LMFDB - Embedded newform 375.2.i.b.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.4
Root			$0.132563 - 1.40799i$ of defining polynomial
Character	$\chi$	$=$	375.349
Dual form			375.2.i.b.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.01846 - 0.655837i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(2.02602 - 1.47199i) q^{4} +(-1.71700 - 1.24748i) q^{6} -4.35840i q^{7} +(0.629102 - 0.865884i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(2.01846 - 0.655837i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(2.02602 - 1.47199i) q^{4} +(-1.71700 - 1.24748i) q^{6} -4.35840i q^{7} +(0.629102 - 0.865884i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.488218 - 1.50258i) q^{11} +(-2.38173 - 0.773871i) q^{12} +(1.13931 + 0.370184i) q^{13} +(-2.85840 - 8.79726i) q^{14} +(-0.845805 + 2.60312i) q^{16} +(0.659691 - 0.907987i) q^{17} +2.12233i q^{18} +(6.21218 + 4.51341i) q^{19} +(-3.52602 + 2.56180i) q^{21} +(-1.97090 - 2.71270i) q^{22} +(2.20671 - 0.717004i) q^{23} -1.07029 q^{24} +2.54243 q^{26} +(0.951057 - 0.309017i) q^{27} +(-6.41552 - 8.83021i) q^{28} +(-4.45307 + 3.23535i) q^{29} +(-3.88495 - 2.82258i) q^{31} +7.94959i q^{32} +(-0.928645 + 1.27817i) q^{33} +(0.736068 - 2.26538i) q^{34} +(0.773871 + 2.38173i) q^{36} +(6.06043 + 1.96915i) q^{37} +(15.4991 + 5.03596i) q^{38} +(-0.370184 - 1.13931i) q^{39} +(-2.30902 + 7.10642i) q^{41} +(-5.43700 + 7.48339i) q^{42} -1.24998i q^{43} +(-3.20092 - 2.32561i) q^{44} +(3.98392 - 2.89449i) q^{46} +(2.42617 + 3.33934i) q^{47} +(2.60312 - 0.845805i) q^{48} -11.9957 q^{49} -1.12233 q^{51} +(2.85317 - 0.927051i) q^{52} +(-2.20166 - 3.03032i) q^{53} +(1.71700 - 1.24748i) q^{54} +(-3.77387 - 2.74188i) q^{56} -7.67867i q^{57} +(-6.86648 + 9.45090i) q^{58} +(-2.82940 + 8.70799i) q^{59} +(0.431351 + 1.32756i) q^{61} +(-9.69276 - 3.14937i) q^{62} +(4.14509 + 1.34682i) q^{63} +(3.52202 + 10.8397i) q^{64} +(-1.03616 + 3.18898i) q^{66} +(2.27044 - 3.12499i) q^{67} -2.81066i q^{68} +(-1.87714 - 1.36382i) q^{69} +(8.57970 - 6.23352i) q^{71} +(0.629102 + 0.865884i) q^{72} +(-4.75216 + 1.54407i) q^{73} +13.5242 q^{74} +19.2297 q^{76} +(-6.54885 + 2.12785i) q^{77} +(-1.49440 - 2.05687i) q^{78} +(11.7737 - 8.55407i) q^{79} +(-0.809017 - 0.587785i) q^{81} +15.8584i q^{82} +(-5.13491 + 7.06760i) q^{83} +(-3.37284 + 10.3805i) q^{84} +(-0.819784 - 2.52304i) q^{86} +(5.23490 + 1.70092i) q^{87} +(-1.60820 - 0.522535i) q^{88} +(3.10195 + 9.54683i) q^{89} +(1.61341 - 4.96556i) q^{91} +(3.41542 - 4.70092i) q^{92} +4.80206i q^{93} +(7.08719 + 5.14914i) q^{94} +(6.43135 - 4.67265i) q^{96} +(-4.40837 - 6.06760i) q^{97} +(-24.2128 + 7.86720i) q^{98} +1.57991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.01846	−	0.655837i	1.42727	−	0.463747i	0.509363	−	0.860552i	$-0.329881\pi$
$2$	2.01846	−	0.655837i	1.42727	−	0.463747i	0.917903	+	0.396805i	$0.129881\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	2.02602	−	1.47199i	1.01301	−	0.735995i
$5$		0			0
$5$		0			0
$6$	−1.71700	−	1.24748i	−0.700964	−	0.509280i
$7$		−	4.35840i		−	1.64732i	−0.567083	−	0.823660i	$-0.691928\pi$
$7$		−	4.35840i		−	1.64732i	0.567083	−	0.823660i	$-0.308072\pi$
$8$	0.629102	−	0.865884i	0.222421	−	0.306136i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−0.488218	−	1.50258i	−0.147203	−	0.453045i	0.850085	−	0.526646i	$-0.176551\pi$
$11$	−0.488218	−	1.50258i	−0.147203	−	0.453045i	−0.997288	+	0.0736014i	$0.976551\pi$
$12$	−2.38173	−	0.773871i	−0.687546	−	0.223397i
$13$	1.13931	+	0.370184i	0.315987	+	0.102670i	0.462717	−	0.886506i	$-0.346875\pi$
$13$	1.13931	+	0.370184i	0.315987	+	0.102670i	−0.146729	+	0.989177i	$0.546875\pi$
$14$	−2.85840	−	8.79726i	−0.763940	−	2.35117i
$15$		0			0
$16$	−0.845805	+	2.60312i	−0.211451	+	0.650780i
$17$	0.659691	−	0.907987i	0.159999	−	0.220219i	−0.721490	−	0.692425i	$-0.756542\pi$
$17$	0.659691	−	0.907987i	0.159999	−	0.220219i	0.881488	+	0.472206i	$0.156542\pi$
$18$			2.12233i			0.500239i
$19$	6.21218	+	4.51341i	1.42517	+	1.03545i	0.990890	+	0.134670i	$0.0429975\pi$
$19$	6.21218	+	4.51341i	1.42517	+	1.03545i	0.434281	+	0.900777i	$0.357002\pi$
$20$		0			0
$21$	−3.52602	+	2.56180i	−0.769441	+	0.559031i
$22$	−1.97090	−	2.71270i	−0.420196	−	0.578351i
$23$	2.20671	−	0.717004i	0.460131	−	0.149506i	−0.0697736	−	0.997563i	$-0.522228\pi$
$23$	2.20671	−	0.717004i	0.460131	−	0.149506i	0.529905	+	0.848057i	$0.322228\pi$
$24$	−1.07029			−0.218472
$25$		0			0
$26$	2.54243			0.498611
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−6.41552	−	8.83021i	−1.21242	−	1.66875i
$29$	−4.45307	+	3.23535i	−0.826915	+	0.600789i	−0.918685	−	0.394992i	$-0.870748\pi$
$29$	−4.45307	+	3.23535i	−0.826915	+	0.600789i	0.0917701	+	0.995780i	$0.470748\pi$
$30$		0			0
$31$	−3.88495	−	2.82258i	−0.697757	−	0.506950i	0.181444	−	0.983401i	$-0.441923\pi$
$31$	−3.88495	−	2.82258i	−0.697757	−	0.506950i	−0.879201	+	0.476451i	$0.841923\pi$
$32$			7.94959i			1.40530i
$33$	−0.928645	+	1.27817i	−0.161656	+	0.222501i
$34$	0.736068	−	2.26538i	0.126235	−	0.388510i
$35$		0			0
$36$	0.773871	+	2.38173i	0.128979	+	0.396955i
$37$	6.06043	+	1.96915i	0.996329	+	0.323727i	0.761398	−	0.648285i	$-0.224514\pi$
$37$	6.06043	+	1.96915i	0.996329	+	0.323727i	0.234931	+	0.972012i	$0.424514\pi$
$38$	15.4991	+	5.03596i	2.51428	+	0.816941i
$39$	−0.370184	−	1.13931i	−0.0592768	−	0.182435i
$40$		0			0
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	0.592078	+	0.805881i	$0.298308\pi$
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	−0.952686	+	0.303956i	$0.901692\pi$
$42$	−5.43700	+	7.48339i	−0.838948	+	1.15471i
$43$		−	1.24998i		−	0.190620i	−0.995448	−	0.0953102i	$-0.969616\pi$
$43$		−	1.24998i		−	0.190620i	0.995448	−	0.0953102i	$-0.0303843\pi$
$44$	−3.20092	−	2.32561i	−0.482557	−	0.350598i
$45$		0			0
$46$	3.98392	−	2.89449i	0.587397	−	0.426769i
$47$	2.42617	+	3.33934i	0.353893	+	0.487092i	0.948435	−	0.316973i	$-0.102666\pi$
$47$	2.42617	+	3.33934i	0.353893	+	0.487092i	−0.594541	+	0.804065i	$0.702666\pi$
$48$	2.60312	−	0.845805i	0.375728	−	0.122081i
$49$	−11.9957			−1.71367
$50$		0			0
$51$	−1.12233			−0.157158
$52$	2.85317	−	0.927051i	0.395663	−	0.128559i
$53$	−2.20166	−	3.03032i	−0.302421	−	0.416247i	0.630578	−	0.776126i	$-0.282818\pi$
$53$	−2.20166	−	3.03032i	−0.302421	−	0.416247i	−0.932999	+	0.359879i	$0.882818\pi$
$54$	1.71700	−	1.24748i	0.233655	−	0.169760i
$55$		0			0
$56$	−3.77387	−	2.74188i	−0.504305	−	0.366399i
$57$		−	7.67867i		−	1.01707i
$58$	−6.86648	+	9.45090i	−0.901613	+	1.24096i
$59$	−2.82940	+	8.70799i	−0.368356	+	1.13368i	0.579496	+	0.814975i	$0.303249\pi$
$59$	−2.82940	+	8.70799i	−0.368356	+	1.13368i	−0.947853	+	0.318709i	$0.896751\pi$
$60$		0			0
$61$	0.431351	+	1.32756i	0.0552288	+	0.169977i	0.974866	−	0.222792i	$-0.0715172\pi$
$61$	0.431351	+	1.32756i	0.0552288	+	0.169977i	−0.919637	+	0.392769i	$0.871517\pi$
$62$	−9.69276	−	3.14937i	−1.23098	−	0.399970i
$63$	4.14509	+	1.34682i	0.522232	+	0.169683i
$64$	3.52202	+	10.8397i	0.440253	+	1.35496i
$65$		0			0
$66$	−1.03616	+	3.18898i	−0.127543	+	0.392536i
$67$	2.27044	−	3.12499i	0.277378	−	0.381778i	−0.647485	−	0.762078i	$-0.724179\pi$
$67$	2.27044	−	3.12499i	0.277378	−	0.381778i	0.924863	+	0.380300i	$0.124179\pi$
$68$		−	2.81066i		−	0.340843i
$69$	−1.87714	−	1.36382i	−0.225981	−	0.164185i
$70$		0			0
$71$	8.57970	−	6.23352i	1.01822	−	0.739783i	0.0523057	−	0.998631i	$-0.483343\pi$
$71$	8.57970	−	6.23352i	1.01822	−	0.739783i	0.965918	+	0.258848i	$0.0833430\pi$
$72$	0.629102	+	0.865884i	0.0741403	+	0.102045i
$73$	−4.75216	+	1.54407i	−0.556198	+	0.180720i	−0.573610	−	0.819129i	$-0.694457\pi$
$73$	−4.75216	+	1.54407i	−0.556198	+	0.180720i	0.0174117	+	0.999848i	$0.494457\pi$
$74$	13.5242			1.57215
$75$		0			0
$76$	19.2297			2.20580
$77$	−6.54885	+	2.12785i	−0.746310	+	0.242491i
$78$	−1.49440	−	2.05687i	−0.169208	−	0.232894i
$79$	11.7737	−	8.55407i	1.32464	−	0.962408i	0.324779	−	0.945790i	$-0.394710\pi$
