LMFDB - Embedded newform 825.2.n.c.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.301
Dual form			825.2.n.c.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.224514i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.224514i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.19098 + 2.48990i) q^{11} -1.85410 q^{12} +(-3.42705 - 2.48990i) q^{13} +(0.118034 - 0.363271i) q^{14} +(-2.54508 + 1.84911i) q^{16} +(-6.35410 + 4.61653i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.263932 + 0.812299i) q^{19} +1.00000 q^{21} +(1.23607 - 0.277515i) q^{22} +4.23607 q^{23} +(1.19098 + 0.865300i) q^{24} +(0.500000 + 1.53884i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.50000 - 1.08981i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-4.11803 - 2.99193i) q^{31} +4.14590 q^{32} +(1.69098 + 2.85317i) q^{33} +3.00000 q^{34} +(-0.572949 + 1.76336i) q^{36} +(0.545085 + 1.67760i) q^{37} +(0.263932 - 0.191758i) q^{38} +(-3.42705 + 2.48990i) q^{39} +(-1.30902 + 4.02874i) q^{41} +(-0.309017 - 0.224514i) q^{42} -6.70820 q^{43} +(5.64590 + 2.43690i) q^{44} +(-1.30902 - 0.951057i) q^{46} +(-0.336881 + 1.03681i) q^{47} +(0.972136 + 2.99193i) q^{48} +(4.85410 - 3.52671i) q^{49} +(2.42705 + 7.46969i) q^{51} +(-2.42705 + 7.46969i) q^{52} +(-2.11803 - 1.53884i) q^{53} +0.381966 q^{54} -1.47214 q^{56} +(0.690983 + 0.502029i) q^{57} +(-0.708204 + 2.17963i) q^{58} +(2.97214 + 9.14729i) q^{59} +(-6.92705 + 5.03280i) q^{61} +(0.600813 + 1.84911i) q^{62} +(0.309017 - 0.951057i) q^{63} +(3.80902 + 2.76741i) q^{64} +(0.118034 - 1.26133i) q^{66} +4.85410 q^{67} +(11.7812 + 8.55951i) q^{68} +(1.30902 - 4.02874i) q^{69} +(4.30902 - 3.13068i) q^{71} +(1.19098 - 0.865300i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(0.208204 - 0.640786i) q^{74} +1.58359 q^{76} +(-3.04508 - 1.31433i) q^{77} +1.61803 q^{78} +(-8.89919 - 6.46564i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.30902 - 0.951057i) q^{82} +(-6.04508 + 4.39201i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(2.07295 + 1.50609i) q^{86} -6.00000 q^{87} +(-2.48936 - 4.20025i) q^{88} -3.76393 q^{89} +(1.30902 - 4.02874i) q^{91} +(-2.42705 - 7.46969i) q^{92} +(-4.11803 + 2.99193i) q^{93} +(0.336881 - 0.244758i) q^{94} +(1.28115 - 3.94298i) q^{96} +(0.927051 + 0.673542i) q^{97} -2.29180 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - 9 * q^4 + q^6 - q^7 - 13 * q^8 - q^9	$ 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9} - 11 q^{11} + 6 q^{12} - 7 q^{13} - 4 q^{14} + q^{16} - 12 q^{17} - 4 q^{18} - 10 q^{19} + 4 q^{21} - 4 q^{22} + 8 q^{23} + 7 q^{24} + 2 