LMFDB - Embedded newform 375.2.i.b.349.1

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			349.1
Root			$-0.132563 + 1.40799i$ of defining polynomial
Character	$\chi$	$=$	375.349
Dual form			375.2.i.b.274.1

$q$-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	−0.917903	−	0.396805i	$-0.870119\pi$
$2$	−2.01846	+	0.655837i	−1.42727	+	0.463747i	−0.509363	+	0.860552i	$0.670119\pi$
$3$	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	$0.308072\pi$
$7$			4.35840i			1.64732i	−0.567083	+	0.823660i	$0.691928\pi$
$8$	−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	0.146729	−	0.989177i	$-0.453125\pi$
$13$	−1.13931	−	0.370184i	−0.315987	−	0.102670i	−0.462717	+	0.886506i	$0.653125\pi$
$14$	−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	−0.881488	−	0.472206i	$-0.843458\pi$
$17$	−0.659691	+	0.907987i	−0.159999	+	0.220219i	0.721490	+	0.692425i	$0.243458\pi$
$18$		−	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	−0.529905	−	0.848057i	$-0.677772\pi$
$23$	−2.20671	+	0.717004i	−0.460131	+	0.149506i	0.0697736	+	0.997563i	$0.477772\pi$
$24$	−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	−0.234931	−	0.972012i	$-0.575486\pi$
$37$	−6.06043	−	1.96915i	−0.996329	−	0.323727i	−0.761398	+	0.648285i	$0.775486\pi$
$38$	−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	$0.0303843\pi$
$43$			1.24998i			0.190620i	−0.995448	+	0.0953102i	$0.969616\pi$
$44$	−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	0.594541	−	0.804065i	$-0.297334\pi$
$47$	−2.42617	−	3.33934i	−0.353893	−	0.487092i	−0.948435	+	0.316973i	$0.897334\pi$
$48$	−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	0.932999	−	0.359879i	$-0.117182\pi$
$53$	2.20166	+	3.03032i	0.302421	+	0.416247i	−0.630578	+	0.776126i	$0.717182\pi$
$54$	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	−0.924863	−	0.380300i	$-0.875821\pi$
$67$	−2.27044	+	3.12499i	−0.277378	+	0.381778i	0.647485	+	0.762078i	$0.275821\pi$
$68$			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	−0.0174117	−	0.999848i	$-0.505543\pi$
$73$	4.75216	−	1.54407i	0.556198	−	0.180720i	0.573610	+	0.819129i	$0.305543\pi$
$74$	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	−0.428153	−	0.903706i	$-0.640835\pi$
$83$	5.13491	−	7.06760i	0.563630	−	0.775770i	0.991782	+	0.127937i	$0.0408355\pi$
$84$	−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	0.971880	−	0.235476i	$-0.0756648\pi$
$97$	4.40837	+	6.06760i	0.447602	+	0.616071i	−0.524278	+	0.851547i	$0.675665\pi$
$98$	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	0.975771	−	0.218796i	$-0.0702130\pi$
$103$	4.73094	+	6.51158i	0.466153	+	0.641605i	−0.509617	+	0.860401i	$0.670213\pi$
$104$	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	$0.151473\pi$
$107$			9.47745i			0.916220i	−0.888896	+	0.458110i	$0.848527\pi$
$108$	−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	0.887736	−	0.460353i	$-0.152277\pi$
$113$	14.1949	+	4.61219i	1.33534	+	0.433879i	0.447605	+	0.894231i	$0.352277\pi$
$114$	−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	0.514190	−	0.857676i	$-0.328092\pi$
$127$	16.1638	−	5.25195i	1.43431	−	0.466035i	0.920118	+	0.391641i	$0.128092\pi$
$128$	−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	0.488460	−	0.872586i	$-0.337559\pi$
$137$	4.33939	+	1.40995i	0.370739	+	0.120461i	−0.117721	+	0.993047i	$0.537559\pi$
