LMFDB - Embedded newform 400.2.q.e.349.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(149,400)]

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, 2]))

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

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

chi := DirichletCharacter("400.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, 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:	$3.19401608085$
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			349.6
Root			$0.618969 + 1.27156i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.e.149.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27156 + 0.618969i) q^{2} +(2.16859 - 2.16859i) q^{3} +(1.23375 + 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519 q^{7} +(0.594467 + 2.76525i) q^{8} -6.40553i q^{9} +O(q^{10})$	\(q+(1.27156 + 0.618969i) q^{2} +(2.16859 - 2.16859i) q^{3} +(1.23375 + 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519 q^{7} +(0.594467 + 2.76525i) q^{8} -6.40553i q^{9} +(2.01163 - 2.01163i) q^{11} +(6.08911 + 0.738111i) q^{12} +(0.794042 - 0.794042i) q^{13} +(-4.20276 - 2.04581i) q^{14} +(-0.955702 + 3.88415i) q^{16} +4.61575i q^{17} +(3.96483 - 8.14504i) q^{18} +(3.48786 + 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +(3.80306 - 1.31278i) q^{22} -7.99801 q^{23} +(7.28583 + 4.70753i) q^{24} +(1.50116 - 0.518188i) q^{26} +(-7.38518 - 7.38518i) q^{27} +(-4.07779 - 5.20276i) q^{28} +(1.95065 + 1.95065i) q^{29} -5.12695 q^{31} +(-3.61941 + 4.34740i) q^{32} -8.72480i q^{33} +(-2.85701 + 5.86922i) q^{34} +(10.0831 - 7.90285i) q^{36} +(0.448156 + 0.448156i) q^{37} +(2.27616 + 6.59391i) q^{38} -3.44390i q^{39} +4.02230i q^{41} +(-13.5506 + 4.67754i) q^{42} +(-4.97000 - 4.97000i) q^{43} +(5.64841 + 0.684690i) q^{44} +(-10.1700 - 4.95052i) q^{46} -5.49112i q^{47} +(6.35059 + 10.4956i) q^{48} +3.92429 q^{49} +(10.0096 + 10.0096i) q^{51} +(2.22957 + 0.270264i) q^{52} +(3.35125 + 3.35125i) q^{53} +(-4.81954 - 13.9619i) q^{54} +(-1.96483 - 9.13968i) q^{56} +15.1274 q^{57} +(1.27299 + 3.68777i) q^{58} +(-2.07673 + 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} +(-6.51925 - 3.17343i) q^{62} +21.1715i q^{63} +(-7.29322 + 3.28770i) q^{64} +(5.40038 - 11.0941i) q^{66} +(0.636094 - 0.636094i) q^{67} +(-7.26573 + 5.69470i) q^{68} +(-17.3444 + 17.3444i) q^{69} -6.85258i q^{71} +(17.7129 - 3.80787i) q^{72} -10.5177 q^{73} +(0.292465 + 0.847255i) q^{74} +(-1.18714 + 9.79346i) q^{76} +(-6.64883 + 6.64883i) q^{77} +(2.13167 - 4.37914i) q^{78} +17.3005 q^{79} -12.8142 q^{81} +(-2.48968 + 5.11461i) q^{82} +(9.48015 - 9.48015i) q^{83} +(-20.1257 - 2.43960i) q^{84} +(-3.24340 - 9.39596i) q^{86} +8.46030 q^{87} +(6.75852 + 4.36682i) q^{88} -7.62073i q^{89} +(-2.62446 + 2.62446i) q^{91} +(-9.86757 - 12.5898i) q^{92} +(-11.1182 + 11.1182i) q^{93} +(3.39883 - 6.98231i) q^{94} +(1.57871 + 17.2767i) q^{96} +0.709082i q^{97} +(4.98999 + 2.42901i) q^{98} +(-12.8856 - 12.8856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8	$ 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26} - 10 q^{27} + 10 q^{28} - 4 q^{31} - 2 q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 28 q^{38} - 10 q^{42} + 44 q^{44} - 10 q^{46} + 58 q^{48} - 4 q^{49} + 10 q^{51} + 16 q^{53} - 10 q^{54} + 6 q^{56} + 16 q^{57} - 4 q^{58} - 20 q^{59} + 4 q^{61} - 22 q^{62} - 38 q^{64} + 32 q^{66} - 50 q^{67} - 50 q^{68} + 54 q^{72} - 40 q^{73} - 10 q^{74} + 60 q^{76} + 8 q^{77} + 48 q^{78} - 12 q^{79} - 8 q^{81} + 12 q^{82} - 2 q^{83} - 34 q^{84} + 6 q^{86} + 64 q^{87} - 56 q^{88} - 50 q^{92} - 44 q^{93} - 32 q^{94} - 34 q^{96} + 30 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * 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 $

$2$	1.27156	+	0.618969i	0.899132	+	0.437677i
$2$	1.27156	+	0.618969i	0.899132	+	0.437677i
$3$	2.16859	−	2.16859i	1.25203	−	1.25203i	0.297227	−	0.954807i	$-0.403938\pi$
$3$	2.16859	−	2.16859i	1.25203	−	1.25203i	0.954807	−	0.297227i	$-0.0960617\pi$
$4$	1.23375	+	1.57412i	0.616877	+	0.787060i
$5$		0			0
$5$		0			0
$6$	4.09979	−	1.41521i	1.67373	−	0.577757i
$7$	−3.30519			−1.24924			−0.624622	−	0.780927i	$-0.714747\pi$
$7$	−3.30519			−1.24924			−0.624622	+	0.780927i	$0.714747\pi$
$8$	0.594467	+	2.76525i	0.210176	+	0.977664i
$9$		−	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	$0.108908\pi$
$12$	6.08911	+	0.738111i	1.75778	+	0.213074i
$13$	0.794042	−	0.794042i	0.220228	−	0.220228i	−0.588367	−	0.808594i	$-0.700229\pi$
$13$	0.794042	−	0.794042i	0.220228	−	0.220228i	0.808594	+	0.588367i	$0.200229\pi$
$14$	−4.20276	−	2.04581i	−1.12324	−	0.546766i
$15$		0			0
$16$	−0.955702	+	3.88415i	−0.238926	+	0.971038i
$17$			4.61575i			1.11948i	0.828667	+	0.559741i	$0.189100\pi$
$17$			4.61575i			1.11948i	−0.828667	+	0.559741i	$0.810900\pi$
$18$	3.96483	−	8.14504i	0.934518	−	1.91981i
$19$	3.48786	+	3.48786i	0.800169	+	0.800169i	0.983122	−	0.182953i	$-0.0585655\pi$
$19$	3.48786	+	3.48786i	0.800169	+	0.800169i	−0.182953	+	0.983122i	$0.558566\pi$
$20$		0			0
$21$	−7.16759	+	7.16759i	−1.56410	+	1.56410i
$22$	3.80306	−	1.31278i	0.810815	−	0.279886i
$23$	−7.99801			−1.66770			−0.833850	−	0.551991i	$-0.813868\pi$
$23$	−7.99801			−1.66770			−0.833850	+	0.551991i	$0.813868\pi$
$24$	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
$28$	−4.07779	−	5.20276i	−0.770630	−	0.983230i
$29$	1.95065	+	1.95065i	0.362227	+	0.362227i	0.864632	−	0.502406i	$-0.167552\pi$
$29$	1.95065	+	1.95065i	0.362227	+	0.362227i	−0.502406	+	0.864632i	$0.667552\pi$
$30$		0			0
$31$	−5.12695			−0.920828			−0.460414	−	0.887704i	$-0.652299\pi$
$31$	−5.12695			−0.920828			−0.460414	+	0.887704i	$0.652299\pi$
$32$	−3.61941	+	4.34740i	−0.639827	+	0.768519i
$33$		−	8.72480i		−	1.51879i
$34$	−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	$-0.233409\pi$
$37$	0.448156	+	0.448156i	0.0736764	+	0.0736764i	−0.669308	+	0.742985i	$0.733409\pi$
$38$	2.27616	+	6.59391i	0.369242	+	1.06967i
$39$		−	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	$0.898301\pi$
$42$	−13.5506	+	4.67754i	−2.09090	+	0.721760i
$43$	−4.97000	−	4.97000i	−0.757918	−	0.757918i	0.218025	−	0.975943i	$-0.430039\pi$
$43$	−4.97000	−	4.97000i	−0.757918	−	0.757918i	−0.975943	+	0.218025i	$0.930039\pi$
$44$	5.64841	+	0.684690i	0.851530	+	0.103221i
$45$		0			0
$46$	−10.1700	−	4.95052i	−1.49948	−	0.729915i