$79$	11.7737	−	8.55407i	1.32464	−	0.962408i	0.999862	−	0.0166185i	$-0.00529009\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			15.8584i			1.75126i
$83$	−5.13491	+	7.06760i	−0.563630	+	0.775770i	−0.991782	−	0.127937i	$-0.959165\pi$
$83$	−5.13491	+	7.06760i	−0.563630	+	0.775770i	0.428153	+	0.903706i	$0.359165\pi$
$84$	−3.37284	+	10.3805i	−0.368007	+	1.13261i
$85$		0			0
$86$	−0.819784	−	2.52304i	−0.0883996	−	0.272066i
$87$	5.23490	+	1.70092i	0.561240	+	0.182358i
$88$	−1.60820	−	0.522535i	−0.171435	−	0.0557025i
$89$	3.10195	+	9.54683i	0.328806	+	1.01196i	0.969693	+	0.244326i	$0.0785668\pi$
$89$	3.10195	+	9.54683i	0.328806	+	1.01196i	−0.640887	+	0.767635i	$0.721433\pi$
$90$		0			0
$91$	1.61341	−	4.96556i	0.169131	−	0.520532i
$92$	3.41542	−	4.70092i	0.356082	−	0.490105i
$93$			4.80206i			0.497950i
$94$	7.08719	+	5.14914i	0.730988	+	0.531094i
$95$		0			0
$96$	6.43135	−	4.67265i	0.656397	−	0.476900i
$97$	−4.40837	−	6.06760i	−0.447602	−	0.616071i	0.524278	−	0.851547i	$-0.324335\pi$
$97$	−4.40837	−	6.06760i	−0.447602	−	0.616071i	−0.971880	+	0.235476i	$0.924335\pi$
$98$	−24.2128	+	7.86720i	−2.44586	+	0.794707i
$99$	1.57991			0.158787
$100$		0			0
$101$	−6.51821			−0.648586			−0.324293	−	0.945957i	$-0.605126\pi$
$101$	−6.51821			−0.648586			−0.324293	+	0.945957i	$0.605126\pi$
$102$	−2.26538	+	0.736068i	−0.224306	+	0.0728816i
$103$	−4.73094	−	6.51158i	−0.466153	−	0.641605i	0.509617	−	0.860401i	$-0.329787\pi$
$103$	−4.73094	−	6.51158i	−0.466153	−	0.641605i	−0.975771	+	0.218796i	$0.929787\pi$
$104$	1.03728	−	0.753626i	0.101713	−	0.0738991i
$105$		0			0
$106$	−6.43135	−	4.67265i	−0.624668	−	0.453848i
$107$		−	9.47745i		−	0.916220i	−0.888896	−	0.458110i	$-0.848527\pi$
$107$		−	9.47745i		−	0.916220i	0.888896	−	0.458110i	$-0.151473\pi$
$108$	1.47199	−	2.02602i	0.141642	−	0.194954i
$109$	3.60491	−	11.0948i	0.345288	−	1.06269i	−0.616142	−	0.787635i	$-0.711305\pi$
$109$	3.60491	−	11.0948i	0.345288	−	1.06269i	0.961429	−	0.275052i	$-0.0886949\pi$
$110$		0			0
$111$	−1.96915	−	6.06043i	−0.186904	−	0.575231i
$112$	11.3454	+	3.68636i	1.07204	+	0.348328i
$113$	−14.1949	−	4.61219i	−1.33534	−	0.433879i	−0.447605	−	0.894231i	$-0.647723\pi$
$113$	−14.1949	−	4.61219i	−1.33534	−	0.433879i	−0.887736	+	0.460353i	$0.847723\pi$
$114$	−5.03596	−	15.4991i	−0.471661	−	1.45162i
$115$		0			0
$116$	−4.25962	+	13.1098i	−0.395496	+	1.21721i
$117$	−0.704131	+	0.969154i	−0.0650970	+	0.0895983i
$118$			19.4324i			1.78889i
$119$	−3.95737	−	2.87520i	−0.362772	−	0.263569i
$120$		0			0
$121$	6.87980	−	4.99847i	0.625436	−	0.454406i
$122$	1.74133	+	2.39673i	0.157652	+	0.216990i
$123$	7.10642	−	2.30902i	0.640765	−	0.208197i
$124$	−12.0258			−1.07995
$125$		0			0
$126$	9.24998			0.824054
$127$	−16.1638	+	5.25195i	−1.43431	+	0.466035i	−0.920118	−	0.391641i	$-0.871908\pi$
$127$	−16.1638	+	5.25195i	−1.43431	+	0.466035i	−0.514190	+	0.857676i	$0.671908\pi$
$128$	4.87282	+	6.70686i	0.430701	+	0.592809i
$129$	−1.01126	+	0.734721i	−0.0890362	+	0.0646886i
$130$		0			0
$131$	0.266063	+	0.193306i	0.0232461	+	0.0168892i	0.599348	−	0.800489i	$-0.295427\pi$
$131$	0.266063	+	0.193306i	0.0232461	+	0.0168892i	−0.576102	+	0.817378i	$0.695427\pi$
$132$			3.95656i			0.344374i
$133$	19.6713	−	27.0752i	1.70571	−	2.34771i
$134$	2.53330	−	7.79670i	0.218844	−	0.673533i
$135$		0			0
$136$	−0.371199	−	1.14243i	−0.0318300	−	0.0979628i
$137$	−4.33939	−	1.40995i	−0.370739	−	0.120461i	0.117721	−	0.993047i	$-0.462441\pi$
$137$	−4.33939	−	1.40995i	−0.370739	−	0.120461i	−0.488460	+	0.872586i	$0.662441\pi$
$138$	−4.68338	−	1.52172i	−0.398676	−	0.129538i
$139$	1.46289	+	4.50230i	0.124080	+	0.381880i	0.993732	−	0.111785i	$-0.0356568\pi$
$139$	1.46289	+	4.50230i	0.124080	+	0.381880i	−0.869652	+	0.493665i	$0.835657\pi$
$140$		0			0
$141$	1.27551	−	3.92563i	0.107418	−	0.330597i
$142$	13.2296	−	18.2090i	1.11020	−	1.52806i
$143$		−	1.89263i		−	0.158270i
$144$	−2.21435	−	1.60882i	−0.184529	−	0.134068i
$145$		0			0
$146$	−8.57938	+	6.23328i	−0.710035	+	0.515870i
$147$	7.05087	+	9.70470i	0.581546	+	0.800430i
$148$	15.1771	−	4.93135i	1.24755	−	0.405355i
$149$	−4.67644			−0.383109			−0.191555	−	0.981482i	$-0.561353\pi$
$149$	−4.67644			−0.383109			−0.191555	+	0.981482i	$0.561353\pi$
$150$		0			0
$151$	−6.54178			−0.532362			−0.266181	−	0.963923i	$-0.585762\pi$
$151$	−6.54178			−0.532362			−0.266181	+	0.963923i	$0.585762\pi$
$152$	7.81618	−	2.53963i	0.633976	−	0.205991i
$153$	0.659691	+	0.907987i	0.0533329	+	0.0734064i
$154$	−11.8231	+	8.58995i	−0.952729	+	0.692198i
$155$		0			0
$156$	−2.42705	−	1.76336i	−0.194320	−	0.141181i
$157$		−	3.99404i		−	0.318759i	−0.987217	−	0.159379i	$-0.949051\pi$
$157$		−	3.99404i		−	0.318759i	0.987217	−	0.159379i	$-0.0509493\pi$
$158$	18.1546	−	24.9877i	1.44430	−	1.98791i
$159$	−1.15748	+	3.56236i	−0.0917941	+	0.282513i
$160$		0			0
$161$	−3.12499	−	9.61773i	−0.246284	−	0.757984i
$162$	−2.01846	−	0.655837i	−0.158585	−	0.0515274i
$163$	4.56641	+	1.48372i	0.357669	+	0.116214i	0.482339	−	0.875985i	$-0.339787\pi$
$163$	4.56641	+	1.48372i	0.357669	+	0.116214i	−0.124670	+	0.992198i	$0.539787\pi$
$164$	5.78247	+	17.7966i	0.451535	+	1.38968i
$165$		0			0
$166$	−5.72941	+	17.6333i	−0.444689	+	1.36861i
$167$	−13.9070	+	19.1414i	−1.07616	+	1.48120i	−0.212474	+	0.977167i	$0.568152\pi$
$167$	−13.9070	+	19.1414i	−1.07616	+	1.48120i	−0.863682	+	0.504036i	$0.831848\pi$
$168$			4.66476i			0.359894i
$169$	−9.35623	−	6.79770i	−0.719710	−	0.522900i
$170$		0			0
$171$	−6.21218	+	4.51341i	−0.475057	+	0.345149i
$172$	−1.83996	−	2.53249i	−0.140296	−	0.193100i
$173$	−13.7944	+	4.48208i	−1.04877	+	0.340766i	−0.782185	−	0.623046i	$-0.785895\pi$
$173$	−13.7944	+	4.48208i	−1.04877	+	0.340766i	−0.266584	+	0.963812i	$0.585895\pi$
$174$	11.6820			0.885607
$175$		0			0
$176$	4.32433			0.325959
$177$	8.70799	−	2.82940i	0.654533	−	0.212671i
$178$	12.5223	+	17.2355i	0.938588	+	1.29186i
$179$	0.644581	−	0.468315i	0.0481782	−	0.0350035i	−0.563436	−	0.826160i	$-0.690521\pi$
$179$	0.644581	−	0.468315i	0.0481782	−	0.0350035i	0.611614	+	0.791157i	$0.290521\pi$
$180$		0			0
$181$	11.5030	+	8.35741i	0.855010	+	0.621201i	0.926523	−	0.376239i	$-0.122783\pi$
$181$	11.5030	+	8.35741i	0.855010	+	0.621201i	−0.0715129	+	0.997440i	$0.522783\pi$
$182$		−	11.0809i		−	0.821372i
$183$	0.820477	−	1.12929i	0.0606514	−	0.0834795i
$184$	0.767403	−	2.36182i	0.0565737	−	0.174116i
$185$		0			0
$186$	3.14937	+	9.69276i	0.230923	+	0.710708i
$187$	−1.68640	−	0.547943i	−0.123321	−	0.0400696i
$188$	9.83094	+	3.19427i	0.716995	+	0.232966i
$189$	−1.34682	−	4.14509i	−0.0979667	−	0.301511i
$190$		0			0
$191$	−3.20441	+	9.86215i	−0.231863	+	0.713600i	0.765659	+	0.643246i	$0.222413\pi$
$191$	−3.20441	+	9.86215i	−0.231863	+	0.713600i	−0.997522	+	0.0703540i	$0.977587\pi$
$192$	6.69929	−	9.22078i	0.483479	−	0.665452i
$193$			4.34712i			0.312913i	0.987685	+	0.156456i	$0.0500071\pi$
$193$			4.34712i			0.312913i	−0.987685	+	0.156456i	$0.949993\pi$
$194$	−12.8775	−	9.35603i	−0.924548	−	0.671724i
$195$		0			0
$196$	−24.3035	+	17.6575i	−1.73596	+	1.26125i
$197$	1.10498	+	1.52087i	0.0787263	+	0.108358i	0.846564	−	0.532287i	$-0.178667\pi$
$197$	1.10498	+	1.52087i	0.0787263	+	0.108358i	−0.767838	+	0.640644i	$0.778667\pi$
$198$	3.18898	−	1.03616i	0.226631	−	0.0736367i
$199$	−4.26028			−0.302003			−0.151002	−	0.988534i	$-0.548250\pi$
$199$	−4.26028			−0.302003			−0.151002	+	0.988534i	$0.548250\pi$
$200$		0			0
$201$	−3.86270			−0.272454
$202$	−13.1567	+	4.27489i	−0.925705	+	0.300780i
$203$	14.1009	+	19.4083i	0.989692	+	1.36219i
$204$	−2.27387	+	1.65206i	−0.159203	+	0.115668i
$205$		0			0
$206$	−13.8197	−	10.0406i	−0.962867	−	0.699564i
$207$			2.32027i			0.161270i
$208$	−1.92727	+	2.65265i	−0.133632	+	0.183928i
$209$	3.74887	−	11.5378i	0.259314	−	0.798088i
$210$		0			0
$211$	−2.87284	−	8.84170i	−0.197775	−	0.608687i	−0.999933	−	0.0115762i	$-0.996315\pi$
$211$	−2.87284	−	8.84170i	−0.197775	−	0.608687i	0.802158	−	0.597111i	$-0.203685\pi$
$212$	−8.92120	−	2.89868i	−0.612711	−	0.199082i