$138$	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	$0.0509493\pi$
$157$			3.99404i			0.318759i	−0.987217	+	0.159379i	$0.949051\pi$
$158$	−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	0.124670	−	0.992198i	$-0.460213\pi$
$163$	−4.56641	−	1.48372i	−0.357669	−	0.116214i	−0.482339	+	0.875985i	$0.660213\pi$
$164$	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	$-0.431848\pi$
$167$	13.9070	−	19.1414i	1.07616	−	1.48120i	0.863682	−	0.504036i	$-0.168152\pi$
$168$		−	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	0.266584	−	0.963812i	$-0.414105\pi$
$173$	13.7944	−	4.48208i	1.04877	−	0.340766i	0.782185	+	0.623046i	$0.214105\pi$
$174$	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	$-0.949993\pi$
$193$		−	4.34712i		−	0.312913i	0.987685	−	0.156456i	$-0.0500071\pi$
$194$	−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	0.767838	−	0.640644i	$-0.221333\pi$
$197$	−1.10498	−	1.52087i	−0.0787263	−	0.108358i	−0.846564	+	0.532287i	$0.821333\pi$
$198$	−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	−0.415203	−	0.909729i	$-0.636289\pi$
$223$	−3.23129	+	1.04991i	−0.216383	+	0.0703072i	0.198819	+	0.980036i	$0.436289\pi$
$224$	34.6475			2.31498
$225$		0			0
$226$	−31.6766			−2.10710
$227$	−25.4858	+	8.28083i	−1.69155	+	0.549618i	−0.987096	−	0.160132i	$-0.948808\pi$
$227$	−25.4858	+	8.28083i	−1.69155	+	0.549618i	−0.704454	+	0.709750i	$0.748808\pi$
$228$	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	−0.923467	−	0.383677i	$-0.874658\pi$
$233$	−4.17024	+	5.73984i	−0.273201	+	0.376030i	0.650266	+	0.759707i	$0.274658\pi$
$234$	−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	$0.160237\pi$
$257$			15.4671i			0.964814i	−0.875947	+	0.482407i	$0.839763\pi$
$258$	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	0.266262	−	0.963901i	$-0.414211\pi$
$263$	−1.37674	−	0.447331i	−0.0848936	−	0.0275836i	−0.351156	+	0.936317i	$0.614211\pi$
$264$	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	−0.456562	−	0.889692i	$-0.650919\pi$
$277$	−5.04259	+	1.63844i	−0.302980	+	0.0984442i	0.153582	+	0.988136i	$0.450919\pi$
$278$	−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	$-0.501688\pi$
$283$	15.9374	−	21.9359i	0.947380	−	1.30396i	0.952682	−	0.303970i	$-0.0983123\pi$
$284$	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	$0.202063\pi$
$293$			20.3016i			1.18603i	−0.805190	+	0.593017i	$0.797937\pi$
$294$	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	$-0.977151\pi$
$307$		−	2.51330i		−	0.143442i	0.997425	−	0.0717208i	$-0.0228491\pi$
$308$	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	0.465511	−	0.885042i	$-0.345871\pi$
$313$	5.69504	+	1.85043i	0.321903	+	0.104592i	−0.143608	+	0.989635i	$0.545871\pi$
$314$	−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	−0.420010	−	0.907520i	$-0.637973\pi$
$317$	10.1999	−	14.0389i	0.572883	−	0.788506i	0.992893	+	0.119014i	$0.0379734\pi$
$318$		−	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	0.998551	−	0.0538048i	$-0.0171349\pi$
$337$	32.5805	+	10.5860i	1.77477	+	0.576658i	0.776219	+	0.630463i	$0.217135\pi$
$338$	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	0.809795	−	0.586713i	$-0.199578\pi$
$347$	0.0290140	+	0.0399344i	0.00155756	+	0.00214379i	−0.808238	+	0.588857i	$0.799578\pi$