$47$		−	5.49112i		−	0.800962i	−0.916305	−	0.400481i	$-0.868843\pi$
$47$		−	5.49112i		−	0.800962i	0.916305	−	0.400481i	$-0.131157\pi$
$48$	6.35059	+	10.4956i	0.916629	+	1.51491i
$49$	3.92429			0.560612
$50$		0			0
$51$	10.0096	+	10.0096i	1.40163	+	1.40163i
$52$	2.22957	+	0.270264i	0.309186	+	0.0374789i
$53$	3.35125	+	3.35125i	0.460330	+	0.460330i	0.898763	−	0.438434i	$-0.144467\pi$
$53$	3.35125	+	3.35125i	0.460330	+	0.460330i	−0.438434	+	0.898763i	$0.644467\pi$
$54$	−4.81954	−	13.9619i	−0.655856	−	1.89998i
$55$		0			0
$56$	−1.96483	−	9.13968i	−0.262561	−	1.22134i
$57$	15.1274			2.00368
$58$	1.27299	+	3.68777i	0.167151	+	0.484228i
$59$	−2.07673	+	2.07673i	−0.270367	+	0.270367i	−0.829248	−	0.558881i	$-0.811231\pi$
$59$	−2.07673	+	2.07673i	−0.270367	+	0.270367i	0.558881	+	0.829248i	$0.311231\pi$
$60$		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	$0.766065\pi$
$62$	−6.51925	−	3.17343i	−0.827946	−	0.403026i
$63$			21.1715i			2.66736i
$64$	−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	−0.667183	−	0.744894i	$-0.732500\pi$
$67$	0.636094	−	0.636094i	0.0777112	−	0.0777112i	0.744894	+	0.667183i	$0.232500\pi$
$68$	−7.26573	+	5.69470i	−0.881100	+	0.690583i
$69$	−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	$-0.133295\pi$
$72$	17.7129	−	3.80787i	2.08748	−	0.448762i
$73$	−10.5177			−1.23101			−0.615504	−	0.788134i	$-0.711047\pi$
$73$	−10.5177			−1.23101			−0.615504	+	0.788134i	$0.711047\pi$
$74$	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
$78$	2.13167	−	4.37914i	0.241364	−	0.495840i
$79$	17.3005			1.94646			0.973230	−	0.229833i	$-0.0738179\pi$
$79$	17.3005			1.94646			0.973230	+	0.229833i	$0.0738179\pi$
$80$		0			0
$81$	−12.8142			−1.42380
$82$	−2.48968	+	5.11461i	−0.274939	+	0.564814i
$83$	9.48015	−	9.48015i	1.04058	−	1.04058i	0.0414412	−	0.999141i	$-0.486805\pi$
$83$	9.48015	−	9.48015i	1.04058	−	1.04058i	0.999141	−	0.0414412i	$-0.0131949\pi$
$84$	−20.1257	−	2.43960i	−2.19589	−	0.266182i
$85$		0			0
$86$	−3.24340	−	9.39596i	−0.349745	−	1.01319i
$87$	8.46030			0.907040
$88$	6.75852	+	4.36682i	0.720460	+	0.465505i
$89$		−	7.62073i		−	0.807796i	−0.914804	−	0.403898i	$-0.867655\pi$
$89$		−	7.62073i		−	0.807796i	0.914804	−	0.403898i	$-0.132345\pi$
$90$		0			0
$91$	−2.62446	+	2.62446i	−0.275118	+	0.275118i
$92$	−9.86757	−	12.5898i	−1.02877	−	1.31258i
$93$	−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
$97$			0.709082i			0.0719964i	0.999352	+	0.0359982i	$0.0114611\pi$
$97$			0.709082i			0.0719964i	−0.999352	+	0.0359982i	$0.988539\pi$
$98$	4.98999	+	2.42901i	0.504065	+	0.245367i
$99$	−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	$0.107253\pi$
$102$	6.53225	+	18.9236i	0.646789	+	1.87371i
$103$	15.9410			1.57072			0.785359	−	0.619040i	$-0.212478\pi$
$103$	15.9410			1.57072			0.785359	+	0.619040i	$0.212478\pi$
$104$	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	$-0.324377\pi$
$107$	−3.38717	−	3.38717i	−0.327450	−	0.327450i	−0.851616	+	0.524166i	$0.824377\pi$
$108$	2.51366	−	20.7367i	0.241877	−	1.99539i
$109$	2.43964	+	2.43964i	0.233675	+	0.233675i	0.814225	−	0.580550i	$-0.197162\pi$
$109$	2.43964	+	2.43964i	0.233675	+	0.233675i	−0.580550	+	0.814225i	$0.697162\pi$
$110$		0			0
$111$	1.94373			0.184491
$112$	3.15878	−	12.8379i	0.298477	−	1.21306i
$113$		−	1.09801i		−	0.103292i	−0.998665	−	0.0516461i	$-0.983553\pi$
$113$		−	1.09801i		−	0.103292i	0.998665	−	0.0516461i	$-0.0164468\pi$
$114$	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
$118$	−3.92612	+	1.35526i	−0.361429	+	0.124762i
$119$		−	15.2559i		−	1.39851i
$120$		0			0
$121$			2.90666i			0.264242i
$122$	−0.363632	−	1.05342i	−0.0329217	−	0.0953723i
$123$	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
$127$		−	1.51159i		−	0.134131i	−0.997749	−	0.0670657i	$-0.978636\pi$
$127$		−	1.51159i		−	0.134131i	0.997749	−	0.0670657i	$-0.0213637\pi$
$128$	−11.3088	−	0.333758i	−0.999565	−	0.0295003i
$129$	−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	$0.942826\pi$
$132$	13.7339	−	10.7643i	1.19538	−	0.936908i
$133$	−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
$137$	−3.38639			−0.289318			−0.144659	−	0.989482i	$-0.546209\pi$
$137$	−3.38639			−0.289318			−0.144659	+	0.989482i	$0.546209\pi$
$138$	−32.7901	+	11.3189i	−2.79128	+	0.963525i
$139$	2.09626	−	2.09626i	0.177802	−	0.177802i	−0.612595	−	0.790397i	$-0.709874\pi$
$139$	2.09626	−	2.09626i	0.177802	−	0.177802i	0.790397	+	0.612595i	$0.209874\pi$
$140$		0			0
$141$	−11.9080	−	11.9080i	−1.00283	−	1.00283i
$142$	4.24154	−	8.71350i	0.355942	−	0.731221i
$143$		−	3.19464i		−	0.267149i
$144$	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
$148$	−0.152537	+	1.25837i	−0.0125384	+	0.103437i
$149$	2.45247	−	2.45247i	0.200915	−	0.200915i	−0.599477	−	0.800392i	$-0.704625\pi$
$149$	2.45247	−	2.45247i	0.200915	−	0.200915i	0.800392	+	0.599477i	$0.204625\pi$
$150$		0			0
$151$		−	1.11727i		−	0.0909222i	−0.998966	−	0.0454611i	$-0.985524\pi$
$151$		−	1.11727i		−	0.0909222i	0.998966	−	0.0454611i	$-0.0144757\pi$
$152$	−7.57138	+	11.7182i	−0.614120	+	0.950472i
$153$	29.5663			2.39029
$154$	−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	−0.314839	+	0.949145i	$0.601950\pi$
$157$	−15.8377	+	15.8377i	−1.26398	+	1.26398i	−0.949145	+	0.314839i	$0.898050\pi$
$158$	21.9987	+	10.7085i	1.75012	+	0.851922i
$159$	14.5349			1.15270
$160$		0			0
$161$	26.4349			2.08337
$162$	−16.2941	−	7.93160i	−1.28019	−	0.623166i
$163$	−7.22102	+	7.22102i	−0.565594	+	0.565594i	−0.930891	−	0.365297i	$-0.880967\pi$
$163$	−7.22102	+	7.22102i	−0.565594	+	0.565594i	0.365297	+	0.930891i	$0.380967\pi$
$164$	−6.33158	+	4.96253i	−0.494413	+	0.387508i
$165$		0			0
$166$	17.9226	−	6.18671i	1.39106	−	0.480182i
$167$	−13.2304			−1.02380			−0.511901	−	0.859044i	$-0.671059\pi$
$167$	−13.2304			−1.02380			−0.511901	+	0.859044i	$0.671059\pi$
$168$	−24.0811	−	15.5593i	−1.85790	−	1.20043i
$169$			11.7390i			0.903000i
$170$		0			0
$171$	22.3416	−	22.3416i	1.70850	−	1.70850i
$172$	1.69162	−	13.9551i	0.128984	−	1.06407i
$173$	11.7503	−	11.7503i	0.893355	−	0.893355i	−0.101482	−	0.994837i	$-0.532359\pi$
$173$	11.7503	−	11.7503i	0.893355	−	0.893355i	0.994837	+	0.101482i	$0.0323585\pi$
$174$	10.7578	+	5.23667i	0.815548	+	0.396991i
$175$		0			0
$176$	5.89097	+	9.73601i	0.444048	+	0.733879i
$177$			9.00712i			0.677017i