$213$	−10.0860	−	3.27716i	−0.691085	−	0.224547i
$214$	−6.21566	−	19.1298i	−0.424894	−	1.30769i
$215$		0			0
$216$	0.330738	−	1.01791i	0.0225039	−	0.0692599i
$217$	−12.3019	+	16.9322i	−0.835110	+	1.14943i
$218$		−	24.7586i		−	1.67686i
$219$	4.04243	+	2.93700i	0.273162	+	0.198464i
$220$		0			0
$221$	1.08771	−	0.790270i	0.0731675	−	0.0531593i
$222$	−7.94931	−	10.9413i	−0.533523	−	0.734331i
$223$	3.23129	−	1.04991i	0.216383	−	0.0703072i	−0.198819	−	0.980036i	$-0.563711\pi$
$223$	3.23129	−	1.04991i	0.216383	−	0.0703072i	0.415203	+	0.909729i	$0.363711\pi$
$224$	34.6475			2.31498
$225$		0			0
$226$	−31.6766			−2.10710
$227$	25.4858	−	8.28083i	1.69155	−	0.549618i	0.704454	−	0.709750i	$-0.251192\pi$
$227$	25.4858	−	8.28083i	1.69155	−	0.549618i	0.987096	+	0.160132i	$0.0511919\pi$
$228$	−11.3029	−	15.5572i	−0.748555	−	1.03030i
$229$	−0.956255	+	0.694760i	−0.0631911	+	0.0459110i	−0.618932	−	0.785444i	$-0.712435\pi$
$229$	−0.956255	+	0.694760i	−0.0631911	+	0.0459110i	0.555741	+	0.831355i	$0.312435\pi$
$230$		0			0
$231$	5.57078	+	4.04741i	0.366530	+	0.266300i
$232$			5.89121i			0.386777i
$233$	4.17024	−	5.73984i	0.273201	−	0.376030i	−0.650266	−	0.759707i	$-0.725342\pi$
$233$	4.17024	−	5.73984i	0.273201	−	0.376030i	0.923467	+	0.383677i	$0.125342\pi$
$234$	−0.785653	+	2.41799i	−0.0513598	+	0.158069i
$235$		0			0
$236$	7.08566	+	21.8074i	0.461237	+	1.41954i
$237$	−13.8408	−	4.49714i	−0.899055	−	0.292121i
$238$	−9.87345	−	3.20808i	−0.640001	−	0.207949i
$239$	−0.0132236	−	0.0406981i	−0.000855365	−	0.00263254i	0.950628	−	0.310333i	$-0.100441\pi$
$239$	−0.0132236	−	0.0406981i	−0.000855365	−	0.00263254i	−0.951483	+	0.307700i	$0.900441\pi$
$240$		0			0
$241$	−3.63746	+	11.1950i	−0.234310	+	0.721131i	0.762903	+	0.646513i	$0.223774\pi$
$241$	−3.63746	+	11.1950i	−0.234310	+	0.721131i	−0.997212	+	0.0746174i	$0.976226\pi$
$242$	10.6084	−	14.6012i	0.681934	−	0.938602i
$243$			1.00000i			0.0641500i
$244$	2.82808	+	2.05472i	0.181049	+	0.131540i
$245$		0			0
$246$	12.8297	−	9.32131i	0.817991	−	0.594305i
$247$	5.40680	+	7.44182i	0.344026	+	0.473511i
$248$	−4.88806	+	1.58823i	−0.310392	+	0.100852i
$249$	8.73603			0.553623
$250$		0			0
$251$	17.4764			1.10310			0.551550	−	0.834142i	$-0.314036\pi$
$251$	17.4764			1.10310			0.551550	+	0.834142i	$0.314036\pi$
$252$	10.3805	−	3.37284i	0.653912	−	0.212469i
$253$	−2.15471	−	2.96571i	−0.135466	−	0.186452i
$254$	−29.1816	+	21.2017i	−1.83102	+	1.33031i
$255$		0			0
$256$	−4.20735	−	3.05682i	−0.262960	−	0.191051i
$257$		−	15.4671i		−	0.964814i	−0.875947	−	0.482407i	$-0.839763\pi$
$257$		−	15.4671i		−	0.964814i	0.875947	−	0.482407i	$-0.160237\pi$
$258$	−1.55932	+	2.14622i	−0.0970792	+	0.133618i
$259$	8.58236	−	26.4138i	0.533282	−	1.64127i
$260$		0			0
$261$	−1.70092	−	5.23490i	−0.105284	−	0.324032i
$262$	0.663815	+	0.215687i	0.0410106	+	0.0133252i
$263$	1.37674	+	0.447331i	0.0848936	+	0.0275836i	0.351156	−	0.936317i	$-0.385789\pi$
$263$	1.37674	+	0.447331i	0.0848936	+	0.0275836i	−0.266262	+	0.963901i	$0.585789\pi$
$264$	0.522535	+	1.60820i	0.0321598	+	0.0989778i
$265$		0			0
$266$	21.9487	−	67.5513i	1.34576	−	4.14183i
$267$	5.90026	−	8.12102i	0.361090	−	0.496998i
$268$		−	9.67336i		−	0.590895i
$269$	−7.04344	−	5.11736i	−0.429446	−	0.312011i	0.351981	−	0.936007i	$-0.385508\pi$
$269$	−7.04344	−	5.11736i	−0.429446	−	0.312011i	−0.781427	+	0.623996i	$0.785508\pi$
$270$		0			0
$271$	23.1652	−	16.8305i	1.40719	−	1.02238i	0.413462	−	0.910521i	$-0.364319\pi$
$271$	23.1652	−	16.8305i	1.40719	−	1.02238i	0.993724	−	0.111860i	$-0.0356807\pi$
$272$	1.80563	+	2.48524i	0.109482	+	0.150690i
$273$	−4.96556	+	1.61341i	−0.300530	+	0.0976480i
$274$	−9.68359			−0.585007
$275$		0			0
$276$	−5.81066			−0.349761
$277$	5.04259	−	1.63844i	0.302980	−	0.0984442i	−0.153582	−	0.988136i	$-0.549081\pi$
$277$	5.04259	−	1.63844i	0.302980	−	0.0984442i	0.456562	+	0.889692i	$0.349081\pi$
$278$	5.90555	+	8.12830i	0.354192	+	0.487503i
$279$	3.88495	−	2.82258i	0.232586	−	0.168983i
$280$		0			0
$281$	19.4837	+	14.1557i	1.16230	+	0.844461i	0.990067	−	0.140595i	$-0.0449015\pi$
$281$	19.4837	+	14.1557i	1.16230	+	0.844461i	0.172234	+	0.985056i	$0.444902\pi$
$282$		−	8.76025i		−	0.521665i
$283$	−15.9374	+	21.9359i	−0.947380	+	1.30396i	0.00530192	+	0.999986i	$0.498312\pi$
$283$	−15.9374	+	21.9359i	−0.947380	+	1.30396i	−0.952682	+	0.303970i	$0.901688\pi$
$284$	8.20698	−	25.2585i	0.486995	−	1.49882i
$285$		0			0
$286$	−1.24126	−	3.82020i	−0.0733971	−	0.225893i
$287$	30.9726	+	10.0636i	1.82826	+	0.594037i
$288$	−7.56051	−	2.45656i	−0.445507	−	0.144754i
$289$	4.86404	+	14.9700i	0.286120	+	0.880587i
$290$		0			0
$291$	−2.31762	+	7.13289i	−0.135861	+	0.418137i
$292$	−7.35512	+	10.1234i	−0.430426	+	0.592430i
$293$		−	20.3016i		−	1.18603i	−0.805190	−	0.593017i	$-0.797937\pi$
$293$		−	20.3016i		−	1.18603i	0.805190	−	0.593017i	$-0.202063\pi$
$294$	20.5966	+	14.9643i	1.20122	+	0.872736i
$295$		0			0
$296$	5.51769	−	4.00883i	0.320709	−	0.233009i
$297$	−0.928645	−	1.27817i	−0.0538855	−	0.0741670i
$298$	−9.43921	+	3.06698i	−0.546799	+	0.177666i
$299$	2.77955			0.160745
$300$		0			0
$301$	−5.44792			−0.314013
$302$	−13.2043	+	4.29034i	−0.759823	+	0.246881i
$303$	3.83131	+	5.27335i	0.220103	+	0.302946i
$304$	−17.0032	+	12.3536i	−0.975203	+	0.708527i
$305$		0			0
$306$	1.92705	+	1.40008i	0.110162	+	0.0800375i
$307$			2.51330i			0.143442i	0.997425	+	0.0717208i	$0.0228491\pi$
$307$			2.51330i			0.143442i	−0.997425	+	0.0717208i	$0.977151\pi$
$308$	−10.1359	+	13.9509i	−0.577548	+	0.794927i
$309$	−2.48720	+	7.65482i	−0.141492	+	0.435468i
$310$		0			0
$311$	1.49075	+	4.58806i	0.0845327	+	0.260165i	0.984385	−	0.176030i	$-0.0563257\pi$
$311$	1.49075	+	4.58806i	0.0845327	+	0.260165i	−0.899852	+	0.436195i	$0.856326\pi$
$312$	−1.21939	−	0.396205i	−0.0690345	−	0.0224307i
$313$	−5.69504	−	1.85043i	−0.321903	−	0.104592i	0.143608	−	0.989635i	$-0.454129\pi$
$313$	−5.69504	−	1.85043i	−0.321903	−	0.104592i	−0.465511	+	0.885042i	$0.654129\pi$
$314$	−2.61944	−	8.06180i	−0.147823	−	0.454954i
$315$		0			0
$316$	11.2622	−	34.6615i	0.633548	−	1.94986i
$317$	−10.1999	+	14.0389i	−0.572883	+	0.788506i	−0.992893	−	0.119014i	$-0.962027\pi$
$317$	−10.1999	+	14.0389i	−0.572883	+	0.788506i	0.420010	+	0.907520i	$0.362027\pi$
$318$			7.94959i			0.445791i
$319$	7.03543	+	5.11154i	0.393909	+	0.286191i
$320$		0			0
$321$	−7.66742	+	5.57071i	−0.427954	+	0.310926i
$322$	−12.6153	−	17.3635i	−0.703025	−	0.967631i
$323$	8.19624	−	2.66312i	0.456051	−	0.148180i
$324$	−2.50430			−0.139128
$325$		0			0
$326$	10.1902			0.564383
$327$	−11.0948	+	3.60491i	−0.613543	+	0.199352i
$328$	4.70073	+	6.47000i	0.259555	+	0.357246i
$329$	14.5542	−	10.5742i	0.802398	−	0.582976i
$330$		0			0
$331$	−16.4518	−	11.9529i	−0.904270	−	0.656991i	0.0352890	−	0.999377i	$-0.488765\pi$
$331$	−16.4518	−	11.9529i	−0.904270	−	0.656991i	−0.939559	+	0.342386i	$0.888765\pi$
$332$			21.8776i			1.20069i
$333$	−3.74555	+	5.15531i	−0.205255	+	0.282509i
$334$	−15.5171	+	47.7568i	−0.849059	+	2.61314i
$335$		0			0
$336$	−3.68636	−	11.3454i	−0.201107	−	0.618945i
$337$	−32.5805	−	10.5860i	−1.77477	−	0.576658i	−0.776219	−	0.630463i	$-0.782865\pi$
$337$	−32.5805	−	10.5860i	−1.77477	−	0.576658i	−0.998551	+	0.0538048i	$0.982865\pi$
$338$	−23.3434	−	7.58472i	−1.26971	−	0.412554i
$339$	4.61219	+	14.1949i	0.250500	+	0.770960i
$340$		0			0
$341$	−2.34445	+	7.21548i	−0.126959	+	0.390740i
$342$	−9.57897	+	13.1843i	−0.517971	+	0.712926i
$343$			21.7731i			1.17564i
$344$	−1.08234	−	0.786366i	−0.0583558	−	0.0423980i
$345$		0			0
$346$	−24.9039	+	18.0938i	−1.33884	+	0.972727i
$347$	−0.0290140	−	0.0399344i	−0.00155756	−	0.00214379i	0.808238	−	0.588857i	$-0.200422\pi$
$347$	−0.0290140	−	0.0399344i	−0.00155756	−	0.00214379i	−0.809795	+	0.586713i	$0.800422\pi$
$348$	13.1098	−	4.25962i	0.702757	−	0.228340i
$349$	7.47437			0.400094			0.200047	−	0.979786i	$-0.435891\pi$
$349$	7.47437			0.400094			0.200047	+	0.979786i	$0.435891\pi$
$350$		0			0
$351$	1.19794			0.0639413