q^{26} - q^{27} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 30 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} - 9 q^{37} + 10 q^{38} - 7 q^{39} - 3 q^{41} + q^{42} + 36 q^{44} - 3 q^{46} - 17 q^{47} - 14 q^{48} + 6 q^{49} + 3 q^{51} - 3 q^{52} - 4 q^{53} + 6 q^{54} + 12 q^{56} + 5 q^{57} + 24 q^{58} - 6 q^{59} - 21 q^{61} + 27 q^{62} - q^{63} + 13 q^{64} - 4 q^{66} + 6 q^{67} + 27 q^{68} + 3 q^{69} + 15 q^{71} + 7 q^{72} - 14 q^{73} - 26 q^{74} + 60 q^{76} - q^{77} + 2 q^{78} - 11 q^{79} - q^{81} + 3 q^{82} - 13 q^{83} - 9 q^{84} + 15 q^{86} - 24 q^{87} + 37 q^{88} - 24 q^{89} + 3 q^{91} - 3 q^{92} - 12 q^{93} + 17 q^{94} - 15 q^{96} - 3 q^{97} - 36 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 - 9 * q^4 + q^6 - q^7 - 13 * q^8 - q^9 - 11 * q^11 + 6 * q^12 - 7 * q^13 - 4 * q^14 + q^16 - 12 * q^17 - 4 * q^18 - 10 * q^19 + 4 * q^21 - 4 * q^22 + 8 * q^23 + 7 * q^24 + 2 * q^26 - q^27 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 30 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 - 9 * q^37 + 10 * q^38 - 7 * q^39 - 3 * q^41 + q^42 + 36 * q^44 - 3 * q^46 - 17 * q^47 - 14 * q^48 + 6 * q^49 + 3 * q^51 - 3 * q^52 - 4 * q^53 + 6 * q^54 + 12 * q^56 + 5 * q^57 + 24 * q^58 - 6 * q^59 - 21 * q^61 + 27 * q^62 - q^63 + 13 * q^64 - 4 * q^66 + 6 * q^67 + 27 * q^68 + 3 * q^69 + 15 * q^71 + 7 * q^72 - 14 * q^73 - 26 * q^74 + 60 * q^76 - q^77 + 2 * q^78 - 11 * q^79 - q^81 + 3 * q^82 - 13 * q^83 - 9 * q^84 + 15 * q^86 - 24 * q^87 + 37 * q^88 - 24 * q^89 + 3 * q^91 - 3 * q^92 - 12 * q^93 + 17 * q^94 - 15 * q^96 - 3 * q^97 - 36 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.224514i	−0.218508	−	0.158755i	0.473147	−	0.880984i	$-0.343118\pi$
$2$	−0.309017	−	0.224514i	−0.218508	−	0.158755i	−0.691655	+	0.722228i	$0.743118\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.572949	−	1.76336i	−0.286475	−	0.881678i
$5$		0			0
$5$		0			0
$6$	−0.309017	+	0.224514i	−0.126156	+	0.0916575i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i	0.992318	−	0.123716i	$-0.0394811\pi$
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i	−0.875520	+	0.483181i	$0.839481\pi$
$8$	−0.454915	+	1.40008i	−0.160837	+	0.495005i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$12$	−1.85410			−0.535233
$13$	−3.42705	−	2.48990i	−0.950493	−	0.690574i	0.000430477	−	1.00000i	$-0.499863\pi$
$13$	−3.42705	−	2.48990i	−0.950493	−	0.690574i	−0.950923	+	0.309426i	$0.899863\pi$
$14$	0.118034	−	0.363271i	0.0315459	−	0.0970883i
$15$		0			0
$16$	−2.54508	+	1.84911i	−0.636271	+	0.462278i
$17$	−6.35410	+	4.61653i	−1.54110	+	1.11967i	−0.591452	+	0.806340i	$0.701445\pi$