$178$	4.71700	−	9.69026i	0.353554	−	0.726315i
$179$	−4.84732	−	4.84732i	−0.362306	−	0.362306i	0.502355	−	0.864661i	$-0.332467\pi$
$179$	−4.84732	−	4.84732i	−0.362306	−	0.362306i	−0.864661	+	0.502355i	$0.832467\pi$
$180$		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	$0.0624240\pi$
$182$	−4.96163	+	1.71271i	−0.367781	+	0.126955i
$183$	−2.41671			−0.178648
$184$	−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
$188$	8.64368	−	6.77469i	0.630405	−	0.494095i
$189$	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	$0.407224\pi$
$192$	−8.68632	+	22.9456i	−0.626881	+	1.65596i
$193$			20.8617i			1.50166i	0.660496	+	0.750829i	$0.270346\pi$
$193$			20.8617i			1.50166i	−0.660496	+	0.750829i	$0.729654\pi$
$194$	−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	$-0.216631\pi$
$197$	2.07707	+	2.07707i	0.147985	+	0.147985i	−0.629232	+	0.777217i	$0.716631\pi$
$198$	−8.40907	−	24.3606i	−0.597606	−	1.73123i
$199$			23.2807i			1.65033i	0.564893	+	0.825164i	$0.308917\pi$
$199$			23.2807i			1.65033i	−0.564893	+	0.825164i	$0.691083\pi$
$200$		0			0
$201$		−	2.75885i		−	0.194594i
$202$	11.6499	−	4.02144i	0.819684	−	0.282948i
$203$	−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
$207$			51.2315i			3.56083i
$208$	2.32531	+	3.84305i	0.161231	+	0.266467i
$209$	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	$0.789082\pi$
$212$	−1.14065	+	9.40989i	−0.0783401	+	0.646274i
$213$	−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
$217$	16.9456			1.15034
$218$	1.59210	+	4.61222i	0.107830	+	0.312379i
$219$	−22.8086	+	22.8086i	−1.54126	+	1.54126i
$220$		0			0
$221$	3.66510	+	3.66510i	0.246541	+	0.246541i
$222$	2.47158	+	1.20311i	0.165882	+	0.0807474i
$223$		−	10.9088i		−	0.730507i	−0.930908	−	0.365253i	$-0.880982\pi$
$223$		−	10.9088i		−	0.730507i	0.930908	−	0.365253i	$-0.119018\pi$
$224$	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	−0.206275	−	0.978494i	$-0.566134\pi$
$227$	11.6347	−	11.6347i	0.772220	−	0.772220i	0.978494	+	0.206275i	$0.0661340\pi$
$228$	18.6635	+	23.8124i	1.23602	+	1.57701i
$229$	1.60760	−	1.60760i	0.106233	−	0.106233i	−0.651992	−	0.758226i	$-0.726067\pi$
$229$	1.60760	−	1.60760i	0.106233	−	0.106233i	0.758226	+	0.651992i	$0.226067\pi$
$230$		0			0
$231$			28.8371i			1.89734i
$232$	−4.23444	+	6.55363i	−0.278005	+	0.430267i
$233$	23.8100			1.55985			0.779924	−	0.625875i	$-0.215258\pi$
$233$	23.8100			1.55985			0.779924	+	0.625875i	$0.215258\pi$
$234$	−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
$238$	9.44295	−	19.3989i	0.612095	−	1.25744i
$239$	0.199630			0.0129130			0.00645649	−	0.999979i	$-0.497945\pi$
$239$	0.199630			0.0129130			0.00645649	+	0.999979i	$0.497945\pi$
$240$		0			0
$241$	−16.8755			−1.08705			−0.543525	−	0.839393i	$-0.682911\pi$
$241$	−16.8755			−1.08705			−0.543525	+	0.839393i	$0.682911\pi$
$242$	−1.79914	+	3.69601i	−0.115653	+	0.237589i
$243$	−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
$247$	5.53901			0.352439
$248$	−3.04780	−	14.1773i	−0.193536	−	0.900260i
$249$		−	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	$0.337773\pi$
$252$	−33.3265	+	26.1204i	−2.09937	+	1.64543i
$253$	−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
$257$		−	19.8360i		−	1.23733i	−0.785653	−	0.618667i	$-0.787673\pi$
$257$		−	19.8360i		−	1.23733i	0.785653	−	0.618667i	$-0.212327\pi$
$258$	−27.4095	−	13.3423i	−1.70644	−	0.830658i
$259$	−1.48124	−	1.48124i	−0.0920399	−	0.0920399i
$260$		0			0
$261$	12.4949	−	12.4949i	0.773418	−	0.773418i
$262$	−6.01471	−	17.4243i	−0.371590	−	1.07648i
$263$	7.14438			0.440542			0.220271	−	0.975439i	$-0.429306\pi$
$263$	7.14438			0.440542			0.220271	+	0.975439i	$0.429306\pi$
$264$	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
$268$	1.78607	+	0.216504i	0.109102	+	0.0132251i
$269$	−21.7716	−	21.7716i	−1.32744	−	1.32744i	−0.907596	−	0.419844i	$-0.862085\pi$
$269$	−21.7716	−	21.7716i	−1.32744	−	1.32744i	−0.419844	−	0.907596i	$-0.637915\pi$
$270$		0			0
$271$	−4.71328			−0.286312			−0.143156	−	0.989700i	$-0.545725\pi$
$271$	−4.71328			−0.286312			−0.143156	+	0.989700i	$0.545725\pi$
$272$	−17.9283	−	4.41128i	−1.08706	−	0.267473i
$273$			11.3827i			0.688915i
$274$	−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	0.964247	+	0.265006i	$0.0853739\pi$
$277$	20.4588	+	20.4588i	1.22925	+	1.22925i	0.265006	+	0.964247i	$0.414626\pi$
$278$	3.96304	−	1.36801i	0.237687	−	0.0820476i
$279$			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	$0.823542\pi$
$282$	−7.77108	−	22.5124i	−0.462761	−	1.34059i
$283$	−18.1525	−	18.1525i	−1.07906	−	1.07906i	−0.996594	−	0.0824607i	$-0.973722\pi$
$283$	−18.1525	−	18.1525i	−1.07906	−	1.07906i	−0.0824607	−	0.996594i	$-0.526278\pi$
$284$	10.7868	−	8.45440i	0.640077	−	0.501676i
$285$		0			0
$286$	1.97739	−	4.06220i	0.116925	−	0.240203i
$287$		−	13.2945i		−	0.784747i
$288$	27.8474	+	23.1842i	1.64092	+	1.36614i
$289$	−4.30511			−0.253242
$290$		0			0
$291$	1.53771	+	1.53771i	0.0901419	+	0.0901419i
$292$	−12.9763	−	16.5562i	−0.759380	−	0.968877i
$293$	0.638480	+	0.638480i	0.0373004	+	0.0373004i	0.725511	−	0.688211i	$-0.241603\pi$
$293$	0.638480	+	0.638480i	0.0373004	+	0.0373004i	−0.688211	+	0.725511i	$0.741603\pi$
$294$	16.0887	−	5.55369i	0.938314	−	0.323898i
$295$		0			0
$296$	−0.972850	+	1.50568i	−0.0565458	+	0.0875157i
$297$	−29.7126			−1.72410
$298$	4.63649	−	1.60047i	0.268584	−	0.0927130i
$299$	−6.35076	+	6.35076i	−0.367274	+	0.367274i
$300$		0			0
$301$	16.4268	+	16.4268i	0.946825	+	0.946825i
$302$	0.691557	−	1.42068i	0.0397946	−	0.0817511i
$303$		−	26.7266i		−	1.53540i
$304$	−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	−0.824280	−	0.566182i	$-0.808420\pi$
$307$	−4.52224	+	4.52224i	−0.258098	+	0.258098i	0.566182	+	0.824280i	$0.308420\pi$
$308$	−18.6691	−	2.26303i	−1.06377	−	0.128948i
$309$	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	$-0.130924\pi$
$312$	9.52324	−	2.04728i	0.539147	−	0.115904i
$313$	11.9204			0.673779			0.336889	−	0.941544i	$-0.390625\pi$
$313$	11.9204			0.673779			0.336889	+	0.941544i	$0.390625\pi$
$314$	−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	−0.999963	−	0.00855359i	$-0.997277\pi$
$317$	−17.6516	+	17.6516i	−0.991410	+	0.991410i	0.00855359	+	0.999963i	$0.497277\pi$
$318$	18.4821	+	8.99669i	1.03643	+	0.504509i
$319$	7.84798			0.439403
$320$		0			0