$352$	11.9449	−	3.88113i	0.636665	−	0.206865i
$353$	10.9122	+	15.0194i	0.580799	+	0.799401i	0.993783	−	0.111337i	$-0.0355133\pi$
$353$	10.9122	+	15.0194i	0.580799	+	0.799401i	−0.412984	+	0.910738i	$0.635513\pi$
$354$	15.7211	−	11.4220i	0.835567	−	0.607075i
$355$		0			0
$356$	20.3375	+	14.7760i	1.07788	+	0.783128i
$357$			4.89158i			0.258890i
$358$	0.993921	−	1.36802i	0.0525304	−	0.0723019i
$359$	−3.27695	+	10.0854i	−0.172951	+	0.532289i	−0.999534	−	0.0305264i	$-0.990282\pi$
$359$	−3.27695	+	10.0854i	−0.172951	+	0.532289i	0.826583	+	0.562815i	$0.190282\pi$
$360$		0			0
$361$	12.3490	+	38.0062i	0.649945	+	2.00032i
$362$	28.6994	+	9.32500i	1.50841	+	0.490111i
$363$	−8.08769	−	2.62785i	−0.424493	−	0.137926i
$364$	−4.04046	−	12.4353i	−0.211778	−	0.651785i
$365$		0			0
$366$	0.915470	−	2.81753i	0.0478524	−	0.147274i
$367$	6.82867	−	9.39886i	0.356454	−	0.490617i	−0.592703	−	0.805421i	$-0.701939\pi$
$367$	6.82867	−	9.39886i	0.356454	−	0.490617i	0.949156	+	0.314805i	$0.101939\pi$
$368$			6.35078i			0.331057i
$369$	−6.04508	−	4.39201i	−0.314695	−	0.228639i
$370$		0			0
$371$	−13.2074	+	9.59570i	−0.685692	+	0.498184i
$372$	7.06859	+	9.72907i	0.366489	+	0.504429i
$373$	21.9953	−	7.14671i	1.13887	−	0.370043i	0.321932	−	0.946763i	$-0.395668\pi$
$373$	21.9953	−	7.14671i	1.13887	−	0.370043i	0.816942	+	0.576720i	$0.195668\pi$
$374$	−3.76328			−0.194595
$375$		0			0
$376$	4.41779			0.227830
$377$	−6.27109	+	2.03760i	−0.322978	+	0.104942i
$378$	−5.43700	−	7.48339i	−0.279649	−	0.384904i
$379$	20.1374	−	14.6307i	1.03439	−	0.751527i	0.0652058	−	0.997872i	$-0.479230\pi$
$379$	20.1374	−	14.6307i	1.03439	−	0.751527i	0.969182	+	0.246345i	$0.0792296\pi$
$380$		0			0
$381$	13.7498	+	9.98980i	0.704423	+	0.511793i
$382$			22.0079i			1.12602i
$383$	−9.24123	+	12.7195i	−0.472205	+	0.649934i	−0.976984	−	0.213315i	$-0.931574\pi$
$383$	−9.24123	+	12.7195i	−0.472205	+	0.649934i	0.504779	+	0.863249i	$0.331574\pi$
$384$	2.56179	−	7.88439i	0.130731	−	0.402349i
$385$		0			0
$386$	2.85100	+	8.77449i	0.145112	+	0.446610i
$387$	1.18880	+	0.386266i	0.0604303	+	0.0196350i
$388$	−17.8629	−	5.80400i	−0.906851	−	0.294654i
$389$	2.62860	+	8.09000i	0.133275	+	0.410179i	0.995318	−	0.0966568i	$-0.0308149\pi$
$389$	2.62860	+	8.09000i	0.133275	+	0.410179i	−0.862042	+	0.506836i	$0.830815\pi$
$390$		0			0
$391$	0.804717	−	2.47667i	0.0406963	−	0.125250i
$392$	−7.54649	+	10.3869i	−0.381155	+	0.524615i
$393$		−	0.328872i		−	0.0165894i
$394$	3.22779	+	2.34513i	0.162614	+	0.118146i
$395$		0			0
$396$	3.20092	−	2.32561i	0.160852	−	0.116866i
$397$	15.4322	+	21.2407i	0.774522	+	1.06604i	0.995865	+	0.0908420i	$0.0289558\pi$
$397$	15.4322	+	21.2407i	0.774522	+	1.06604i	−0.221343	+	0.975196i	$0.571044\pi$
$398$	−8.59921	+	2.79405i	−0.431039	+	0.140053i
$399$	−33.4667			−1.67543
$400$		0			0
$401$	−25.2815			−1.26250			−0.631250	−	0.775579i	$-0.717458\pi$
$401$	−25.2815			−1.26250			−0.631250	+	0.775579i	$0.717458\pi$
$402$	−7.79670	+	2.53330i	−0.388864	+	0.126350i
$403$	−3.38128	−	4.65393i	−0.168434	−	0.231829i
$404$	−13.2060	+	9.59475i	−0.657025	+	0.477356i
$405$		0			0
$406$	41.1908	+	29.9269i	2.04427	+	1.48525i
$407$		−	10.0677i		−	0.499035i
$408$	−0.706062	+	0.971811i	−0.0349553	+	0.0481118i
$409$	−10.4427	+	32.1392i	−0.516357	+	1.58918i	0.264443	+	0.964401i	$0.414812\pi$
$409$	−10.4427	+	32.1392i	−0.516357	+	1.58918i	−0.780800	+	0.624781i	$0.785188\pi$
$410$		0			0
$411$	1.40995	+	4.33939i	0.0695479	+	0.214046i
$412$	−19.1700	−	6.22870i	−0.944437	−	0.306866i
$413$	37.9529	+	12.3317i	1.86754	+	0.606801i
$414$	1.52172	+	4.68338i	0.0747885	+	0.230175i
$415$		0			0
$416$	−2.94281	+	9.05703i	−0.144283	+	0.444057i
$417$	2.78258	−	3.82989i	0.136263	−	0.187550i
$418$		−	25.7473i		−	1.25934i
$419$	6.41819	+	4.66309i	0.313549	+	0.227807i	0.733418	−	0.679778i	$-0.237924\pi$
$419$	6.41819	+	4.66309i	0.313549	+	0.227807i	−0.419869	+	0.907585i	$0.637924\pi$
$420$		0			0
$421$	−6.05788	+	4.40131i	−0.295243	+	0.214507i	−0.725539	−	0.688181i	$-0.758409\pi$
$421$	−6.05788	+	4.40131i	−0.295243	+	0.214507i	0.430296	+	0.902688i	$0.358409\pi$
$422$	−11.5974	−	15.9625i	−0.564554	−	0.777042i
$423$	−3.92563	+	1.27551i	−0.190870	+	0.0620176i
$424$	−4.00897			−0.194693
$425$		0			0
$426$	−22.5076			−1.09049
$427$	5.78604	−	1.88000i	0.280006	−	0.0909795i
$428$	−13.9507	−	19.2015i	−0.674333	−	0.928140i
$429$	−1.53117	+	1.11246i	−0.0739257	+	0.0537101i
$430$		0			0
$431$	−18.8882	−	13.7231i	−0.909811	−	0.661016i	0.0311564	−	0.999515i	$-0.490081\pi$
$431$	−18.8882	−	13.7231i	−0.909811	−	0.661016i	−0.940967	+	0.338498i	$0.890081\pi$
$432$			2.73708i			0.131688i
$433$	−1.97306	+	2.71569i	−0.0948193	+	0.130508i	−0.853791	−	0.520616i	$-0.825702\pi$
$433$	−1.97306	+	2.71569i	−0.0948193	+	0.130508i	0.758971	+	0.651124i	$0.225702\pi$
$434$	−13.7262	+	42.2449i	−0.658879	+	2.02782i
$435$		0			0
$436$	−9.02778	−	27.7846i	−0.432352	−	1.33064i
$437$	16.9446	+	5.50564i	0.810571	+	0.263370i
$438$	10.0857	+	3.27703i	0.481912	+	0.156583i
$439$	2.93072	+	9.01984i	0.139876	+	0.430493i	0.996317	−	0.0857520i	$-0.0273293\pi$
$439$	2.93072	+	9.01984i	0.139876	+	0.430493i	−0.856441	+	0.516245i	$0.827329\pi$
$440$		0			0
$441$	3.70686	−	11.4086i	0.176517	−	0.543264i
$442$	1.67722	−	2.30849i	0.0797771	−	0.109804i
$443$			9.65446i			0.458697i	0.973344	+	0.229349i	$0.0736596\pi$
$443$			9.65446i			0.458697i	−0.973344	+	0.229349i	$0.926340\pi$
$444$	−12.9104	−	9.37999i	−0.612703	−	0.445154i
$445$		0			0
$446$	5.83366	−	4.23840i	0.276232	−	0.200694i
$447$	2.74874	+	3.78332i	0.130011	+	0.178945i
$448$	47.2437	−	15.3504i	2.23205	−	0.725238i
$449$	−31.5260			−1.48780			−0.743902	−	0.668289i	$-0.767027\pi$
$449$	−31.5260			−1.48780			−0.743902	+	0.668289i	$0.767027\pi$
$450$		0			0
$451$	11.8053			0.555888
$452$	−35.5482	+	11.5503i	−1.67205	+	0.543281i
$453$	3.84516	+	5.29241i	0.180661	+	0.248659i
$454$	46.0111	−	33.4290i	2.15941	−	1.56890i
$455$		0			0
$456$	−6.64884	−	4.83067i	−0.311361	−	0.226217i
$457$			9.94467i			0.465192i	0.972573	+	0.232596i	$0.0747220\pi$
$457$			9.94467i			0.465192i	−0.972573	+	0.232596i	$0.925278\pi$
$458$	−1.47451	+	2.02949i	−0.0688994	+	0.0948319i
$459$	0.346820	−	1.06740i	0.0161882	−	0.0498221i
$460$		0			0
$461$	−7.31863	−	22.5244i	−0.340863	−	1.04907i	−0.963762	−	0.266765i	$-0.914045\pi$
$461$	−7.31863	−	22.5244i	−0.340863	−	1.04907i	0.622899	−	0.782302i	$-0.285955\pi$
$462$	13.8988	+	4.51601i	0.646632	+	0.210104i
$463$	26.2971	+	8.54443i	1.22213	+	0.397094i	0.847857	−	0.530226i	$-0.177893\pi$
$463$	26.2971	+	8.54443i	1.22213	+	0.397094i	0.374272	+	0.927319i	$0.377893\pi$
$464$	−4.65556	−	14.3284i	−0.216129	−	0.665177i
$465$		0			0
$466$	4.65306	−	14.3206i	0.215549	−	0.663391i
$467$	−2.56180	+	3.52602i	−0.118546	+	0.163165i	−0.864166	−	0.503207i	$-0.832153\pi$
$467$	−2.56180	+	3.52602i	−0.118546	+	0.163165i	0.745620	+	0.666371i	$0.232153\pi$
$468$			3.00000i			0.138675i
$469$	−13.6200	−	9.89548i	−0.628912	−	0.456931i
$470$		0			0
$471$	−3.23124	+	2.34764i	−0.148888	+	0.108173i
$472$	5.76013	+	7.92814i	0.265132	+	0.364922i
$473$	−1.87820	+	0.610263i	−0.0863596	+	0.0280599i
$474$	−30.8864			−1.41866
$475$		0			0
$476$	−12.2500			−0.561477
$477$	3.56236	−	1.15748i	0.163109	−	0.0529973i
$478$	−0.0533827	−	0.0734750i	−0.00244167	−	0.00336067i
$479$	10.3670	−	7.53204i	0.473679	−	0.344148i	−0.325195	−	0.945647i	$-0.605430\pi$
$479$	10.3670	−	7.53204i	0.473679	−	0.344148i	0.798873	+	0.601499i	$0.205430\pi$
$480$		0			0
$481$	6.17575	+	4.48695i	0.281590	+	0.204587i
$482$			24.9822i			1.13791i
$483$	−5.94409	+	8.18133i	−0.270465	+	0.372263i
$484$	6.58092	−	20.2540i	0.299133	−	0.920636i
$485$		0			0
$486$	0.655837	+	2.01846i	0.0297494	+	0.0915592i
$487$	6.58330	+	2.13904i	0.298318	+	0.0969293i	0.454352	−	0.890822i	$-0.349871\pi$
$487$	6.58330	+	2.13904i	0.298318	+	0.0969293i	−0.156034	+	0.987752i	$0.549871\pi$
$488$	1.42088	+	0.461671i	0.0643201	+	0.0208989i
$489$	−1.48372	−	4.56641i	−0.0670960	−	0.206500i
$490$		0			0