$17$	−6.35410	+	4.61653i	−1.54110	+	1.11967i	−0.949644	+	0.313332i	$0.898555\pi$
$18$	0.118034	+	0.363271i	0.0278209	+	0.0856239i
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$	1.23607	−	0.277515i	0.263531	−	0.0591663i
$23$	4.23607			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$23$	4.23607			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$24$	1.19098	+	0.865300i	0.243108	+	0.176629i
$25$		0			0
$26$	0.500000	+	1.53884i	0.0980581	+	0.301792i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	1.50000	−	1.08981i	0.283473	−	0.205955i
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	−0.961958	−	0.273196i	$-0.911919\pi$
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	0.617660	−	0.786445i	$-0.288081\pi$
$30$		0			0
$31$	−4.11803	−	2.99193i	−0.739621	−	0.537366i	0.152972	−	0.988231i	$-0.451116\pi$
$31$	−4.11803	−	2.99193i	−0.739621	−	0.537366i	−0.892592	+	0.450865i	$0.851116\pi$
$32$	4.14590			0.732898
$33$	1.69098	+	2.85317i	0.294362	+	0.496673i
$34$	3.00000			0.514496
$35$		0			0
$36$	−0.572949	+	1.76336i	−0.0954915	+	0.293893i
$37$	0.545085	+	1.67760i	0.0896114	+	0.275796i	0.985812	−	0.167854i	$-0.0536836\pi$
$37$	0.545085	+	1.67760i	0.0896114	+	0.275796i	−0.896201	+	0.443649i	$0.853684\pi$
$38$	0.263932	−	0.191758i	0.0428154	−	0.0311072i
$39$	−3.42705	+	2.48990i	−0.548767	+	0.398703i
$40$		0			0
$41$	−1.30902	+	4.02874i	−0.204434	+	0.629183i	0.795302	+	0.606213i	$0.207312\pi$
$41$	−1.30902	+	4.02874i	−0.204434	+	0.629183i	−0.999736	+	0.0229701i	$0.992688\pi$
$42$	−0.309017	−	0.224514i	−0.0476824	−	0.0346433i
$43$	−6.70820			−1.02299			−0.511496	−	0.859286i	$-0.670908\pi$
$43$	−6.70820			−1.02299			−0.511496	+	0.859286i	$0.670908\pi$
$44$	5.64590	+	2.43690i	0.851151	+	0.367376i
$45$		0			0
$46$	−1.30902	−	0.951057i	−0.193004	−	0.140226i
$47$	−0.336881	+	1.03681i	−0.0491391	+	0.151235i	−0.972615	−	0.232421i	$-0.925335\pi$
$47$	−0.336881	+	1.03681i	−0.0491391	+	0.151235i	0.923476	+	0.383656i	$0.125335\pi$
$48$	0.972136	+	2.99193i	0.140316	+	0.431847i
$49$	4.85410	−	3.52671i	0.693443	−	0.503816i
$50$		0			0
$51$	2.42705	+	7.46969i	0.339855	+	1.04597i
$52$	−2.42705	+	7.46969i	−0.336571	+	1.03586i
$53$	−2.11803	−	1.53884i	−0.290934	−	0.211376i	0.432738	−	0.901520i	$-0.357547\pi$
$53$	−2.11803	−	1.53884i	−0.290934	−	0.211376i	−0.723673	+	0.690143i	$0.757547\pi$
$54$	0.381966			0.0519790
$55$		0			0
$56$	−1.47214			−0.196722
$57$	0.690983	+	0.502029i	0.0915229	+	0.0664953i
$58$	−0.708204	+	2.17963i	−0.0929917	+	0.286199i
$59$	2.97214	+	9.14729i	0.386939	+	1.19088i	0.935064	+	0.354480i	$0.115342\pi$
$59$	2.97214	+	9.14729i	0.386939	+	1.19088i	−0.548125	+	0.836397i	$0.684658\pi$