$321$	−14.6907			−0.819958
$322$	33.6137	+	16.3624i	1.87322	+	0.911842i
$323$	−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
$327$	10.5811			0.585138
$328$	−11.1227	+	2.39112i	−0.614146	+	0.132028i
$329$			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	$0.827090\pi$
$332$	26.6191	+	3.22671i	1.46091	+	0.177089i
$333$	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
$337$		−	24.3167i		−	1.32462i	−0.749231	−	0.662308i	$-0.769577\pi$
$337$		−	24.3167i		−	1.32462i	0.749231	−	0.662308i	$-0.230423\pi$
$338$	−7.26608	+	14.9269i	−0.395223	+	0.811916i
$339$	−2.38113	−	2.38113i	−0.129325	−	0.129325i
$340$		0			0
$341$	−10.3136	+	10.3136i	−0.558510	+	0.558510i
$342$	42.2375	−	14.5800i	2.28394	−	0.788396i
$343$	10.1658			0.548903
$344$	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	$-0.0206387\pi$
$347$	17.3818	+	17.3818i	0.933106	+	0.933106i	−0.0647931	+	0.997899i	$0.520639\pi$
$348$	10.4379	+	13.3175i	0.559532	+	0.713894i
$349$	0.773103	+	0.773103i	0.0413832	+	0.0413832i	0.727496	−	0.686112i	$-0.240684\pi$
$349$	0.773103	+	0.773103i	0.0413832	+	0.0413832i	−0.686112	+	0.727496i	$0.740684\pi$
$350$		0			0
$351$	−11.7283			−0.626010
$352$	1.46445	+	16.0263i	0.0780556	+	0.854204i
$353$		−	13.3720i		−	0.711720i	−0.934539	−	0.355860i	$-0.884188\pi$
$353$		−	13.3720i		−	0.711720i	0.934539	−	0.355860i	$-0.115812\pi$
$354$	−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
$358$	−3.16334	−	9.16403i	−0.167188	−	0.484334i
$359$		−	28.5413i		−	1.50635i	−0.657818	−	0.753177i	$-0.728520\pi$
$359$		−	28.5413i		−	1.50635i	0.657818	−	0.753177i	$-0.271480\pi$
$360$		0			0
$361$			5.33027i			0.280541i
$362$	19.9909	−	6.90069i	1.05070	−	0.362692i
$363$	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
$367$		−	0.909186i		−	0.0474591i	−0.999718	−	0.0237296i	$-0.992446\pi$
$367$		−	0.909186i		−	0.0474591i	0.999718	−	0.0237296i	$-0.00755406\pi$
$368$	7.64371	−	31.0655i	0.398456	−	1.61940i
$369$	25.7649			1.34127
$370$		0			0
$371$	−11.0765	−	11.0765i	−0.575064	−	0.575064i
$372$	−31.2186	−	3.78426i	−1.61861	−	0.196205i
$373$	26.5010	+	26.5010i	1.37217	+	1.37217i	0.857223	+	0.514946i	$0.172188\pi$
$373$	26.5010	+	26.5010i	1.37217	+	1.37217i	0.514946	+	0.857223i	$0.327812\pi$
$374$	6.05947	+	17.5540i	0.313328	+	0.907694i
$375$		0			0
$376$	15.1843	−	3.26429i	0.783071	−	0.168343i
$377$	3.09780			0.159545
$378$	15.9295	+	46.1469i	0.819324	+	2.37354i
$379$	−1.23724	+	1.23724i	−0.0635529	+	0.0635529i	−0.738169	−	0.674616i	$-0.764309\pi$
$379$	−1.23724	+	1.23724i	−0.0635529	+	0.0635529i	0.674616	+	0.738169i	$0.264309\pi$
$380$		0			0
$381$	−3.27800	−	3.27800i	−0.167937	−	0.167937i
$382$	10.0996	+	4.91628i	0.516742	+	0.251539i
$383$			15.7161i			0.803057i	0.915846	+	0.401529i	$0.131521\pi$
$383$			15.7161i			0.803057i	−0.915846	+	0.401529i	$0.868479\pi$
$384$	−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
$388$	−1.11618	+	0.874833i	−0.0566655	+	0.0444129i
$389$	−16.2799	+	16.2799i	−0.825423	+	0.825423i	−0.986880	−	0.161457i	$-0.948381\pi$
$389$	−16.2799	+	16.2799i	−0.825423	+	0.825423i	0.161457	+	0.986880i	$0.448381\pi$
$390$		0			0
$391$		−	36.9168i		−	1.86696i
$392$	2.33286	+	10.8516i	0.117827	+	0.548090i
$393$	−39.9740			−2.01642
$394$	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	−0.162292	+	0.986743i	$0.551889\pi$
$397$	−22.8944	+	22.8944i	−1.14903	+	1.14903i	−0.986743	+	0.162292i	$0.948111\pi$
$398$	−14.4101	+	29.6030i	−0.722311	+	1.48386i
$399$	−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	$0.370437\pi$
$402$	1.70764	−	3.50805i	0.0851694	−	0.174966i
$403$	−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
$407$	1.80305			0.0893740
$408$	−21.7288	+	33.6296i	−1.07573	+	1.66491i
$409$		−	10.0220i		−	0.495557i	−0.968817	−	0.247779i	$-0.920299\pi$
$409$		−	10.0220i		−	0.495557i	0.968817	−	0.247779i	$-0.0797006\pi$
$410$		0			0
$411$	−7.34367	+	7.34367i	−0.362236	+	0.362236i
$412$	19.6673	+	25.0931i	0.968940	+	1.23625i
$413$	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
$417$		−	9.09182i		−	0.445228i
$418$	17.8433	+	8.68573i	0.872745	+	0.424833i
$419$	−14.4998	−	14.4998i	−0.708362	−	0.708362i	0.257829	−	0.966191i	$-0.416993\pi$
$419$	−14.4998	−	14.4998i	−0.708362	−	0.708362i	−0.966191	+	0.257829i	$0.916993\pi$
$420$		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	$0.102154\pi$
$422$	−1.64184	−	4.75632i	−0.0799235	−	0.231534i
$423$	−35.1735			−1.71020
$424$	−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
$428$	1.15288	−	9.51075i	0.0557263	−	0.459720i
$429$	−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	$0.811357\pi$
$432$	35.7432	−	21.6271i	1.71970	−	1.04054i
$433$			14.5895i			0.701128i	0.936539	+	0.350564i	$0.114010\pi$
$433$			14.5895i			0.701128i	−0.936539	+	0.350564i	$0.885990\pi$
$434$	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
$438$	−43.1205	+	14.8848i	−2.06038	+	0.711223i
$439$			5.70179i			0.272131i	0.990700	+	0.136066i	$0.0434458\pi$
$439$			5.70179i			0.272131i	−0.990700	+	0.136066i	$0.956554\pi$
$440$		0			0
$441$		−	25.1371i		−	1.19701i
$442$	2.39183	+	6.92899i	0.113768	+	0.329578i
$443$	−5.03375	−	5.03375i	−0.239161	−	0.239161i	0.577342	−	0.816503i	$-0.304090\pi$
$443$	−5.03375	−	5.03375i	−0.239161	−	0.239161i	−0.816503	+	0.577342i	$0.804090\pi$
$444$	2.39808	+	3.05966i	0.113808	+	0.145205i
$445$		0			0
$446$	6.75221	−	13.8712i	0.319726	−	0.656822i
$447$		−	10.6368i		−	0.503104i
$448$	24.1055	−	10.8665i	1.13888	−	0.513392i
$449$	−22.2502			−1.05005			−0.525025	−	0.851087i	$-0.675944\pi$
$449$	−22.2502			−1.05005			−0.525025	+	0.851087i	$0.675944\pi$
$450$		0			0
$451$	8.09139	+	8.09139i	0.381009	+	0.381009i
$452$	1.72840	−	1.35468i	0.0812971	−	0.0637186i
$453$	−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
$457$	−8.92927			−0.417694			−0.208847	−	0.977948i	$-0.566971\pi$
$457$	−8.92927			−0.417694			−0.208847	+	0.977948i	$0.566971\pi$
$458$	3.03923	−	1.04912i	0.142014	−	0.0490219i
$459$	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	$0.836472\pi$
$462$	−17.8493	+	36.6683i	−0.830424	+	1.70596i
$463$			31.7058i			1.47349i	0.676168	+	0.736747i	$0.263639\pi$
$463$			31.7058i			1.47349i	−0.676168	+	0.736747i	$0.736361\pi$
$464$	−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	−0.164207	−	0.986426i	$-0.552506\pi$