$348$	−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	0.412984	−	0.910738i	$-0.364487\pi$
$353$	−10.9122	−	15.0194i	−0.580799	−	0.799401i	−0.993783	+	0.111337i	$0.964487\pi$
$354$	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	−0.949156	−	0.314805i	$-0.898061\pi$
$367$	−6.82867	+	9.39886i	−0.356454	+	0.490617i	0.592703	+	0.805421i	$0.298061\pi$
$368$		−	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	−0.816942	−	0.576720i	$-0.804332\pi$
$373$	−21.9953	+	7.14671i	−1.13887	+	0.370043i	−0.321932	+	0.946763i	$0.604332\pi$
$374$	−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	−0.504779	−	0.863249i	$-0.668426\pi$
$383$	9.24123	−	12.7195i	0.472205	−	0.649934i	0.976984	+	0.213315i	$0.0684259\pi$
$384$	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	$-0.971044\pi$
$397$	−15.4322	−	21.2407i	−0.774522	−	1.06604i	0.221343	−	0.975196i	$-0.428956\pi$
$398$	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	−0.758971	−	0.651124i	$-0.774298\pi$
$433$	1.97306	−	2.71569i	0.0948193	−	0.130508i	0.853791	+	0.520616i	$0.174298\pi$
$434$	−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	$-0.926340\pi$
$443$		−	9.65446i		−	0.458697i	0.973344	−	0.229349i	$-0.0736596\pi$
$444$	−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	$-0.925278\pi$
$457$		−	9.94467i		−	0.465192i	0.972573	−	0.232596i	$-0.0747220\pi$
$458$	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	−0.374272	−	0.927319i	$-0.622107\pi$
$463$	−26.2971	−	8.54443i	−1.22213	−	0.397094i	−0.847857	+	0.530226i	$0.822107\pi$
$464$	−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	−0.745620	−	0.666371i	$-0.767847\pi$
$467$	2.56180	−	3.52602i	0.118546	−	0.163165i	0.864166	+	0.503207i	$0.167847\pi$
$468$		−	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	0.156034	−	0.987752i	$-0.450129\pi$
$487$	−6.58330	−	2.13904i	−0.298318	−	0.0969293i	−0.454352	+	0.890822i	$0.650129\pi$
$488$	−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	0.963640	−	0.267203i	$-0.0860996\pi$
$503$	9.23422	+	12.7098i	0.411733	+	0.566702i	−0.551907	+	0.833906i	$0.686100\pi$
$504$	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	0.339144	−	0.940735i	$-0.389863\pi$
$523$	26.6761	−	8.66761i	1.16647	−	0.379008i	0.827323	+	0.561727i	$0.189863\pi$
$524$	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	0.596665	−	0.802490i	$-0.296492\pi$
$547$	−8.20751	−	11.2967i	−0.350928	−	0.483011i	−0.947593	+	0.319479i	$0.896492\pi$
$548$	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	$-0.955374\pi$
$557$		−	6.59585i		−	0.279475i	0.990189	−	0.139738i	$-0.0446259\pi$
$558$	−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	0.611967	−	0.790883i	$-0.290379\pi$
$563$	15.2376	+	4.95100i	0.642189	+	0.208660i	0.0302222	+	0.999543i	$0.490379\pi$
$564$	−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	−0.178175	−	0.983999i	$-0.557019\pi$
$577$	6.15074	−	1.99850i	0.256059	−	0.0831985i	0.434233	+	0.900800i	$0.357019\pi$
$578$	−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	0.943301	−	0.331940i	$-0.107703\pi$
$587$	36.6168	+	11.8975i	1.51134	+	0.491063i	0.568037	+	0.823003i	$0.307703\pi$
$588$	−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	$-0.967719\pi$
$593$		−	4.93069i		−	0.202479i	0.994862	−	0.101240i	$-0.0322808\pi$
$594$	−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	$0.451144\pi$