$60$		0			0
$61$	−6.92705	+	5.03280i	−0.886918	+	0.644384i	−0.935073	−	0.354456i	$-0.884666\pi$
$61$	−6.92705	+	5.03280i	−0.886918	+	0.644384i	0.0481546	+	0.998840i	$0.484666\pi$
$62$	0.600813	+	1.84911i	0.0763033	+	0.234838i
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$	3.80902	+	2.76741i	0.476127	+	0.345927i
$65$		0			0
$66$	0.118034	−	1.26133i	0.0145290	−	0.155259i
$67$	4.85410			0.593023			0.296511	−	0.955029i	$-0.404177\pi$
$67$	4.85410			0.593023			0.296511	+	0.955029i	$0.404177\pi$
$68$	11.7812	+	8.55951i	1.42867	+	1.03799i
$69$	1.30902	−	4.02874i	0.157587	−	0.485003i
$70$		0			0
$71$	4.30902	−	3.13068i	0.511386	−	0.371544i	−0.301963	−	0.953320i	$-0.597642\pi$
$71$	4.30902	−	3.13068i	0.511386	−	0.371544i	0.813349	+	0.581776i	$0.197642\pi$
$72$	1.19098	−	0.865300i	0.140359	−	0.101977i
$73$	−2.38197	−	7.33094i	−0.278788	−	0.858021i	−0.988192	−	0.153219i	$-0.951036\pi$
$73$	−2.38197	−	7.33094i	−0.278788	−	0.858021i	0.709404	−	0.704802i	$-0.248964\pi$
$74$	0.208204	−	0.640786i	0.0242032	−	0.0744898i
$75$		0			0
$76$	1.58359			0.181650
$77$	−3.04508	−	1.31433i	−0.347020	−	0.149782i
$78$	1.61803			0.183206
$79$	−8.89919	−	6.46564i	−1.00124	−	0.727441i	−0.0388837	−	0.999244i	$-0.512380\pi$
$79$	−8.89919	−	6.46564i	−1.00124	−	0.727441i	−0.962353	+	0.271803i	$0.912380\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.30902	−	0.951057i	0.144557	−	0.105027i
$83$	−6.04508	+	4.39201i	−0.663534	+	0.482086i	−0.867855	−	0.496818i	$-0.834502\pi$
$83$	−6.04508	+	4.39201i	−0.663534	+	0.482086i	0.204320	+	0.978904i	$0.434502\pi$
$84$	−0.572949	−	1.76336i	−0.0625139	−	0.192398i
$85$		0			0
$86$	2.07295	+	1.50609i	0.223532	+	0.162405i
$87$	−6.00000			−0.643268
$88$	−2.48936	−	4.20025i	−0.265366	−	0.447749i
$89$	−3.76393			−0.398976			−0.199488	−	0.979900i	$-0.563928\pi$
$89$	−3.76393			−0.398976			−0.199488	+	0.979900i	$0.563928\pi$
$90$		0			0
$91$	1.30902	−	4.02874i	0.137222	−	0.422327i
$92$	−2.42705	−	7.46969i	−0.253038	−	0.778770i
$93$	−4.11803	+	2.99193i	−0.427020	+	0.310248i
$94$	0.336881	−	0.244758i	0.0347466	−	0.0252449i
$95$		0			0
$96$	1.28115	−	3.94298i	0.130757	−	0.402429i
$97$	0.927051	+	0.673542i	0.0941278	+	0.0683878i	0.633854	−	0.773453i	$-0.281472\pi$
$97$	0.927051	+	0.673542i	0.0941278	+	0.0683878i	−0.539726	+	0.841841i	$0.681472\pi$
$98$	−2.29180			−0.231506
$99$	3.23607	−	0.726543i	0.325237	−	0.0730203i
$100$		0			0
$101$	4.66312	+	3.38795i	0.463998	+	0.337114i	0.795097	−	0.606482i	$-0.207420\pi$
$101$	4.66312	+	3.38795i	0.463998	+	0.337114i	−0.331100	+	0.943596i	$0.607420\pi$
$102$	0.927051	−	2.85317i	0.0917917	−	0.282506i