$491$	8.28665	−	25.5037i	0.373971	−	1.15096i	−0.570199	−	0.821507i	$-0.693134\pi$
$491$	8.28665	−	25.5037i	0.373971	−	1.15096i	0.944170	−	0.329458i	$-0.106866\pi$
$492$	10.9989	−	15.1387i	0.495869	−	0.682505i
$493$			6.17766i			0.278228i
$494$	15.7940	+	11.4750i	0.710606	+	0.516286i
$495$		0			0
$496$	10.6334	−	7.72564i	0.477455	−	0.346891i
$497$	−27.1682	−	37.3938i	−1.21866	−	1.67734i
$498$	17.6333	−	5.72941i	0.790168	−	0.256741i
$499$	−2.75460			−0.123313			−0.0616565	−	0.998097i	$-0.519638\pi$
$499$	−2.75460			−0.123313			−0.0616565	+	0.998097i	$0.519638\pi$
$500$		0			0
$501$	23.6600			1.05705
$502$	35.2754	−	11.4617i	1.57442	−	0.511559i
$503$	−9.23422	−	12.7098i	−0.411733	−	0.566702i	0.551907	−	0.833906i	$-0.313900\pi$
$503$	−9.23422	−	12.7098i	−0.411733	−	0.566702i	−0.963640	+	0.267203i	$0.913900\pi$
$504$	3.77387	−	2.74188i	0.168102	−	0.122133i
$505$		0			0
$506$	−6.29422	−	4.57302i	−0.279812	−	0.203295i
$507$			11.5649i			0.513617i
$508$	−25.0175	+	34.4336i	−1.10997	+	1.52774i
$509$	12.6970	−	39.0774i	0.562785	−	1.73207i	−0.111657	−	0.993747i	$-0.535616\pi$
$509$	12.6970	−	39.0774i	0.562785	−	1.73207i	0.674442	−	0.738328i	$-0.264384\pi$
$510$		0			0
$511$	6.72968	+	20.7118i	0.297703	+	0.916237i
$512$	−26.2659	−	8.53432i	−1.16080	−	0.377167i
$513$	7.30285	+	2.37284i	0.322429	+	0.104763i
$514$	−10.1439	−	31.2198i	−0.447430	−	1.37705i
$515$		0			0
$516$	−0.967325	+	2.97712i	−0.0425841	+	0.131060i
$517$	3.83312	−	5.27584i	0.168580	−	0.232031i
$518$		−	58.9438i		−	2.58984i
$519$	11.7342	+	8.52541i	0.515075	+	0.374224i
$520$		0			0
$521$	−29.2630	+	21.2608i	−1.28203	+	0.931452i	−0.999612	−	0.0278383i	$-0.991138\pi$
$521$	−29.2630	+	21.2608i	−1.28203	+	0.931452i	−0.282421	+	0.959290i	$0.591138\pi$
$522$	−6.86648	−	9.45090i	−0.300538	−	0.413655i
$523$	−26.6761	+	8.66761i	−1.16647	+	0.379008i	−0.827323	−	0.561727i	$-0.810137\pi$
$523$	−26.6761	+	8.66761i	−1.16647	+	0.379008i	−0.339144	+	0.940735i	$0.610137\pi$
$524$	0.823595			0.0359789
$525$		0			0
$526$	3.07228			0.133958
$527$	−5.12573	+	1.66545i	−0.223280	+	0.0725482i
$528$	−2.54178	−	3.49846i	−0.110617	−	0.152251i
$529$	−14.2519	+	10.3546i	−0.619648	+	0.450201i
$530$		0			0
$531$	−7.40746	−	5.38184i	−0.321456	−	0.233552i
$532$		−	83.8108i		−	3.63366i
$533$	−5.26137	+	7.24165i	−0.227895	+	0.313671i
$534$	6.58338	−	20.2616i	0.284891	−	0.876803i
$535$		0			0
$536$	−1.27754	−	3.93187i	−0.0551815	−	0.169831i
$537$	−0.757750	−	0.246208i	−0.0326993	−	0.0106247i
$538$	−17.5731	−	5.70983i	−0.757628	−	0.246168i
$539$	5.85650	+	18.0244i	0.252257	+	0.776368i
$540$		0			0
$541$	1.06865	−	3.28896i	0.0459448	−	0.141404i	−0.925452	−	0.378864i	$-0.876315\pi$
$541$	1.06865	−	3.28896i	0.0459448	−	0.141404i	0.971397	+	0.237460i	$0.0763149\pi$
$542$	35.7200	−	49.1643i	1.53430	−	2.11179i
$543$		−	14.2185i		−	0.610173i
$544$	7.21812	+	5.24427i	0.309474	+	0.224846i
$545$		0			0
$546$	−8.96465	+	6.51320i	−0.383652	+	0.278739i
$547$	8.20751	+	11.2967i	0.350928	+	0.483011i	0.947593	−	0.319479i	$-0.103508\pi$
$547$	8.20751	+	11.2967i	0.350928	+	0.483011i	−0.596665	+	0.802490i	$0.703508\pi$
$548$	−10.8671	+	3.53095i	−0.464221	+	0.150835i
$549$	−1.39588			−0.0595747
$550$		0			0
$551$	−42.2657			−1.80058
$552$	−2.36182	+	0.767403i	−0.100526	+	0.0326629i
$553$	−37.2821	−	51.3144i	−1.58540	−	2.18211i
$554$	9.10372	−	6.61424i	0.386780	−	0.281012i
$555$		0			0
$556$	9.59118	+	6.96840i	0.406757	+	0.295526i
$557$			6.59585i			0.279475i	0.990189	+	0.139738i	$0.0446259\pi$
$557$			6.59585i			0.279475i	−0.990189	+	0.139738i	$0.955374\pi$
$558$	5.99046	−	8.24516i	0.253596	−	0.349045i
$559$	0.462723	−	1.42411i	0.0195711	−	0.0602336i
$560$		0			0
$561$	0.547943	+	1.68640i	0.0231342	+	0.0711997i
$562$	48.6110	+	15.7947i	2.05053	+	0.666257i
$563$	−15.2376	−	4.95100i	−0.642189	−	0.208660i	−0.0302222	−	0.999543i	$-0.509621\pi$
$563$	−15.2376	−	4.95100i	−0.642189	−	0.208660i	−0.611967	+	0.790883i	$0.709621\pi$
$564$	−3.19427	−	9.83094i	−0.134503	−	0.413957i
$565$		0			0
$566$	−17.7826	+	54.7291i	−0.747457	+	2.30044i
$567$	−2.56180	+	3.52602i	−0.107586	+	0.148079i
$568$		−	11.3505i		−	0.476258i
$569$	18.6813	+	13.5728i	0.783162	+	0.569001i	0.905926	−	0.423435i	$-0.139176\pi$
$569$	18.6813	+	13.5728i	0.783162	+	0.569001i	−0.122764	+	0.992436i	$0.539176\pi$
$570$		0			0
$571$	27.5148	−	19.9907i	1.15146	−	0.836583i	0.162784	−	0.986662i	$-0.447953\pi$
$571$	27.5148	−	19.9907i	1.15146	−	0.836583i	0.988674	+	0.150078i	$0.0479526\pi$
$572$	−2.78594	−	3.83451i	−0.116486	−	0.160329i
$573$	9.86215	−	3.20441i	0.411997	−	0.133866i
$574$	69.1171			2.88489
$575$		0			0
$576$	−11.3975			−0.474896
$577$	−6.15074	+	1.99850i	−0.256059	+	0.0831985i	−0.434233	−	0.900800i	$-0.642981\pi$
$577$	−6.15074	+	1.99850i	−0.256059	+	0.0831985i	0.178175	+	0.983999i	$0.442981\pi$
$578$	19.6357	+	27.0263i	0.816739	+	1.12414i
$579$	3.51690	−	2.55517i	0.146157	−	0.106189i
$580$		0			0
$581$	30.8034	+	22.3800i	1.27794	+	0.928479i
$582$			15.9174i			0.659798i
$583$	−3.47841	+	4.78762i	−0.144061	+	0.198283i
$584$	−1.65261	+	5.08620i	−0.0683853	+	0.210468i
$585$		0			0
$586$	−13.3146	−	40.9780i	−0.550019	−	1.69279i
$587$	−36.6168	−	11.8975i	−1.51134	−	0.491063i	−0.568037	−	0.823003i	$-0.692297\pi$
$587$	−36.6168	−	11.8975i	−1.51134	−	0.491063i	−0.943301	+	0.331940i	$0.892297\pi$
$588$	28.5704	+	9.28310i	1.17822	+	0.382828i
$589$	−11.3945	−	35.0687i	−0.469503	−	1.44498i
$590$		0			0
$591$	0.580921	−	1.78789i	0.0238959	−	0.0735440i
$592$	−10.2519	+	14.1105i	−0.421350	+	0.579939i
$593$			4.93069i			0.202479i	0.994862	+	0.101240i	$0.0322808\pi$
$593$			4.93069i			0.202479i	−0.994862	+	0.101240i	$0.967719\pi$
$594$	−2.71270	−	1.97090i	−0.111304	−	0.0808668i
$595$		0			0
$596$	−9.47457	+	6.88368i	−0.388093	+	0.281966i
$597$	2.50413	+	3.44664i	0.102487	+	0.141062i
$598$	5.61040	−	1.82293i	0.229426	−	0.0745452i
$599$	35.0268			1.43116			0.715578	−	0.698533i	$-0.246164\pi$
$599$	35.0268			1.43116			0.715578	+	0.698533i	$0.246164\pi$
$600$		0			0
$601$	−4.90570			−0.200108			−0.100054	−	0.994982i	$-0.531901\pi$
$601$	−4.90570			−0.200108			−0.100054	+	0.994982i	$0.531901\pi$
$602$	−10.9964	+	3.57295i	−0.448180	+	0.145623i
$603$	2.27044	+	3.12499i	0.0924594	+	0.127259i
$604$	−13.2538	+	9.62943i	−0.539289	+	0.391816i
$605$		0			0
$606$	11.1918	+	8.13132i	0.454636	+	0.330312i
$607$		−	48.6955i		−	1.97649i	−0.152884	−	0.988244i	$-0.548856\pi$
$607$		−	48.6955i		−	1.97649i	0.152884	−	0.988244i	$-0.451144\pi$
$608$	−35.8798	+	49.3842i	−1.45512	+	2.00280i
$609$	7.41330	−	22.8158i	0.300402	−	0.924543i
$610$		0			0
$611$	1.52799	+	4.70266i	0.0618158	+	0.190249i
$612$	2.67310	+	0.868541i	0.108053	+	0.0351087i
$613$	16.3714	+	5.31938i	0.661234	+	0.214848i	0.620361	−	0.784317i	$-0.286986\pi$
$613$	16.3714	+	5.31938i	0.661234	+	0.214848i	0.0408728	+	0.999164i	$0.486986\pi$
$614$	1.64832	+	5.07299i	0.0665206	+	0.204729i
$615$		0			0
$616$	−2.27742	+	7.00918i	−0.0917598	+	0.282408i
$617$	18.5794	−	25.5723i	0.747978	−	1.02950i	−0.250141	−	0.968209i	$-0.580477\pi$
$617$	18.5794	−	25.5723i	0.747978	−	1.02950i	0.998120	−	0.0612947i	$-0.0195229\pi$
$618$			17.0821i			0.687145i
$619$	−18.4615	−	13.4130i	−0.742029	−	0.539116i	0.151317	−	0.988485i	$-0.451649\pi$
$619$	−18.4615	−	13.4130i	−0.742029	−	0.539116i	−0.893346	+	0.449370i	$0.851649\pi$
$620$		0			0
$621$	1.87714	−	1.36382i	0.0753271	−	0.0547283i
$622$	6.01804	+	8.28312i	0.241301	+	0.332123i
$623$	41.6089	−	13.5196i	1.66703	−	0.541649i
$624$	3.27886			0.131259
$625$		0			0
$626$	−12.7088			−0.507945
$627$	−11.5378	+	3.74887i	−0.460776	+	0.149715i
$628$	−5.87918	−	8.09200i	−0.234605	−	0.322906i
$629$	5.78598	−	4.20376i	0.230702	−	0.167615i
$630$		0			0
$631$	−30.7830	−	22.3652i	−1.22545	−	0.890344i	−0.228913	−	0.973447i	$-0.573517\pi$
$631$	−30.7830	−	22.3652i	−1.22545	−	0.890344i	−0.996541	+	0.0831027i	$0.973517\pi$
$632$		−	15.5760i		−	0.619581i
$633$	−5.46447	+	7.52120i	−0.217193	+	0.298941i