$467$	17.7683	−	17.7683i	0.822219	−	0.822219i	0.986426	+	0.164207i	$0.0525065\pi$
$468$	1.73119	−	14.2816i	0.0800241	−	0.660166i
$469$	−2.10241	+	2.10241i	−0.0970803	+	0.0970803i
$470$		0			0
$471$			68.6907i			3.16510i
$472$	−6.97721	−	4.50812i	−0.321152	−	0.207503i
$473$	−19.9956			−0.919401
$474$	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
$478$	0.253842	+	0.123565i	0.0116105	+	0.00565172i
$479$	7.80806			0.356759			0.178380	−	0.983962i	$-0.442914\pi$
$479$	7.80806			0.356759			0.178380	+	0.983962i	$0.442914\pi$
$480$		0			0
$481$	0.711710			0.0324512
$482$	−21.4584	−	10.4454i	−0.977401	−	0.475777i
$483$	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
$487$	−27.6753			−1.25409			−0.627044	−	0.778984i	$-0.715735\pi$
$487$	−27.6753			−1.25409			−0.627044	+	0.778984i	$0.715735\pi$
$488$	1.20958	−	1.87206i	0.0547551	−	0.0847443i
$489$			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	$0.372886\pi$
$492$	−2.96890	+	24.4922i	−0.133848	+	1.10419i
$493$	−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
$497$			22.6491i			1.01595i
$498$	25.4502	−	52.2830i	1.14045	−	2.34286i
$499$	25.0477	+	25.0477i	1.12129	+	1.12129i	0.991548	+	0.129743i	$0.0414153\pi$
$499$	25.0477	+	25.0477i	1.12129	+	1.12129i	0.129743	+	0.991548i	$0.458585\pi$
$500$		0			0
$501$	−28.6914	+	28.6914i	−1.28184	+	1.28184i
$502$	−11.5327	+	3.98098i	−0.514729	+	0.177680i
$503$	−22.8644			−1.01947			−0.509736	−	0.860331i	$-0.670257\pi$
$503$	−22.8644			−1.01947			−0.509736	+	0.860331i	$0.670257\pi$
$504$	−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
$508$	2.37942	−	1.86492i	0.105569	−	0.0827426i
$509$	17.1633	+	17.1633i	0.760748	+	0.760748i	0.976458	−	0.215710i	$-0.0692065\pi$
$509$	17.1633	+	17.1633i	0.760748	+	0.760748i	−0.215710	+	0.976458i	$0.569206\pi$
$510$		0			0
$511$	34.7631			1.53783
$512$	−13.4269	−	18.2131i	−0.593390	−	0.804915i
$513$		−	51.5169i		−	2.27453i
$514$	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
$518$	−0.966652	−	2.80034i	−0.0424722	−	0.123040i
$519$		−	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	$-0.0812077\pi$
$522$	23.6221	−	8.15414i	1.03391	−	0.356897i
$523$	25.4249	+	25.4249i	1.11175	+	1.11175i	0.992913	+	0.118841i	$0.0379180\pi$
$523$	25.4249	+	25.4249i	1.11175	+	1.11175i	0.118841	+	0.992913i	$0.462082\pi$
$524$	3.13701	−	25.8790i	0.137041	−	1.13053i
$525$		0			0
$526$	9.08455	+	4.42215i	0.396105	+	0.192815i
$527$		−	23.6647i		−	1.03085i
$528$	33.8884	+	8.33831i	1.47481	+	0.362878i
$529$	40.9681			1.78122
$530$		0			0
$531$	13.3025	+	13.3025i	0.577281	+	0.577281i
$532$	3.92374	−	32.3692i	0.170116	−	1.40338i
$533$	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
$537$	−21.0237			−0.907239
$538$	−14.2081	−	41.1600i	−0.612554	−	1.77454i
$539$	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	$-0.610832\pi$
$542$	−5.99325	−	2.91738i	−0.257432	−	0.125312i
$543$		−	45.8622i		−	1.96814i
$544$	−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	−0.242979	+	0.970032i	$0.578125\pi$
$547$	−28.3699	+	28.3699i	−1.21301	+	1.21301i	−0.970032	+	0.242979i	$0.921875\pi$
$548$	−4.17797	−	5.33057i	−0.178474	−	0.227711i
$549$	−3.56921	+	3.56921i	−0.152330	+	0.152330i
$550$		0			0
$551$			13.6072i			0.579685i
$552$	−58.2722	−	37.6509i	−2.48023	−	1.60253i
$553$	−57.1815			−2.43161
$554$	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	−0.0745028	−	0.997221i	$-0.523737\pi$
$557$	21.7769	−	21.7769i	0.922718	−	0.922718i	0.997221	+	0.0745028i	$0.0237370\pi$
$558$	−20.3275	+	41.7593i	−0.860531	+	1.76781i
$559$	−7.89278			−0.333829
$560$		0			0
$561$	40.2715			1.70026
$562$	−10.9236	+	22.4407i	−0.460785	+	0.946602i
$563$	−10.9022	+	10.9022i	−0.459473	+	0.459473i	−0.898482	−	0.439010i	$-0.855329\pi$
$563$	−10.9022	+	10.9022i	−0.459473	+	0.459473i	0.439010	+	0.898482i	$0.355329\pi$
$564$	4.05306	−	33.4361i	0.170664	−	1.40791i
$565$		0			0
$566$	−11.8462	−	34.3179i	−0.497935	−	1.44249i
$567$	42.3534			1.77868
$568$	18.9491	−	4.07363i	0.795087	−	0.170926i
$569$			31.1881i			1.30747i	0.756723	+	0.653736i	$0.226799\pi$
$569$			31.1881i			1.30747i	−0.756723	+	0.653736i	$0.773201\pi$
$570$		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	$0.270770\pi$
$572$	5.02875	−	3.94140i	0.210263	−	0.164798i
$573$	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
$577$		−	8.42524i		−	0.350747i	−0.984502	−	0.175374i	$-0.943887\pi$
$577$		−	8.42524i		−	0.350747i	0.984502	−	0.175374i	$-0.0561134\pi$
$578$	−5.47423	−	2.66473i	−0.227698	−	0.110838i
$579$	45.2404	+	45.2404i	1.88013	+	1.88013i
$580$		0			0
$581$	−31.3337	+	31.3337i	−1.29994	+	1.29994i
$582$	1.00350	+	2.90709i	0.0415964	+	0.120503i
$583$	13.4830			0.558408
$584$	−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	$-0.0591231\pi$
$587$	19.3370	+	19.3370i	0.798125	+	0.798125i	−0.184675	+	0.982800i	$0.559123\pi$
$588$	23.8954	+	2.89656i	0.985431	+	0.119452i
$589$	−17.8821	−	17.8821i	−0.736818	−	0.736818i
$590$		0			0
$591$	9.00862			0.370565
$592$	−2.16901	+	1.31240i	−0.0891458	+	0.0539394i
$593$			18.1804i			0.746580i	0.927715	+	0.373290i	$0.121770\pi$
$593$			18.1804i			0.746580i	−0.927715	+	0.373290i	$0.878230\pi$
$594$	−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
$598$	−12.0063	+	4.14447i	−0.490975	+	0.169480i
$599$		−	1.64695i		−	0.0672927i	−0.999434	−	0.0336463i	$-0.989288\pi$
$599$		−	1.64695i		−	0.0672927i	0.999434	−	0.0336463i	$-0.0107120\pi$
$600$		0			0
$601$		−	12.7485i		−	0.520021i	−0.965606	−	0.260011i	$-0.916274\pi$
$601$		−	12.7485i		−	0.520021i	0.965606	−	0.260011i	$-0.0837261\pi$
$602$	10.7201	+	31.0554i	0.436917	+	1.26572i
$603$	−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
$607$		−	15.6773i		−	0.636322i	−0.948037	−	0.318161i	$-0.896935\pi$
$607$		−	15.6773i		−	0.636322i	0.948037	−	0.318161i	$-0.103065\pi$
$608$	−27.7871	+	2.53913i	−1.12691	+	0.102975i
$609$	−27.9629			−1.13311
$610$		0			0
$611$	−4.36018	−	4.36018i	−0.176394	−	0.176394i
$612$	36.4775	+	46.5409i	1.47452	+	1.88130i
$613$	8.29399	+	8.29399i	0.334991	+	0.334991i	0.854478	−	0.519487i	$-0.173877\pi$
$613$	8.29399	+	8.29399i	0.334991	+	0.334991i	−0.519487	+	0.854478i	$0.673877\pi$
$614$	−8.54945	+	2.95119i	−0.345028	+	0.119100i
$615$		0			0
$616$	−22.3382	−	14.4332i	−0.900031	−	0.581529i
$617$	20.3330			0.818575			0.409287	−	0.912406i	$-0.365777\pi$