$103$	−2.14590	−	6.60440i	−0.211442	−	0.650750i	−0.999387	−	0.0350054i	$-0.988855\pi$
$103$	−2.14590	−	6.60440i	−0.211442	−	0.650750i	0.787946	−	0.615745i	$-0.211145\pi$
$104$	5.04508	−	3.66547i	0.494711	−	0.359429i
$105$		0			0
$106$	0.309017	+	0.951057i	0.0300144	+	0.0923748i
$107$	0.781153	−	2.40414i	0.0755169	−	0.232417i	−0.906172	−	0.422910i	$-0.861009\pi$
$107$	0.781153	−	2.40414i	0.0755169	−	0.232417i	0.981689	+	0.190493i	$0.0610086\pi$
$108$	1.50000	+	1.08981i	0.144338	+	0.104867i
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$		0			0
$111$	1.76393			0.167425
$112$	−2.54508	−	1.84911i	−0.240488	−	0.174725i
$113$	−1.39919	+	4.30625i	−0.131624	+	0.405098i	−0.995050	−	0.0993784i	$-0.968315\pi$
$113$	−1.39919	+	4.30625i	−0.131624	+	0.405098i	0.863425	+	0.504477i	$0.168315\pi$
$114$	−0.100813	−	0.310271i	−0.00944201	−	0.0290595i
$115$		0			0
$116$	−9.00000	+	6.53888i	−0.835629	+	0.607120i
$117$	1.30902	+	4.02874i	0.121019	+	0.372457i
$118$	1.13525	−	3.49396i	0.104509	−	0.321645i
$119$	−6.35410	−	4.61653i	−0.582480	−	0.423196i
$120$		0			0
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	3.27051			0.296098
$123$	3.42705	+	2.48990i	0.309007	+	0.224507i
$124$	−2.91641	+	8.97578i	−0.261901	+	0.806049i
$125$		0			0
$126$	−0.309017	+	0.224514i	−0.0275294	+	0.0200013i
$127$	−4.61803	+	3.35520i	−0.409784	+	0.297726i	−0.773514	−	0.633779i	$-0.781503\pi$
$127$	−4.61803	+	3.35520i	−0.409784	+	0.297726i	0.363730	+	0.931504i	$0.381503\pi$
$128$	−3.11803	−	9.59632i	−0.275598	−	0.848203i
$129$	−2.07295	+	6.37988i	−0.182513	+	0.561717i
$130$		0			0
$131$	12.7984			1.11820			0.559100	−	0.829101i	$-0.311147\pi$
$131$	12.7984			1.11820			0.559100	+	0.829101i	$0.311147\pi$
$132$	4.06231	−	4.61653i	0.353578	−	0.401817i
$133$	−0.854102			−0.0740600
$134$	−1.50000	−	1.08981i	−0.129580	−	0.0941456i
$135$		0			0
$136$	−3.57295	−	10.9964i	−0.306378	−	0.942934i
$137$	11.5172	−	8.36775i	0.983983	−	0.714905i	0.0253875	−	0.999678i	$-0.491918\pi$
$137$	11.5172	−	8.36775i	0.983983	−	0.714905i	0.958595	+	0.284772i	$0.0919181\pi$
$138$	−1.30902	+	0.951057i	−0.111431	+	0.0809593i
$139$	−1.71885	−	5.29007i	−0.145791	−	0.448698i	0.851321	−	0.524645i	$-0.175802\pi$
$139$	−1.71885	−	5.29007i	−0.145791	−	0.448698i	−0.997112	+	0.0759473i	$0.975802\pi$
$140$		0			0
$141$	0.881966	+	0.640786i	0.0742749	+	0.0539639i
$142$	−2.03444			−0.170727
$143$	13.7082	−	3.07768i	1.14634	−	0.257369i
$144$	3.14590			0.262158
$145$		0			0
$146$	−0.909830	+	2.80017i	−0.0752981	+	0.231744i
$147$	−1.85410	−	5.70634i	−0.152924	−	0.470651i
$148$	2.64590	−	1.92236i	0.217491	−	0.158017i