$634$	−11.3808	+	35.0265i	−0.451989	+	1.39108i
$635$		0			0
$636$	2.89868	+	8.92120i	0.114940	+	0.353749i
$637$	−13.6668	−	4.44060i	−0.541497	−	0.175943i
$638$	17.5531	+	5.70334i	0.694933	+	0.225797i
$639$	3.27716	+	10.0860i	0.129642	+	0.398998i
$640$		0			0
$641$	8.19229	−	25.2133i	0.323576	−	0.995864i	−0.648504	−	0.761212i	$-0.724605\pi$
$641$	8.19229	−	25.2133i	0.323576	−	0.995864i	0.972079	−	0.234652i	$-0.0753952\pi$
$642$	−11.8229	+	16.2728i	−0.466612	+	0.642237i
$643$		−	36.0014i		−	1.41976i	−0.704324	−	0.709879i	$-0.748750\pi$
$643$		−	36.0014i		−	1.41976i	0.704324	−	0.709879i	$-0.251250\pi$
$644$	−20.4885	−	14.8858i	−0.807360	−	0.586582i
$645$		0			0
$646$	14.7972	−	10.7508i	0.582188	−	0.422984i
$647$	24.5600	+	33.8040i	0.965554	+	1.32897i	0.944261	+	0.329197i	$0.106778\pi$
$647$	24.5600	+	33.8040i	0.965554	+	1.32897i	0.0212924	+	0.999773i	$0.493222\pi$
$648$	−1.01791	+	0.330738i	−0.0399872	+	0.0129926i
$649$	14.4658			0.567833
$650$		0			0
$651$	20.9293			0.820284
$652$	11.4357	−	3.71567i	0.447855	−	0.145517i
$653$	−12.6023	−	17.3456i	−0.493168	−	0.678787i	0.487801	−	0.872955i	$-0.337799\pi$
$653$	−12.6023	−	17.3456i	−0.493168	−	0.678787i	−0.980968	+	0.194168i	$0.937799\pi$
$654$	−20.0301	+	14.5527i	−0.783240	+	0.569057i
$655$		0			0
$656$	−16.5459	−	12.0213i	−0.646009	−	0.469353i
$657$		−	4.99672i		−	0.194940i
$658$	22.4420	−	30.8888i	0.874882	−	1.20417i
$659$	5.20135	−	16.0081i	0.202616	−	0.623587i	−0.797187	−	0.603732i	$-0.793680\pi$
$659$	5.20135	−	16.0081i	0.202616	−	0.623587i	0.999803	−	0.0198549i	$-0.00632042\pi$
$660$		0			0
$661$	0.629918	+	1.93869i	0.0245010	+	0.0754062i	0.962559	−	0.271071i	$-0.0873778\pi$
$661$	0.629918	+	1.93869i	0.0245010	+	0.0754062i	−0.938058	+	0.346477i	$0.887378\pi$
$662$	−41.0463	−	13.3368i	−1.59531	−	0.518348i
$663$	−1.27868	−	0.415470i	−0.0496600	−	0.0161355i
$664$	2.88934	+	8.89248i	0.112128	+	0.345095i
$665$		0			0
$666$	−4.17920	+	12.8623i	−0.161941	+	0.498402i
$667$	−7.50689	+	10.3323i	−0.290668	+	0.400070i
$668$			59.2518i			2.29252i
$669$	−2.74870	−	1.99705i	−0.106271	−	0.0772104i
$670$		0			0
$671$	1.78417	−	1.29628i	0.0688772	−	0.0500422i
$672$	−20.3653	−	28.0304i	−0.785608	−	1.08130i
$673$	−33.6461	+	10.9323i	−1.29696	+	0.421409i	−0.874524	−	0.484983i	$-0.838826\pi$
$673$	−33.6461	+	10.9323i	−1.29696	+	0.421409i	−0.422439	+	0.906391i	$0.638826\pi$
$674$	−72.7050			−2.80049
$675$		0			0
$676$	−28.9621			−1.11393
$677$	42.2434	−	13.7257i	1.62354	−	0.527522i	0.650770	−	0.759275i	$-0.274446\pi$
$677$	42.2434	−	13.7257i	1.62354	−	0.527522i	0.972775	+	0.231753i	$0.0744462\pi$
$678$	18.6190	+	25.6269i	0.715060	+	0.984196i
$679$	−26.4450	+	19.2134i	−1.01487	+	0.737344i
$680$		0			0
$681$	−21.6795	−	15.7511i	−0.830760	−	0.603582i
$682$			16.1017i			0.616567i
$683$	24.9780	−	34.3793i	0.955758	−	1.31549i	0.00683639	−	0.999977i	$-0.497824\pi$
$683$	24.9780	−	34.3793i	0.955758	−	1.31549i	0.948922	−	0.315512i	$-0.102176\pi$
$684$	−5.94230	+	18.2885i	−0.227210	+	0.699280i
$685$		0			0
$686$	14.2796	+	43.9481i	0.545198	+	1.67795i
$687$	1.12415	+	0.365257i	0.0428888	+	0.0139354i
$688$	3.25385	+	1.05724i	0.124052	+	0.0403069i
$689$	−1.38659	−	4.26749i	−0.0528249	−	0.162578i
$690$		0			0
$691$	8.67746	−	26.7065i	0.330106	−	1.01596i	−0.638977	−	0.769226i	$-0.720642\pi$
$691$	8.67746	−	26.7065i	0.330106	−	1.01596i	0.969083	−	0.246736i	$-0.0793580\pi$
$692$	−21.3502	+	29.3860i	−0.811612	+	1.11709i
$693$		−	6.88586i		−	0.261572i
$694$	−0.0847541	−	0.0615775i	−0.00321722	−	0.00233745i
$695$		0			0
$696$	4.76609	−	3.46276i	0.180658	−	0.131256i
$697$	4.92930	+	6.78460i	0.186711	+	0.256985i
$698$	15.0867	−	4.90197i	0.571040	−	0.185542i
$699$	−7.09483			−0.268351
$700$		0			0
$701$	46.4314			1.75369			0.876845	−	0.480772i	$-0.159644\pi$
$701$	46.4314			1.75369			0.876845	+	0.480772i	$0.159644\pi$
$702$	2.41799	−	0.785653i	0.0912612	−	0.0296526i
$703$	28.7609	+	39.5860i	1.08474	+	1.49301i
$704$	14.5680	−	10.5842i	0.549051	−	0.398909i
$705$		0			0
$706$	31.8762	+	23.1594i	1.19967	+	0.871615i
$707$			28.4090i			1.06843i
$708$	13.4777	−	18.5505i	0.506524	−	0.697171i
$709$	−15.0285	+	46.2529i	−0.564406	+	1.73706i	0.105305	+	0.994440i	$0.466418\pi$
$709$	−15.0285	+	46.2529i	−0.564406	+	1.73706i	−0.669710	+	0.742622i	$0.733582\pi$
$710$		0			0
$711$	4.49714	+	13.8408i	0.168656	+	0.519070i
$712$	10.2179	+	3.31999i	0.382932	+	0.124422i
$713$	−10.5968	−	3.44310i	−0.396852	−	0.128945i
$714$	3.20808	+	9.87345i	0.120059	+	0.369505i
$715$		0			0
$716$	0.616579	−	1.89763i	0.0230426	−	0.0709179i
$717$	−0.0251528	+	0.0346199i	−0.000939350	+	0.00129290i
$718$			22.5062i			0.839923i
$719$	−17.1475	−	12.4584i	−0.639493	−	0.464619i	0.220183	−	0.975459i	$-0.429334\pi$
$719$	−17.1475	−	12.4584i	−0.639493	−	0.464619i	−0.859676	+	0.510840i	$0.829334\pi$
$720$		0			0
$721$	−28.3801	+	20.6193i	−1.05693	+	0.767904i
$722$	49.8517	+	68.6150i	1.85529	+	2.55359i
$723$	11.1950	−	3.63746i	0.416345	−	0.135279i
$724$	35.6073			1.32333
$725$		0			0
$726$	−18.0481			−0.669828
$727$	12.9259	−	4.19988i	0.479396	−	0.155765i	−0.0593437	−	0.998238i	$-0.518901\pi$
$727$	12.9259	−	4.19988i	0.479396	−	0.155765i	0.538739	+	0.842473i	$0.318901\pi$
$728$	−3.28460	−	4.52087i	−0.121736	−	0.167555i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−1.13497	−	0.824602i	−0.0419783	−	0.0304990i
$732$		−	3.49570i		−	0.129205i
$733$	10.9640	−	15.0907i	0.404965	−	0.557386i	−0.557017	−	0.830501i	$-0.688054\pi$
$733$	10.9640	−	15.0907i	0.404965	−	0.557386i	0.961981	+	0.273115i	$0.0880540\pi$
$734$	7.61927	−	23.4497i	0.281233	−	0.865545i
$735$		0			0
$736$	5.69988	+	17.5424i	0.210101	+	0.646623i
$737$	−5.80402	−	1.88584i	−0.213794	−	0.0694658i
$738$	−15.0822	−	4.90050i	−0.555183	−	0.180390i
$739$	−8.17202	−	25.1509i	−0.300613	−	0.925191i	−0.981278	−	0.192596i	$-0.938309\pi$
$739$	−8.17202	−	25.1509i	−0.300613	−	0.925191i	0.680665	−	0.732594i	$-0.261691\pi$
$740$		0			0
$741$	2.84252	−	8.74838i	0.104423	−	0.321380i
$742$	−20.3653	+	28.0304i	−0.747633	+	1.02903i
$743$		−	29.0191i		−	1.06461i	−0.846553	−	0.532304i	$-0.821326\pi$
$743$		−	29.0191i		−	1.06461i	0.846553	−	0.532304i	$-0.178674\pi$
$744$	4.15803	+	3.02098i	0.152441	+	0.110755i
$745$		0			0
$746$	39.7096	−	28.8507i	1.45387	−	1.05630i
$747$	−5.13491	−	7.06760i	−0.187877	−	0.258590i
$748$	−4.22324	+	1.37221i	−0.154417	+	0.0501731i
$749$	−41.3065			−1.50931
$750$		0			0
$751$	15.9489			0.581985			0.290992	−	0.956725i	$-0.406015\pi$
$751$	15.9489			0.581985			0.290992	+	0.956725i	$0.406015\pi$
$752$	−10.7448	+	3.49119i	−0.391821	+	0.127310i
$753$	−10.2724	−	14.1387i	−0.374346	−	0.515243i
$754$	−11.3216	+	8.22563i	−0.412309	+	0.299560i
$755$		0			0
$756$	−8.83021	−	6.41552i	−0.321152	−	0.233330i
$757$			16.4183i			0.596734i	0.954451	+	0.298367i	$0.0964419\pi$
$757$			16.4183i			0.596734i	−0.954451	+	0.298367i	$0.903558\pi$
$758$	31.0512	−	42.7382i	1.12783	−	1.55232i
$759$	−1.13280	+	3.48640i	−0.0411180	+	0.126548i
$760$		0			0
$761$	−15.2257	−	46.8600i	−0.551932	−	1.69867i	−0.703910	−	0.710289i	$-0.748564\pi$
$761$	−15.2257	−	46.8600i	−0.551932	−	1.69867i	0.151978	−	0.988384i	$-0.451436\pi$
$762$	34.3051	+	11.1464i	1.24274	+	0.403791i
$763$	−48.3555	−	15.7117i	−1.75059	−	0.568800i
$764$	8.02480	+	24.6978i	0.290327	+	0.893534i
$765$		0			0
$766$	−10.3111	+	31.7345i	−0.372557	+	1.14661i
$767$	−6.44711	+	8.87369i	−0.232792	+	0.320410i
$768$			5.20057i			0.187660i
$769$	39.9845	+	29.0504i	1.44188	+	1.04759i	0.987646	+	0.156702i	$0.0500862\pi$
$769$	39.9845	+	29.0504i	1.44188	+	1.04759i	0.454232	+	0.890884i	$0.349914\pi$
$770$		0			0
$771$	−12.5132	+	9.09136i	−0.450651	+	0.327417i
$772$	6.39892	+	8.80736i	0.230302	+	0.316984i
$773$	−24.6403	+	8.00613i	−0.886251	+	0.287960i	−0.716550	−	0.697535i	$-0.754280\pi$
$773$	−24.6403	+	8.00613i	−0.886251	+	0.287960i	−0.169701	+	0.985496i	$0.554280\pi$
$774$	2.65288			0.0953557
$775$		0			0
$776$	−8.02715			−0.288158
$777$	−26.4138	+	8.58236i	−0.947590	+	0.307891i