$617$	20.3330			0.818575			0.409287	+	0.912406i	$0.365777\pi$
$618$	65.3549	−	22.5599i	2.62896	−	0.907493i
$619$	−12.5878	+	12.5878i	−0.505946	+	0.505946i	−0.913280	−	0.407333i	$-0.866459\pi$
$619$	−12.5878	+	12.5878i	−0.505946	+	0.505946i	0.407333	+	0.913280i	$0.366459\pi$
$620$		0			0
$621$	59.0667	+	59.0667i	2.37027	+	2.37027i
$622$	8.72836	−	17.9309i	0.349975	−	0.718964i
$623$			25.1880i			1.00914i
$624$	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
$628$	−44.4702	−	5.39059i	−1.77455	−	0.215108i
$629$	−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	$-0.140685\pi$
$632$	10.2846	+	47.8403i	0.409099	+	1.90298i
$633$	−10.9117			−0.433702
$634$	−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
$638$	9.97922	+	4.85766i	0.395081	+	0.192317i
$639$	−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	$0.327123\pi$
$642$	−18.6802	−	9.09312i	−0.737250	−	0.358877i
$643$	14.6501	−	14.6501i	0.577743	−	0.577743i	−0.356538	−	0.934281i	$-0.616043\pi$
$643$	14.6501	−	14.6501i	0.577743	−	0.577743i	0.934281	+	0.356538i	$0.116043\pi$
$644$	32.6142	+	41.6118i	1.28518	+	1.63973i
$645$		0			0
$646$	−30.4358	+	10.5062i	−1.19748	+	0.413360i
$647$	16.2623			0.639337			0.319668	−	0.947530i	$-0.396429\pi$
$647$	16.2623			0.639337			0.319668	+	0.947530i	$0.396429\pi$
$648$	−7.61762	−	35.4345i	−0.299248	−	1.39200i
$649$			8.35522i			0.327971i
$650$		0			0
$651$	36.7479	−	36.7479i	1.44026	−	1.44026i
$652$	−20.2757	−	2.45778i	−0.794058	−	0.0962543i
$653$	32.0639	−	32.0639i	1.25476	−	1.25476i	0.301194	−	0.953563i	$-0.402615\pi$
$653$	32.0639	−	32.0639i	1.25476	−	1.25476i	0.953563	−	0.301194i	$-0.0973851\pi$
$654$	13.4546	+	6.54939i	0.526116	+	0.256101i
$655$		0			0
$656$	−15.6232	−	3.84412i	−0.609984	−	0.150088i
$657$			67.3717i			2.62842i
$658$	−11.2338	+	23.0779i	−0.437939	+	0.899669i
$659$	7.04696	+	7.04696i	0.274511	+	0.274511i	0.830913	−	0.556402i	$-0.187819\pi$
$659$	7.04696	+	7.04696i	0.274511	+	0.274511i	−0.556402	+	0.830913i	$0.687819\pi$
$660$		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	$0.199125\pi$
$662$	−47.2226	+	16.3008i	−1.83536	+	0.633550i
$663$	15.8962			0.617355
$664$	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
$668$	−16.3231	−	20.8263i	−0.631560	−	0.805794i
$669$	−23.6567	−	23.6567i	−0.914619	−	0.914619i
$670$		0			0
$671$	−2.24180			−0.0865436
$672$	−5.21795	−	57.1028i	−0.201287	−	2.20279i
$673$		−	35.3380i		−	1.36218i	−0.732200	−	0.681090i	$-0.761506\pi$
$673$		−	35.3380i		−	1.36218i	0.732200	−	0.681090i	$-0.238494\pi$
$674$	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	$-0.182695\pi$
$677$	7.72259	+	7.72259i	0.296803	+	0.296803i	−0.542957	+	0.839760i	$0.682695\pi$
$678$	−1.55391	−	4.50161i	−0.0596777	−	0.172883i
$679$		−	2.34365i		−	0.0899411i
$680$		0			0
$681$		−	50.4615i		−	1.93369i
$682$	−19.4981	+	6.73058i	−0.746622	+	0.257727i
$683$	15.6011	+	15.6011i	0.596958	+	0.596958i	0.939502	−	0.342544i	$-0.111289\pi$
$683$	15.6011	+	15.6011i	0.596958	+	0.596958i	−0.342544	+	0.939502i	$0.611289\pi$
$684$	62.7323	+	7.60429i	2.39863	+	0.290757i
$685$		0			0
$686$	12.9265	+	6.29233i	0.493536	+	0.240242i
$687$		−	6.97246i		−	0.266016i
$688$	24.0541	−	14.5544i	0.917053	−	0.554881i
$689$	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	$0.449678\pi$
$692$	32.9932	+	3.99938i	1.25421	+	0.152033i
$693$	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
$697$	−18.5659			−0.703234
$698$	0.504523	+	1.46158i	0.0190965	+	0.0553215i
$699$	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	$0.620513\pi$
$702$	−14.9133	−	7.25945i	−0.562865	−	0.273990i
$703$			3.12621i			0.117907i
$704$	−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
$708$	−14.1783	+	11.1126i	−0.532852	+	0.417636i
$709$	−9.26566	+	9.26566i	−0.347979	+	0.347979i	−0.859356	−	0.511377i	$-0.829136\pi$
$709$	−9.26566	+	9.26566i	−0.347979	+	0.347979i	0.511377	+	0.859356i	$0.329136\pi$
$710$		0			0
$711$		−	110.819i		−	4.15604i
$712$	21.0732	−	4.53027i	0.789753	−	0.169779i
$713$	41.0054			1.53567
$714$	−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
$718$	17.6662	−	36.2922i	0.659297	−	1.35441i
$719$	−40.8143			−1.52212			−0.761058	−	0.648684i	$-0.775320\pi$
$719$	−40.8143			−1.52212			−0.761058	+	0.648684i	$0.775320\pi$
$720$		0			0
$721$	−52.6882			−1.96221
$722$	−3.29927	+	6.77778i	−0.122786	+	0.252243i
$723$	−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
$727$	5.20944			0.193208			0.0966038	−	0.995323i	$-0.469202\pi$
$727$	5.20944			0.193208			0.0966038	+	0.995323i	$0.469202\pi$
$728$	−8.81744	−	5.69714i	−0.326796	−	0.211150i
$729$		−	14.0106i		−	0.518911i
$730$		0			0
$731$	22.9403	−	22.9403i	0.848476	−	0.848476i
$732$	−2.98162	−	3.80419i	−0.110204	−	0.140607i
$733$	−14.7039	+	14.7039i	−0.543099	+	0.543099i	−0.924436	−	0.381337i	$-0.875464\pi$
$733$	−14.7039	+	14.7039i	−0.543099	+	0.543099i	0.381337	+	0.924436i	$0.375464\pi$
$734$	0.562758	−	1.15609i	0.0207718	−	0.0426720i
$735$		0			0
$736$	28.9481	−	34.7705i	1.06704	−	1.28166i
$737$		−	2.55917i		−	0.0942684i
$738$	32.7618	+	15.9477i	1.20598	+	0.587043i
$739$	−7.68017	−	7.68017i	−0.282520	−	0.282520i	0.551594	−	0.834113i	$-0.314020\pi$
$739$	−7.68017	−	7.68017i	−0.282520	−	0.282520i	−0.834113	+	0.551594i	$0.814020\pi$
$740$		0			0
$741$	12.0118	−	12.0118i	0.441265	−	0.441265i
$742$	−7.22849	−	20.9405i	−0.265366	−	0.768752i
$743$	−34.9882			−1.28359			−0.641796	−	0.766876i	$-0.721810\pi$
$743$	−34.9882			−1.28359			−0.641796	+	0.766876i	$0.721810\pi$
$744$	−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
$748$	−3.16035	+	26.0716i	−0.115554	+	0.953273i
$749$	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	$0.706720\pi$
$752$	21.3283	+	5.24788i	0.777765	+	0.191370i
$753$			26.4577i			0.964174i
$754$	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	$-0.0571771\pi$
$757$	22.1553	+	22.1553i	0.805248	+	0.805248i	−0.178663	+	0.983910i	$0.557177\pi$
$758$	−2.33905	+	0.807419i	−0.0849581	+	0.0293268i
$759$			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	$0.662443\pi$
$762$	−2.13921	−	6.19717i	−0.0774954	−	0.224500i
$763$	−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
$767$			3.29802i			0.119084i
$768$	−46.8359	+	14.6360i	−1.69005	+	0.528130i
$769$	41.1054			1.48230			0.741150	−	0.671339i	$-0.234281\pi$
$769$	41.1054			1.48230			0.741150	+	0.671339i	$0.234281\pi$