$149$	−0.190983	+	0.138757i	−0.0156459	+	0.0113674i	−0.595581	−	0.803295i	$-0.703078\pi$
$149$	−0.190983	+	0.138757i	−0.0156459	+	0.0113674i	0.579935	+	0.814663i	$0.303078\pi$
$150$		0			0
$151$	5.85410	−	18.0171i	0.476400	−	1.46621i	−0.367660	−	0.929960i	$-0.619841\pi$
$151$	5.85410	−	18.0171i	0.476400	−	1.46621i	0.844060	−	0.536248i	$-0.180159\pi$
$152$	−1.01722	−	0.739054i	−0.0825075	−	0.0599452i
$153$	7.85410			0.634967
$154$	0.645898	+	1.08981i	0.0520479	+	0.0878197i
$155$		0			0
$156$	6.35410	+	4.61653i	0.508735	+	0.369618i
$157$	−0.708204	+	2.17963i	−0.0565208	+	0.173953i	−0.975331	−	0.220745i	$-0.929151\pi$
$157$	−0.708204	+	2.17963i	−0.0565208	+	0.173953i	0.918811	+	0.394699i	$0.129151\pi$
$158$	1.29837	+	3.99598i	0.103293	+	0.317903i
$159$	−2.11803	+	1.53884i	−0.167971	+	0.122038i
$160$		0			0
$161$	1.30902	+	4.02874i	0.103165	+	0.317509i
$162$	0.118034	−	0.363271i	0.00927363	−	0.0285413i
$163$	−9.59017	−	6.96767i	−0.751160	−	0.545750i	0.145026	−	0.989428i	$-0.453673\pi$
$163$	−9.59017	−	6.96767i	−0.751160	−	0.545750i	−0.896186	+	0.443678i	$0.853673\pi$
$164$	7.85410			0.613302
$165$		0			0
$166$	2.85410			0.221521
$167$	−13.7812	−	10.0126i	−1.06642	−	0.774798i	−0.0911527	−	0.995837i	$-0.529055\pi$
$167$	−13.7812	−	10.0126i	−1.06642	−	0.774798i	−0.975265	+	0.221039i	$0.929055\pi$
$168$	−0.454915	+	1.40008i	−0.0350975	+	0.108019i
$169$	1.52786	+	4.70228i	0.117528	+	0.361714i
$170$		0			0
$171$	0.690983	−	0.502029i	0.0528408	−	0.0383911i
$172$	3.84346	+	11.8290i	0.293061	+	0.901949i
$173$	−3.40983	+	10.4944i	−0.259245	+	0.797873i	0.733719	+	0.679453i	$0.237783\pi$
$173$	−3.40983	+	10.4944i	−0.259245	+	0.797873i	−0.992964	+	0.118420i	$0.962217\pi$
$174$	1.85410	+	1.34708i	0.140559	+	0.102122i
$175$		0			0
$176$	0.972136	−	10.3884i	0.0732775	−	0.783053i
$177$	9.61803			0.722936
$178$	1.16312	+	0.845055i	0.0871795	+	0.0633396i
$179$	−5.39919	+	16.6170i	−0.403554	+	1.24201i	0.518542	+	0.855052i	$0.326475\pi$
$179$	−5.39919	+	16.6170i	−0.403554	+	1.24201i	−0.922096	+	0.386960i	$0.873525\pi$
$180$		0			0
$181$	−9.28115	+	6.74315i	−0.689863	+	0.501215i	−0.876615	−	0.481192i	$-0.840204\pi$
$181$	−9.28115	+	6.74315i	−0.689863	+	0.501215i	0.186752	+	0.982407i	$0.440204\pi$
$182$	−1.30902	+	0.951057i	−0.0970308	+	0.0704970i
$183$	2.64590	+	8.14324i	0.195590	+	0.601965i
$184$	−1.92705	+	5.93085i	−0.142064	+	0.437228i
$185$		0			0
$186$	1.94427			0.142561
$187$	2.42705	−	25.9358i	0.177484	−	1.89661i
$188$	2.02129			0.147417
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$		0			0
$191$	−7.16312	−	22.0458i	−0.518305	−	1.59518i	−0.777187	−	0.629270i	$-0.783354\pi$