$778$	10.6114	+	14.6054i	0.380439	+	0.523629i
$779$	−46.4182	+	33.7248i	−1.66311	+	1.20832i
$780$		0			0
$781$	−13.5551	−	9.84838i	−0.485041	−	0.352403i
$782$		−	5.52681i		−	0.197638i
$783$	−3.23535	+	4.45307i	−0.115622	+	0.159140i
$784$	10.1460	−	31.2262i	0.362357	−	1.11522i
$785$		0			0
$786$	−0.215687	−	0.663815i	−0.00769329	−	0.0236775i
$787$	−29.2122	−	9.49160i	−1.04130	−	0.338339i	−0.262052	−	0.965054i	$-0.584399\pi$
$787$	−29.2122	−	9.49160i	−1.04130	−	0.338339i	−0.779249	+	0.626715i	$0.784399\pi$
$788$	4.47741	+	1.45480i	0.159501	+	0.0518251i
$789$	−0.447331	−	1.37674i	−0.0159254	−	0.0490134i
$790$		0			0
$791$	−20.1018	+	61.8670i	−0.714737	+	2.19974i
$792$	0.993921	−	1.36802i	0.0353175	−	0.0486103i
$793$			1.67218i			0.0593808i
$794$	45.0798	+	32.7524i	1.59982	+	1.16234i
$795$		0			0
$796$	−8.63142	+	6.27109i	−0.305933	+	0.222273i
$797$	−19.8166	−	27.2753i	−0.701942	−	0.966140i	−0.999933	−	0.0115713i	$-0.996317\pi$
$797$	−19.8166	−	27.2753i	−0.701942	−	0.966140i	0.297991	−	0.954569i	$-0.403683\pi$
$798$	−67.5513	+	21.9487i	−2.39129	+	0.776977i
$799$	4.63260			0.163890
$800$		0			0
$801$	−10.0381			−0.354680
$802$	−51.0298	+	16.5806i	−1.80192	+	0.585480i
$803$	4.64018	+	6.38665i	0.163748	+	0.225380i
$804$	−7.82591	+	5.68586i	−0.275999	+	0.200525i
$805$		0			0
$806$	−9.87720	−	7.17621i	−0.347910	−	0.252771i
$807$			8.70617i			0.306472i
$808$	−4.10062	+	5.64402i	−0.144259	+	0.198556i
$809$	0.285227	−	0.877838i	0.0100280	−	0.0308632i	−0.945917	−	0.324408i	$-0.894835\pi$
$809$	0.285227	−	0.877838i	0.0100280	−	0.0308632i	0.955945	+	0.293545i	$0.0948350\pi$
$810$		0			0
$811$	8.27593	+	25.4707i	0.290607	+	0.894397i	0.984662	+	0.174474i	$0.0558226\pi$
$811$	8.27593	+	25.4707i	0.290607	+	0.894397i	−0.694055	+	0.719922i	$0.744177\pi$
$812$	57.1376	+	18.5651i	2.00514	+	0.651508i
$813$	−27.2323	−	8.84832i	−0.955080	−	0.310324i
$814$	−6.60274	−	20.3212i	−0.231426	−	0.712256i
$815$		0			0
$816$	0.949275	−	2.92157i	0.0332313	−	0.102275i
$817$	5.64168	−	7.76511i	0.197377	−	0.271667i
$818$			71.7204i			2.50765i
$819$	4.22396	+	3.06889i	0.147597	+	0.107236i
$820$		0			0
$821$	29.8114	−	21.6592i	1.04042	−	0.755912i	0.0700559	−	0.997543i	$-0.477682\pi$
$821$	29.8114	−	21.6592i	1.04042	−	0.755912i	0.970368	+	0.241631i	$0.0776822\pi$
$822$	5.69187	+	7.83419i	0.198527	+	0.273249i
$823$	−19.4265	+	6.31204i	−0.677164	+	0.220024i	−0.627353	−	0.778735i	$-0.715862\pi$
$823$	−19.4265	+	6.31204i	−0.677164	+	0.220024i	−0.0498106	+	0.998759i	$0.515862\pi$
$824$	−8.61452			−0.300101
$825$		0			0
$826$	84.6940			2.94688
$827$	4.11824	−	1.33810i	0.143205	−	0.0465302i	−0.236537	−	0.971622i	$-0.576013\pi$
$827$	4.11824	−	1.33810i	0.143205	−	0.0465302i	0.379743	+	0.925092i	$0.376013\pi$
$828$	3.41542	+	4.70092i	0.118694	+	0.163368i
$829$	−0.497018	+	0.361104i	−0.0172621	+	0.0125417i	−0.596383	−	0.802700i	$-0.703396\pi$
$829$	−0.497018	+	0.361104i	−0.0172621	+	0.0125417i	0.579121	+	0.815242i	$0.303396\pi$
$830$		0			0
$831$	−4.28949	−	3.11649i	−0.148801	−	0.108110i
$832$			13.6535i			0.473351i
$833$	−7.91343	+	10.8919i	−0.274184	+	0.377382i
$834$	3.10473	−	9.55539i	0.107508	−	0.330876i
$835$		0			0
$836$	−9.38828	−	28.8942i	−0.324701	−	0.999325i
$837$	−4.56703	−	1.48392i	−0.157860	−	0.0512917i
$838$	16.0131	+	5.20297i	0.553163	+	0.179733i
$839$	−1.66863	−	5.13553i	−0.0576077	−	0.177298i	0.918112	−	0.396321i	$-0.129713\pi$
$839$	−1.66863	−	5.13553i	−0.0576077	−	0.177298i	−0.975720	+	0.219023i	$0.929713\pi$
$840$		0			0
$841$	0.400892	−	1.23382i	0.0138239	−	0.0425455i
$842$	−9.34105	+	12.8568i	−0.321914	+	0.443076i
$843$		−	24.0832i		−	0.829469i
$844$	−18.8353	−	13.6847i	−0.648339	−	0.471046i
$845$		0			0
$846$	−7.08719	+	5.14914i	−0.243663	+	0.177031i
$847$	−21.7853	−	29.9849i	−0.748552	−	1.03029i
$848$	9.75046	−	3.16812i	0.334832	−	0.108794i
$849$	27.1143			0.930561
$850$		0			0
$851$	14.7855			0.506841
$852$	−25.2585	+	8.20698i	−0.865341	+	0.281166i
$853$	23.3900	+	32.1936i	0.800860	+	1.10229i	0.992670	+	0.120857i	$0.0385642\pi$
$853$	23.3900	+	32.1936i	0.800860	+	1.10229i	−0.191810	+	0.981432i	$0.561436\pi$
$854$	10.4459	−	7.58940i	0.357452	−	0.259704i
$855$		0			0
$856$	−8.20637	−	5.96228i	−0.280488	−	0.203787i
$857$			42.8643i			1.46422i	0.681188	+	0.732109i	$0.261464\pi$
$857$			42.8643i			1.46422i	−0.681188	+	0.732109i	$0.738536\pi$
$858$	−2.36101	+	3.24966i	−0.0806037	+	0.110941i
$859$	1.41064	−	4.34152i	0.0481306	−	0.148131i	−0.924103	−	0.382144i	$-0.875186\pi$
$859$	1.41064	−	4.34152i	0.0481306	−	0.148131i	0.972233	+	0.234013i	$0.0751859\pi$
$860$		0			0
$861$	−10.0636	−	30.9726i	−0.342967	−	1.05554i
$862$	−47.1251	−	15.3119i	−1.60509	−	0.521524i
$863$	−35.7857	−	11.6275i	−1.21816	−	0.395804i	−0.371747	−	0.928334i	$-0.621241\pi$
$863$	−35.7857	−	11.6275i	−1.21816	−	0.395804i	−0.846411	+	0.532530i	$0.821241\pi$
$864$	2.45656	+	7.56051i	0.0835738	+	0.257214i
$865$		0			0
$866$	−2.20150	+	6.77551i	−0.0748099	+	0.230241i
$867$	9.25196	−	12.7342i	0.314213	−	0.432477i
$868$			52.4133i			1.77902i
$869$	−18.6013	−	13.5146i	−0.631006	−	0.458452i
$870$		0			0
$871$	3.74355	−	2.71985i	0.126845	−	0.0921586i
$872$	−7.33894	−	10.1012i	−0.248528	−	0.342069i
$873$	7.13289	−	2.31762i	0.241412	−	0.0784394i
$874$	37.8128			1.27904
$875$		0			0
$876$	12.5133			0.422784
$877$	49.8393	−	16.1938i	1.68295	−	0.546825i	0.697472	−	0.716612i	$-0.254308\pi$
$877$	49.8393	−	16.1938i	1.68295	−	0.546825i	0.985481	+	0.169787i	$0.0543080\pi$
$878$	11.8311	+	16.2841i	0.399280	+	0.549562i
$879$	−16.4244	+	11.9330i	−0.553980	+	0.402490i
$880$		0			0
$881$	6.42180	+	4.66571i	0.216356	+	0.157192i	0.690685	−	0.723156i	$-0.257309\pi$
$881$	6.42180	+	4.66571i	0.216356	+	0.157192i	−0.474329	+	0.880348i	$0.657309\pi$
$882$		−	25.4588i		−	0.857242i
$883$	18.6280	−	25.6393i	0.626883	−	0.862831i	−0.370948	−	0.928654i	$-0.620967\pi$
$883$	18.6280	−	25.6393i	0.626883	−	0.862831i	0.997831	+	0.0658227i	$0.0209672\pi$
$884$	1.04046	−	3.20221i	0.0349945	−	0.107702i
$885$		0			0
$886$	6.33175	+	19.4871i	0.212719	+	0.654683i
$887$	−2.68297	−	0.871749i	−0.0900853	−	0.0292705i	0.263628	−	0.964625i	$-0.415081\pi$
$887$	−2.68297	−	0.871749i	−0.0900853	−	0.0292705i	−0.353713	+	0.935354i	$0.615081\pi$
$888$	−6.48643	−	2.10757i	−0.217670	−	0.0707254i
$889$	22.8901	+	70.4485i	0.767709	+	2.36277i
$890$		0			0
$891$	−0.488218	+	1.50258i	−0.0163559	+	0.0503383i
$892$	5.00121	−	6.88357i	0.167453	−	0.230479i
$893$			31.6949i			1.06063i
$894$	8.02947	+	5.83375i	0.268546	+	0.195110i
$895$		0			0
$896$	29.2312	−	21.2377i	0.976546	−	0.709502i
$897$	−1.63378	−	2.24870i	−0.0545502	−	0.0750820i
$898$	−63.6340	+	20.6759i	−2.12349	+	0.689965i
$899$	26.4320			0.881556
$900$		0			0
$901$	−4.20390			−0.140052
$902$	23.8285	−	7.74233i	0.793401	−	0.257792i
$903$	3.20221	+	4.40746i	0.106563	+	0.146671i
$904$	−12.9236	+	9.38958i	−0.429834	+	0.312293i
$905$		0			0
$906$	11.2323	+	8.16071i	0.373167	+	0.271122i
$907$			44.1799i			1.46697i	0.679705	+	0.733485i	$0.262108\pi$
$907$			44.1799i			1.46697i	−0.679705	+	0.733485i	$0.737892\pi$
$908$	39.4454	−	54.2919i	1.30904	−	1.80174i
$909$	2.01424	−	6.19919i	0.0668081	−	0.205614i
$910$		0			0
$911$	−10.6691	−	32.8362i	−0.353484	−	1.08791i	−0.956883	−	0.290472i	$-0.906188\pi$
$911$	−10.6691	−	32.8362i	−0.353484	−	1.08791i	0.603400	−	0.797439i	$-0.293812\pi$
$912$	19.9885	+	6.49466i	0.661886	+	0.215060i
$913$	13.1266	+	4.26509i	0.434426	+	0.141154i
$914$	6.52209	+	20.0729i	0.215731	+	0.663953i
$915$		0			0
$916$	−0.914713	+	2.81520i	−0.0302230	+	0.0930167i
$917$	0.842506	−	1.15961i	0.0278220	−	0.0382937i
$918$		−	2.38197i		−	0.0786166i
$919$	−0.429648	−	0.312158i	−0.0141728	−	0.0102971i	0.580676	−	0.814135i	$-0.302788\pi$
$919$	−0.429648	−	0.312158i	−0.0141728	−	0.0102971i	−0.594849	+	0.803837i	$0.702788\pi$
$920$		0			0
$921$	2.03330	−	1.47728i	0.0669996	−	0.0486781i
$922$	−29.5447	−	40.6648i	−0.973003	−	1.33922i
$923$	12.0825	−	3.92584i	0.397700	−	0.129220i