$770$		0			0
$771$	−43.0160	−	43.0160i	−1.54918	−	1.54918i
$772$	−32.8388	+	25.7382i	−1.18189	+	0.926339i
$773$	−10.8044	−	10.8044i	−0.388607	−	0.388607i	0.485583	−	0.874190i	$-0.338607\pi$
$773$	−10.8044	−	10.8044i	−0.388607	−	0.388607i	−0.874190	+	0.485583i	$0.838607\pi$
$774$	−60.1861	+	20.7757i	−2.16334	+	0.746767i
$775$		0			0
$776$	−1.96079	+	0.421526i	−0.0703883	+	0.0151319i
$777$	−6.42440			−0.230474
$778$	−30.7777	+	10.6242i	−1.10343	+	0.380895i
$779$	−14.0292	+	14.0292i	−0.502648	+	0.502648i
$780$		0			0
$781$	−13.7849	−	13.7849i	−0.493262	−	0.493262i
$782$	22.8504	−	46.9421i	0.817127	−	1.67865i
$783$		−	28.8118i		−	1.02965i
$784$	−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	−0.884799	−	0.465973i	$-0.845704\pi$
$787$	−11.7496	+	11.7496i	−0.418826	+	0.418826i	0.465973	+	0.884799i	$0.345704\pi$
$788$	−0.706963	+	5.83215i	−0.0251845	+	0.207762i
$789$	15.4932	−	15.4932i	0.551573	−	0.551573i
$790$		0			0
$791$			3.62914i			0.129037i
$792$	27.9718	−	43.2919i	0.993934	−	1.53831i
$793$	−0.884894			−0.0314235
$794$	−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	−0.930343	−	0.366691i	$-0.880491\pi$
$797$	−15.9126	+	15.9126i	−0.563652	+	0.563652i	0.366691	+	0.930343i	$0.380491\pi$
$798$	−63.5770	−	30.9479i	−2.25060	−	1.09554i
$799$	25.3456			0.896663
$800$		0			0
$801$	−48.8148			−1.72479
$802$	20.1611	+	9.81397i	0.711913	+	0.346543i
$803$	−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
$807$	−94.4274			−3.32400
$808$	20.7033	+	13.3769i	0.728341	+	0.470596i
$809$			9.06814i			0.318819i	0.987213	+	0.159409i	$0.0509590\pi$
$809$			9.06814i			0.318819i	−0.987213	+	0.159409i	$0.949041\pi$
$810$		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	$0.389430\pi$
$812$	2.19443	−	18.1031i	0.0770093	−	0.635295i
$813$	−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
$817$		−	34.6693i		−	1.21293i
$818$	6.20333	−	12.7437i	0.216894	−	0.445571i
$819$	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	$0.103020\pi$
$822$	−13.8835	+	4.79244i	−0.484241	+	0.167156i
$823$	25.3535			0.883767			0.441884	−	0.897072i	$-0.354310\pi$
$823$	25.3535			0.883767			0.441884	+	0.897072i	$0.354310\pi$
$824$	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	$-0.126895\pi$
$827$	15.3396	+	15.3396i	0.533410	+	0.533410i	−0.388176	+	0.921585i	$0.626895\pi$
$828$	−80.6444	+	63.2070i	−2.80259	+	2.19660i
$829$	−37.2546	−	37.2546i	−1.29391	−	1.29391i	−0.932351	−	0.361555i	$-0.882246\pi$
$829$	−37.2546	−	37.2546i	−1.29391	−	1.29391i	−0.361555	−	0.932351i	$-0.617754\pi$
$830$		0			0
$831$	88.7335			3.07813
$832$	−3.18055	+	8.40169i	−0.110266	+	0.291276i
$833$			18.1135i			0.627596i
$834$	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
$838$	−9.46250	−	27.4124i	−0.326877	−	0.946945i
$839$			17.9621i			0.620120i	0.950717	+	0.310060i	$0.100349\pi$
$839$			17.9621i			0.620120i	−0.950717	+	0.310060i	$0.899651\pi$
$840$		0			0
$841$		−	21.3899i		−	0.737584i
$842$	24.5737	−	8.48262i	0.846866	−	0.292331i
$843$	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
$847$		−	9.60708i		−	0.330103i
$848$	−16.2196	+	9.81397i	−0.556982	+	0.337013i
$849$	−78.7306			−2.70203
$850$		0			0
$851$	−3.58436	−	3.58436i	−0.122870	−	0.122870i
$852$	5.05797	−	41.7261i	0.173283	−	1.42951i
$853$	9.29007	+	9.29007i	0.318086	+	0.318086i	0.848032	−	0.529946i	$-0.177788\pi$
$853$	9.29007	+	9.29007i	0.318086	+	0.318086i	−0.529946	+	0.848032i	$0.677788\pi$
$854$	1.20187	+	3.48176i	0.0411272	+	0.119143i
$855$		0			0
$856$	7.35282	−	11.3799i	0.251314	−	0.388958i
$857$	10.3997			0.355246			0.177623	−	0.984099i	$-0.443159\pi$
$857$	10.3997			0.355246			0.177623	+	0.984099i	$0.443159\pi$
$858$	−4.52109	−	13.0973i	−0.154347	−	0.447136i
$859$	−15.3452	+	15.3452i	−0.523571	+	0.523571i	−0.918648	−	0.395077i	$-0.870718\pi$
$859$	−15.3452	+	15.3452i	−0.523571	+	0.523571i	0.395077	+	0.918648i	$0.370718\pi$
$860$		0			0
$861$	−28.8302	−	28.8302i	−0.982530	−	0.982530i
$862$	−43.7932	−	21.3176i	−1.49160	−	0.726079i
$863$		−	8.81329i		−	0.300008i	−0.988685	−	0.150004i	$-0.952071\pi$
$863$		−	8.81329i		−	0.300008i	0.988685	−	0.150004i	$-0.0479286\pi$
$864$	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
$868$	20.9067	+	26.6743i	0.709618	+	0.905386i
$869$	34.8023	−	34.8023i	1.18059	−	1.18059i
$870$		0			0
$871$		−	1.01017i		−	0.0342283i
$872$	−5.29592	+	8.19649i	−0.179343	+	0.277568i
$873$	4.54205			0.153725
$874$	−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	−0.604508	−	0.796599i	$-0.706630\pi$
$877$	5.68862	−	5.68862i	0.192091	−	0.192091i	0.796599	+	0.604508i	$0.206630\pi$
$878$	−3.52923	+	7.25019i	−0.119106	+	0.244682i
$879$	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	$0.611419\pi$
$882$	15.5591	−	31.9635i	0.523903	−	1.07627i
$883$	−19.3524	+	19.3524i	−0.651262	+	0.651262i	−0.953297	−	0.302035i	$-0.902334\pi$
$883$	−19.3524	+	19.3524i	−0.651262	+	0.651262i	0.302035	+	0.953297i	$0.402334\pi$
$884$	−1.24747	+	10.2911i	−0.0419570	+	0.346128i
$885$		0			0
$886$	−3.28500	−	9.51647i	−0.110362	−	0.319712i
$887$	−12.7863			−0.429323			−0.214661	−	0.976689i	$-0.568865\pi$
$887$	−12.7863			−0.429323			−0.214661	+	0.976689i	$0.568865\pi$
$888$	1.15548	+	5.37490i	0.0387755	+	0.180370i
$889$			4.99608i			0.167563i
$890$		0			0
$891$	−25.7775	+	25.7775i	−0.863579	+	0.863579i
$892$	17.1717	−	13.4588i	0.574953	−	0.450633i
$893$	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
$897$			27.5443i			0.919678i
$898$	−28.2925	−	13.7722i	−0.944134	−	0.459584i
$899$	−10.0009	−	10.0009i	−0.333548	−	0.333548i
$900$		0			0
$901$	−15.4685	+	15.4685i	−0.515331	+	0.515331i
$902$	5.28040	+	15.2970i	0.175818	+	0.509336i
$903$	71.2459			2.37091
$904$	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	$-0.271574\pi$
$907$	−2.88449	−	2.88449i	−0.0957780	−	0.0957780i	−0.753372	+	0.657594i	$0.771574\pi$
$908$	32.6687	+	3.96003i	1.08415	+	0.131418i
$909$	−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	$0.0671550\pi$
$912$	−14.4573	+	58.7572i	−0.478730	+	1.94565i
$913$		−	38.1412i		−	1.26229i
$914$	−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
$918$	64.4448	−	22.2458i	2.12699	−	0.734219i
$919$		−	24.0062i		−	0.791893i	−0.918274	−	0.395946i	$-0.870417\pi$
$919$		−	24.0062i		−	0.791893i	0.918274	−	0.395946i	$-0.129583\pi$
$920$		0			0
