66 - 50 * q^67 + 60 * q^68 + 14 * q^72 + 10 * q^74 + 60 * q^76 + 8 * q^77 - 4 * q^78 + 12 * q^79 - 8 * q^81 - 42 * q^82 + 2 * q^83 + 34 * q^84 + 6 * q^86 - 30 * q^88 + 2 * q^92 + 44 * q^93 + 32 * q^94 - 34 * q^96 - 64 * q^98 + 12 * q^99

Introduction

L-functions

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