$607$			48.6955i			1.97649i	−0.152884	+	0.988244i	$0.548856\pi$
$608$	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	−0.0408728	−	0.999164i	$-0.513014\pi$
$613$	−16.3714	−	5.31938i	−0.661234	−	0.214848i	−0.620361	+	0.784317i	$0.713014\pi$
$614$	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	$0.419523\pi$
$617$	−18.5794	+	25.5723i	−0.747978	+	1.02950i	−0.998120	+	0.0612947i	$0.980477\pi$
$618$		−	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	$0.251250\pi$
$643$			36.0014i			1.41976i	−0.704324	+	0.709879i	$0.748750\pi$
$644$	−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	$-0.893222\pi$
$647$	−24.5600	−	33.8040i	−0.965554	−	1.32897i	−0.0212924	−	0.999773i	$-0.506778\pi$
$648$	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	0.980968	−	0.194168i	$-0.0622007\pi$
$653$	12.6023	+	17.3456i	0.493168	+	0.678787i	−0.487801	+	0.872955i	$0.662201\pi$
$654$	−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	0.422439	−	0.906391i	$-0.361174\pi$
$673$	33.6461	−	10.9323i	1.29696	−	0.421409i	0.874524	+	0.484983i	$0.161174\pi$
$674$	−72.7050			−2.80049
$675$		0			0
$676$	−28.9621			−1.11393
$677$	−42.2434	+	13.7257i	−1.62354	+	0.527522i	−0.972775	−	0.231753i	$-0.925554\pi$
$677$	−42.2434	+	13.7257i	−1.62354	+	0.527522i	−0.650770	+	0.759275i	$0.725554\pi$
$678$	−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	$0.502176\pi$
$683$	−24.9780	+	34.3793i	−0.955758	+	1.31549i	−0.948922	+	0.315512i	$0.897824\pi$
$684$	−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	−0.538739	−	0.842473i	$-0.681099\pi$
$727$	−12.9259	+	4.19988i	−0.479396	+	0.155765i	0.0593437	+	0.998238i	$0.481099\pi$
$728$	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	−0.961981	−	0.273115i	$-0.911946\pi$
$733$	−10.9640	+	15.0907i	−0.404965	+	0.557386i	0.557017	+	0.830501i	$0.311946\pi$
$734$	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	$0.178674\pi$
$743$			29.0191i			1.06461i	−0.846553	+	0.532304i	$0.821326\pi$
$744$	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	$-0.903558\pi$
$757$		−	16.4183i		−	0.596734i	0.954451	−	0.298367i	$-0.0964419\pi$
$758$	−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	0.169701	−	0.985496i	$-0.445720\pi$
$773$	24.6403	−	8.00613i	0.886251	−	0.287960i	0.716550	+	0.697535i	$0.245720\pi$
$774$	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	0.779249	−	0.626715i	$-0.215601\pi$
$787$	29.2122	+	9.49160i	1.04130	+	0.338339i	0.262052	+	0.965054i	$0.415601\pi$
$788$	−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	$0.00368333\pi$
$797$	19.8166	+	27.2753i	0.701942	+	0.966140i	−0.297991	+	0.954569i	$0.596317\pi$
$798$	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	0.0498106	−	0.998759i	$-0.484138\pi$
$823$	19.4265	−	6.31204i	0.677164	−	0.220024i	0.627353	+	0.778735i	$0.284138\pi$
$824$	−8.61452			−0.300101
$825$		0			0
$826$	84.6940			2.94688
$827$	−4.11824	+	1.33810i	−0.143205	+	0.0465302i	−0.379743	−	0.925092i	$-0.623987\pi$
$827$	−4.11824	+	1.33810i	−0.143205	+	0.0465302i	0.236537	+	0.971622i	$0.423987\pi$
$828$	−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	$-0.961436\pi$
$853$	−23.3900	−	32.1936i	−0.800860	−	1.10229i	0.191810	−	0.981432i	$-0.438564\pi$
$854$	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	$-0.738536\pi$
$857$		−	42.8643i		−	1.46422i	0.681188	−	0.732109i	$-0.261464\pi$