$924$	17.2443			0.567295
$925$		0			0
$926$	58.6833			1.92845
$927$	7.65482	−	2.48720i	0.251417	−	0.0816905i
$928$	−25.7197	−	35.4001i	−0.844289	−	1.16206i
$929$	37.3735	−	27.1534i	1.22618	−	0.890874i	0.229585	−	0.973289i	$-0.426263\pi$
$929$	37.3735	−	27.1534i	1.22618	−	0.890874i	0.996598	+	0.0824143i	$0.0262631\pi$
$930$		0			0
$931$	−74.5192	−	54.1414i	−2.44227	−	1.77441i
$932$		−	17.7676i		−	0.581997i
$933$	2.83558	−	3.90284i	0.0928326	−	0.127773i
$934$	−2.85840	+	8.79726i	−0.0935298	+	0.287855i
$935$		0			0
$936$	0.396205	+	1.21939i	0.0129504	+	0.0398571i
$937$	28.6477	+	9.30820i	0.935880	+	0.304086i	0.736965	−	0.675931i	$-0.236258\pi$
$937$	28.6477	+	9.30820i	0.935880	+	0.304086i	0.198915	+	0.980017i	$0.436258\pi$
$938$	−33.9812	−	11.0412i	−1.10952	−	0.360506i
$939$	1.85043	+	5.69504i	0.0603865	+	0.185851i
$940$		0			0
$941$	17.6382	−	54.2847i	0.574988	−	1.76963i	−0.0612315	−	0.998124i	$-0.519503\pi$
$941$	17.6382	−	54.2847i	0.574988	−	1.76963i	0.636220	−	0.771508i	$-0.280497\pi$
$942$	−4.98246	+	6.85777i	−0.162337	+	0.223438i
$943$			17.3374i			0.564583i
$944$	−20.2748	−	14.7305i	−0.659890	−	0.479438i
$945$		0			0
$946$	−3.39083	+	2.46358i	−0.110245	+	0.0800980i
$947$	−24.1727	−	33.2708i	−0.785506	−	1.08116i	−0.994653	−	0.103273i	$-0.967069\pi$
$947$	−24.1727	−	33.2708i	−0.785506	−	1.08116i	0.209147	−	0.977884i	$-0.432931\pi$
$948$	−34.6615	+	11.2622i	−1.12575	+	0.365779i
$949$	−5.98576			−0.194306
$950$		0			0
$951$	17.3531			0.562712
$952$	−4.97918	+	1.61783i	−0.161376	+	0.0524343i
$953$	−20.4633	−	28.1654i	−0.662873	−	0.912366i	0.336700	−	0.941612i	$-0.390689\pi$
$953$	−20.4633	−	28.1654i	−0.662873	−	0.912366i	−0.999572	+	0.0292462i	$0.990689\pi$
$954$	6.43135	−	4.67265i	0.208223	−	0.151283i
$955$		0			0
$956$	−0.0866986	−	0.0629902i	−0.00280403	−	0.00203725i
$957$		−	8.69627i		−	0.281111i
$958$	15.9855	−	22.0022i	0.516468	−	0.710857i
$959$	−6.14515	+	18.9128i	−0.198437	+	0.610727i
$960$		0			0
$961$	−2.45366	−	7.55160i	−0.0791504	−	0.243600i
$962$	15.4082	+	5.00643i	0.496781	+	0.161414i
$963$	9.01359	+	2.92869i	0.290459	+	0.0943758i
$964$	9.10930	+	28.0355i	0.293391	+	0.902964i
$965$		0			0
$966$	−6.63227	+	20.4120i	−0.213390	+	0.656746i
$967$	21.9066	−	30.1519i	0.704469	−	0.969618i	−0.295430	−	0.955365i	$-0.595463\pi$
$967$	21.9066	−	30.1519i	0.704469	−	0.969618i	0.999898	−	0.0142537i	$-0.00453725\pi$
$968$		−	9.10165i		−	0.292538i
$969$	−6.97214	−	5.06555i	−0.223977	−	0.162729i
$970$		0			0
$971$	21.0419	−	15.2879i	0.675267	−	0.490611i	−0.196517	−	0.980500i	$-0.562963\pi$
$971$	21.0419	−	15.2879i	0.675267	−	0.490611i	0.871784	+	0.489890i	$0.162963\pi$
$972$	1.47199	+	2.02602i	0.0472141	+	0.0649846i
$973$	19.6228	−	6.37585i	0.629079	−	0.204400i
$974$	14.6910			0.470729
$975$		0			0
$976$	−3.82064			−0.122296
$977$	0.436134	−	0.141709i	0.0139532	−	0.00453366i	−0.302032	−	0.953298i	$-0.597665\pi$
$977$	0.436134	−	0.141709i	0.0139532	−	0.00453366i	0.315985	+	0.948764i	$0.397665\pi$
$978$	−5.98965	−	8.24404i	−0.191528	−	0.263615i
$979$	12.8304	−	9.32186i	0.410063	−	0.297928i
$980$		0			0
$981$	9.43778	+	6.85695i	0.301325	+	0.218926i
$982$		−	56.9128i		−	1.81616i
$983$	5.25812	−	7.23718i	0.167708	−	0.230830i	−0.716888	−	0.697188i	$-0.754434\pi$
$983$	5.25812	−	7.23718i	0.167708	−	0.230830i	0.884596	+	0.466358i	$0.154434\pi$
$984$	2.47132	−	7.60595i	0.0787829	−	0.242469i
$985$		0			0
$986$	4.05154	+	12.4694i	0.129027	+	0.397105i
$987$	−17.1095	−	5.55920i	−0.544600	−	0.176951i
$988$	21.9086	+	7.11852i	0.697004	+	0.226470i
$989$	−0.896242	−	2.75835i	−0.0284988	−	0.0877104i
$990$		0			0
$991$	−17.4699	+	53.7667i	−0.554949	+	1.70796i	0.141130	+	0.989991i	$0.454926\pi$
$991$	−17.4699	+	53.7667i	−0.554949	+	1.70796i	−0.696079	+	0.717965i	$0.745074\pi$
$992$	22.4383	−	30.8837i	0.712418	−	0.980559i
$993$			20.3355i			0.645327i
$994$	−79.3621	−	57.6599i	−2.51721	−	1.82886i
$995$		0			0
$996$	17.6994	−	12.8594i	0.560826	−	0.407464i
$997$	23.2830	+	32.0463i	0.737380	+	1.01492i	0.998765	+	0.0496816i	$0.0158207\pi$
$997$	23.2830	+	32.0463i	0.737380	+	1.01492i	−0.261385	+	0.965235i	$0.584179\pi$
$998$	−5.56005	+	1.80657i	−0.176000	+	0.0571860i
$999$	6.37232			0.201611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.b.349.4		16
5.2	odd	4		75.2.g.b.31.2	✓	8
5.3	odd	4		375.2.g.b.151.1		8
5.4	even	2	inner	375.2.i.b.349.1		16
15.2	even	4		225.2.h.c.181.1		8
25.2	odd	20		1875.2.a.h.1.3		4
25.3	odd	20		375.2.g.b.226.1		8
25.4	even	10	inner	375.2.i.b.274.4		16
25.11	even	5		1875.2.b.c.1249.2		8
25.14	even	10		1875.2.b.c.1249.7		8
25.21	even	5	inner	375.2.i.b.274.1		16
25.22	odd	20		75.2.g.b.46.2	yes	8
25.23	odd	20		1875.2.a.e.1.2		4
75.2	even	20		5625.2.a.i.1.2		4
75.23	even	20		5625.2.a.n.1.3		4
75.47	even	20		225.2.h.c.46.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.31.2	✓	8	5.2	odd	4
75.2.g.b.46.2	yes	8	25.22	odd	20
225.2.h.c.46.1		8	75.47	even	20
225.2.h.c.181.1		8	15.2	even	4
375.2.g.b.151.1		8	5.3	odd	4
375.2.g.b.226.1		8	25.3	odd	20
375.2.i.b.274.1		16	25.21	even	5	inner
375.2.i.b.274.4		16	25.4	even	10	inner
375.2.i.b.349.1		16	5.4	even	2	inner
375.2.i.b.349.4		16	1.1	even	1	trivial
1875.2.a.e.1.2		4	25.23	odd	20
1875.2.a.h.1.3		4	25.2	odd	20
1875.2.b.c.1249.2		8	25.11	even	5
1875.2.b.c.1249.7		8	25.14	even	10
5625.2.a.i.1.2		4	75.2	even	20
5625.2.a.n.1.3		4	75.23	even	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.01846 - 0.655837i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(2.02602 - 1.47199i) q^{4} +(-1.71700 - 1.24748i) q^{6} -4.35840i q^{7} +(0.629102 - 0.865884i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(2.01846 - 0.655837i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(2.02602 - 1.47199i) q^{4} +(-1.71700 - 1.24748i) q^{6} -4.35840i q^{7} +(0.629102 - 0.865884i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.488218 - 1.50258i) q^{11} +(-2.38173 - 0.773871i) q^{12} +(1.13931 + 0.370184i) q^{13} +(-2.85840 - 8.79726i) q^{14} +(-0.845805 + 2.60312i) q^{16} +(0.659691 - 0.907987i) q^{17} +2.12233i q^{18} +(6.21218 + 4.51341i) q^{19} +(-3.52602 + 2.56180i) q^{21} +(-1.97090 - 2.71270i) q^{22} +(2.20671 - 0.717004i) q^{23} -1.07029 q^{24} +2.54243 q^{26} +(0.951057 - 0.309017i) q^{27} +(-6.41552 - 8.83021i) q^{28} +(-4.45307 + 3.23535i) q^{29} +(-3.88495 - 2.82258i) q^{31} +7.94959i q^{32} +(-0.928645 + 1.27817i) q^{33} +(0.736068 - 2.26538i) q^{34} +(0.773871 + 2.38173i) q^{36} +(6.06043 + 1.96915i) q^{37} +(15.4991 + 5.03596i) q^{38} +(-0.370184 - 1.13931i) q^{39} +(-2.30902 + 7.10642i) q^{41} +(-5.43700 + 7.48339i) q^{42} -1.24998i q^{43} +(-3.20092 - 2.32561i) q^{44} +(3.98392 - 2.89449i) q^{46} +(2.42617 + 3.33934i) q^{47} +(2.60312 - 0.845805i) q^{48} -11.9957 q^{49} -1.12233 q^{51} +(2.85317 - 0.927051i) q^{52} +(-2.20166 - 3.03032i) q^{53} +(1.71700 - 1.24748i) q^{54} +(-3.77387 - 2.74188i) q^{56} -7.67867i q^{57} +(-6.86648 + 9.45090i) q^{58} +(-2.82940 + 8.70799i) q^{59} +(0.431351 + 1.32756i) q^{61} +(-9.69276 - 3.14937i) q^{62} +(4.14509 + 1.34682i) q^{63} +(3.52202 + 10.8397i) q^{64} +(-1.03616 + 3.18898i) q^{66} +(2.27044 - 3.12499i) q^{67} -2.81066i q^{68} +(-1.87714 - 1.36382i) q^{69} +(8.57970 - 6.23352i) q^{71} +(0.629102 + 0.865884i) q^{72} +(-4.75216 + 1.54407i) q^{73} +13.5242 q^{74} +19.2297 q^{76} +(-6.54885 + 2.12785i) q^{77} +(-1.49440 - 2.05687i) q^{78} +(11.7737 - 8.55407i) q^{79} +(-0.809017 - 0.587785i) q^{81} +15.8584i q^{82} +(-5.13491 + 7.06760i) q^{83} +(-3.37284 + 10.3805i) q^{84} +(-0.819784 - 2.52304i) q^{86} +(5.23490 + 1.70092i) q^{87} +(-1.60820 - 0.522535i) q^{88} +(3.10195 + 9.54683i) q^{89} +(1.61341 - 4.96556i) q^{91} +(3.41542 - 4.70092i) q^{92} +4.80206i q^{93} +(7.08719 + 5.14914i) q^{94} +(6.43135 - 4.67265i) q^{96} +(-4.40837 - 6.06760i) q^{97} +(-24.2128 + 7.86720i) q^{98} +1.57991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Introduction

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