$921$			19.6137i			0.646294i
$922$	−5.31719	−	15.4036i	−0.175112	−	0.507291i
$923$	−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
$927$		−	102.111i		−	3.35376i
$928$	−15.5405	+	1.42006i	−0.510140	+	0.0466157i
$929$	−15.1568			−0.497279			−0.248639	−	0.968596i	$-0.579983\pi$
$929$	−15.1568			−0.497279			−0.248639	+	0.968596i	$0.579983\pi$
$930$		0			0
$931$	13.6873	+	13.6873i	0.448585	+	0.448585i
$932$	29.3757	+	37.4798i	0.962234	+	1.22769i
$933$	−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
$937$	39.9323			1.30453			0.652266	−	0.757991i	$-0.273819\pi$
$937$	39.9323			1.30453			0.652266	+	0.757991i	$0.273819\pi$
$938$	−3.97468	+	1.37202i	−0.129778	+	0.0447982i
$939$	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	$0.915897\pi$
$942$	−42.5174	+	87.3447i	−1.38529	+	2.84584i
$943$		−	32.1704i		−	1.04761i
$944$	−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	−0.390925	−	0.920423i	$-0.627845\pi$
$947$	16.2944	−	16.2944i	0.529498	−	0.529498i	0.920423	+	0.390925i	$0.127845\pi$
$948$	105.345	+	12.7697i	3.42144	+	0.414741i
$949$	−8.35152	+	8.35152i	−0.271102	+	0.271102i
$950$		0			0
$951$			76.5578i			2.48256i
$952$	42.1864	−	9.06914i	1.36727	−	0.293932i
$953$	12.0232			0.389468			0.194734	−	0.980856i	$-0.437616\pi$
$953$	12.0232			0.389468			0.194734	+	0.980856i	$0.437616\pi$
$954$	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
$958$	9.92846	+	4.83295i	0.320774	+	0.156146i
$959$	11.1927			0.361430
$960$		0			0
$961$	−4.71434			−0.152076
$962$	0.904985	+	0.440526i	0.0291779	+	0.0142031i
$963$	−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
$967$	43.8237			1.40927			0.704637	−	0.709568i	$-0.251110\pi$
$967$	43.8237			1.40927			0.704637	+	0.709568i	$0.251110\pi$
$968$	−8.03765	+	1.72791i	−0.258340	+	0.0555373i
$969$			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	$-0.0543011\pi$
$972$	−15.8172	−	1.91734i	−0.507338	−	0.0614986i
$973$	−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
$977$			0.204913i			0.00655576i	0.999995	+	0.00327788i	$0.00104338\pi$
$977$			0.204913i			0.00655576i	−0.999995	+	0.00327788i	$0.998957\pi$
$978$	−19.3854	+	39.8239i	−0.619876	+	1.27343i
$979$	−15.3301	−	15.3301i	−0.489953	−	0.489953i
$980$		0			0
$981$	15.6272	−	15.6272i	0.498937	−	0.498937i
$982$	−22.3074	+	7.70032i	−0.711858	+	0.245727i
$983$	−34.0060			−1.08462			−0.542312	−	0.840177i	$-0.682451\pi$
$983$	−34.0060			−1.08462			−0.542312	+	0.840177i	$0.682451\pi$
$984$	−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
$988$	6.83377	+	8.71906i	0.217411	+	0.277390i
$989$	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	$0.429545\pi$
$992$	18.5565	−	22.2889i	0.589171	−	0.707674i
$993$			108.336i			3.43794i
$994$	−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	$-0.295626\pi$
$997$	−6.37875	−	6.37875i	−0.202017	−	0.202017i	−0.800864	+	0.598847i	$0.795626\pi$
$998$	16.3460	+	47.3536i	0.517425	+	1.49895i
$999$		−	6.61943i		−	0.209429i

Twists

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

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

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.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.27156 + 0.618969i) q^{2} +(2.16859 - 2.16859i) q^{3} +(1.23375 + 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519 q^{7} +(0.594467 + 2.76525i) q^{8} -6.40553i q^{9} +O(q^{10})\)	\(q+(1.27156 + 0.618969i) q^{2} +(2.16859 - 2.16859i) q^{3} +(1.23375 + 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} -3.30519 q^{7} +(0.594467 + 2.76525i) q^{8} -6.40553i q^{9} +(2.01163 - 2.01163i) q^{11} +(6.08911 + 0.738111i) q^{12} +(0.794042 - 0.794042i) q^{13} +(-4.20276 - 2.04581i) q^{14} +(-0.955702 + 3.88415i) q^{16} +4.61575i q^{17} +(3.96483 - 8.14504i) q^{18} +(3.48786 + 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +(3.80306 - 1.31278i) q^{22} -7.99801 q^{23} +(7.28583 + 4.70753i) q^{24} +(1.50116 - 0.518188i) q^{26} +(-7.38518 - 7.38518i) q^{27} +(-4.07779 - 5.20276i) q^{28} +(1.95065 + 1.95065i) q^{29} -5.12695 q^{31} +(-3.61941 + 4.34740i) q^{32} -8.72480i q^{33} +(-2.85701 + 5.86922i) q^{34} +(10.0831 - 7.90285i) q^{36} +(0.448156 + 0.448156i) q^{37} +(2.27616 + 6.59391i) q^{38} -3.44390i q^{39} +4.02230i q^{41} +(-13.5506 + 4.67754i) q^{42} +(-4.97000 - 4.97000i) q^{43} +(5.64841 + 0.684690i) q^{44} +(-10.1700 - 4.95052i) q^{46} -5.49112i q^{47} +(6.35059 + 10.4956i) q^{48} +3.92429 q^{49} +(10.0096 + 10.0096i) q^{51} +(2.22957 + 0.270264i) q^{52} +(3.35125 + 3.35125i) q^{53} +(-4.81954 - 13.9619i) q^{54} +(-1.96483 - 9.13968i) q^{56} +15.1274 q^{57} +(1.27299 + 3.68777i) q^{58} +(-2.07673 + 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} +(-6.51925 - 3.17343i) q^{62} +21.1715i q^{63} +(-7.29322 + 3.28770i) q^{64} +(5.40038 - 11.0941i) q^{66} +(0.636094 - 0.636094i) q^{67} +(-7.26573 + 5.69470i) q^{68} +(-17.3444 + 17.3444i) q^{69} -6.85258i q^{71} +(17.7129 - 3.80787i) q^{72} -10.5177 q^{73} +(0.292465 + 0.847255i) q^{74} +(-1.18714 + 9.79346i) q^{76} +(-6.64883 + 6.64883i) q^{77} +(2.13167 - 4.37914i) q^{78} +17.3005 q^{79} -12.8142 q^{81} +(-2.48968 + 5.11461i) q^{82} +(9.48015 - 9.48015i) q^{83} +(-20.1257 - 2.43960i) q^{84} +(-3.24340 - 9.39596i) q^{86} +8.46030 q^{87} +(6.75852 + 4.36682i) q^{88} -7.62073i q^{89} +(-2.62446 + 2.62446i) q^{91} +(-9.86757 - 12.5898i) q^{92} +(-11.1182 + 11.1182i) q^{93} +(3.39883 - 6.98231i) q^{94} +(1.57871 + 17.2767i) q^{96} +0.709082i q^{97} +(4.98999 + 2.42901i) q^{98} +(-12.8856 - 12.8856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8	\( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26} - 10 q^{27} + 10 q^{28} - 4 q^{31} - 2 q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 28 q^{38} - 10 q^{42} + 44 q^{44} - 10 q^{46} + 58 q^{48} - 4 q^{49} + 10 q^{51} + 16 q^{53} - 10 q^{54} + 6 q^{56} + 16 q^{57} - 4 q^{58} - 20 q^{59} + 4 q^{61} - 22 q^{62} - 38 q^{64} + 32 q^{66} - 50 q^{67} - 50 q^{68} + 54 q^{72} - 40 q^{73} - 10 q^{74} + 60 q^{76} + 8 q^{77} + 48 q^{78} - 12 q^{79} - 8 q^{81} + 12 q^{82} - 2 q^{83} - 34 q^{84} + 6 q^{86} + 64 q^{87} - 56 q^{88} - 50 q^{92} - 44 q^{93} - 32 q^{94} - 34 q^{96} + 30 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * q^98 - 12 * q^99

Introduction

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