$858$	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	0.846411	−	0.532530i	$-0.178759\pi$
$863$	35.7857	+	11.6275i	1.21816	+	0.395804i	0.371747	+	0.928334i	$0.378759\pi$
$864$	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	−0.985481	−	0.169787i	$-0.945692\pi$
$877$	−49.8393	+	16.1938i	−1.68295	+	0.546825i	−0.697472	+	0.716612i	$0.745692\pi$
$878$	−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	−0.997831	−	0.0658227i	$-0.979033\pi$
$883$	−18.6280	+	25.6393i	−0.626883	+	0.862831i	0.370948	+	0.928654i	$0.379033\pi$
$884$	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	0.353713	−	0.935354i	$-0.384919\pi$
$887$	2.68297	+	0.871749i	0.0900853	+	0.0292705i	−0.263628	+	0.964625i	$0.584919\pi$
$888$	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	$-0.737892\pi$
$907$		−	44.1799i		−	1.46697i	0.679705	−	0.733485i	$-0.262108\pi$
$908$	−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	−0.198915	−	0.980017i	$-0.563742\pi$
$937$	−28.6477	−	9.30820i	−0.935880	−	0.304086i	−0.736965	+	0.675931i	$0.763742\pi$
$938$	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	$0.0329314\pi$
$947$	24.1727	+	33.2708i	0.785506	+	1.08116i	−0.209147	+	0.977884i	$0.567069\pi$
$948$	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	0.999572	−	0.0292462i	$-0.00931067\pi$
$953$	20.4633	+	28.1654i	0.662873	+	0.912366i	−0.336700	+	0.941612i	$0.609311\pi$
$954$	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	$0.404537\pi$
$967$	−21.9066	+	30.1519i	−0.704469	+	0.969618i	−0.999898	+	0.0142537i	$0.995463\pi$
$968$			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	−0.315985	−	0.948764i	$-0.602335\pi$
$977$	−0.436134	+	0.141709i	−0.0139532	+	0.00453366i	0.302032	+	0.953298i	$0.402335\pi$
$978$	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	−0.884596	−	0.466358i	$-0.845566\pi$
$983$	−5.25812	+	7.23718i	−0.167708	+	0.230830i	0.716888	+	0.697188i	$0.245566\pi$
$984$	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	$-0.984179\pi$
$997$	−23.2830	−	32.0463i	−0.737380	−	1.01492i	0.261385	−	0.965235i	$-0.415821\pi$
$998$	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.349.1		16
5.2	odd	4		375.2.g.b.151.1		8
5.3	odd	4		75.2.g.b.31.2	✓	8
5.4	even	2	inner	375.2.i.b.349.4		16
15.8	even	4		225.2.h.c.181.1		8
25.2	odd	20		1875.2.a.e.1.2		4
25.3	odd	20		75.2.g.b.46.2	yes	8
25.4	even	10	inner	375.2.i.b.274.1		16
25.11	even	5		1875.2.b.c.1249.7		8
25.14	even	10		1875.2.b.c.1249.2		8
25.21	even	5	inner	375.2.i.b.274.4		16
25.22	odd	20		375.2.g.b.226.1		8
25.23	odd	20		1875.2.a.h.1.3		4
75.2	even	20		5625.2.a.n.1.3		4
75.23	even	20		5625.2.a.i.1.2		4
75.53	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	5.3	odd	4
75.2.g.b.46.2	yes	8	25.3	odd	20
225.2.h.c.46.1		8	75.53	even	20
225.2.h.c.181.1		8	15.8	even	4
375.2.g.b.151.1		8	5.2	odd	4
375.2.g.b.226.1		8	25.22	odd	20
375.2.i.b.274.1		16	25.4	even	10	inner
375.2.i.b.274.4		16	25.21	even	5	inner
375.2.i.b.349.1		16	1.1	even	1	trivial
375.2.i.b.349.4		16	5.4	even	2	inner
1875.2.a.e.1.2		4	25.2	odd	20
1875.2.a.h.1.3		4	25.23	odd	20
1875.2.b.c.1249.2		8	25.14	even	10
1875.2.b.c.1249.7		8	25.11	even	5
5625.2.a.i.1.2		4	75.23	even	20
5625.2.a.n.1.3		4	75.2	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

L-functions

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