$191$	−7.16312	−	22.0458i	−0.518305	−	1.59518i	0.258882	−	0.965909i	$-0.416646\pi$
$192$	3.80902	−	2.76741i	0.274892	−	0.199721i
$193$	−7.97214	+	5.79210i	−0.573847	+	0.416924i	−0.836501	−	0.547966i	$-0.815402\pi$
$193$	−7.97214	+	5.79210i	−0.573847	+	0.416924i	0.262654	+	0.964890i	$0.415402\pi$
$194$	−0.135255	−	0.416272i	−0.00971074	−	0.0298866i
$195$		0			0
$196$	−9.00000	−	6.53888i	−0.642857	−	0.467063i
$197$	16.0344			1.14241			0.571203	−	0.820809i	$-0.306477\pi$
$197$	16.0344			1.14241			0.571203	+	0.820809i	$0.306477\pi$
$198$	−1.16312	−	0.502029i	−0.0826593	−	0.0356776i
$199$	−6.70820			−0.475532			−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820			−0.475532			−0.237766	+	0.971322i	$0.576415\pi$
$200$		0			0
$201$	1.50000	−	4.61653i	0.105802	−	0.325625i
$202$	−0.680340	−	2.09387i	−0.0478685	−	0.147324i
$203$	4.85410	−	3.52671i	0.340691	−	0.247527i
$204$	11.7812	−	8.55951i	0.824846	−	0.599285i
$205$		0			0
$206$	−0.819660	+	2.52265i	−0.0571084	+	0.175762i
$207$	−3.42705	−	2.48990i	−0.238197	−	0.173060i
$208$	13.3262			0.924008
$209$	−1.44427	−	2.43690i	−0.0999024	−	0.168564i
$210$		0			0
$211$	−1.11803	−	0.812299i	−0.0769686	−	0.0559210i	0.548636	−	0.836062i	$-0.315147\pi$
$211$	−1.11803	−	0.812299i	−0.0769686	−	0.0559210i	−0.625604	+	0.780141i	$0.715147\pi$
$212$	−1.50000	+	4.61653i	−0.103020	+	0.317064i
$213$	−1.64590	−	5.06555i	−0.112775	−	0.347086i
$214$	−0.781153	+	0.567541i	−0.0533985	+	0.0387963i
$215$		0			0
$216$	−0.454915	−	1.40008i	−0.0309530	−	0.0952637i
$217$	1.57295	−	4.84104i	0.106779	−	0.328631i
$218$	3.70820	+	2.69417i	0.251151	+	0.182472i
$219$	−7.70820			−0.520872
$220$		0			0
$221$	33.2705			2.23802
$222$	−0.545085	−	0.396027i	−0.0365837	−	0.0265796i
$223$	4.69098	−	14.4374i	0.314131	−	0.966797i	−0.661979	−	0.749522i	$-0.730283\pi$
$223$	4.69098	−	14.4374i	0.314131	−	0.966797i	0.976110	−	0.217275i	$-0.0697168\pi$
$224$	1.28115	+	3.94298i	0.0856006	+	0.263452i
$225$		0			0
$226$	1.39919	−	1.01657i	0.0930725	−	0.0676212i
$227$	2.83688	+	8.73102i	0.188290	+	0.579498i	0.999990	−	0.00457752i	$-0.00145707\pi$
$227$	2.83688	+	8.73102i	0.188290	+	0.579498i	−0.811699	+	0.584076i	$0.801457\pi$
$228$	0.489357	−	1.50609i	0.0324085	−	0.0997430i
$229$	6.85410	+	4.97980i	0.452932	+	0.329074i	0.790752	−	0.612136i	$-0.209690\pi$
$229$	6.85410	+	4.97980i	0.452932	+	0.329074i	−0.337820	+	0.941211i	$0.609690\pi$
$230$		0			0
$231$	−2.19098	+	2.48990i	−0.144156	+	0.163823i
$232$	8.83282			0.579903
$233$	−8.78115	−	6.37988i	−0.575272	−	0.417960i	0.261744	−	0.965137i	$-0.415702\pi$
$233$	−8.78115	−	6.37988i	−0.575272	−	0.417960i	−0.837017	+	0.547177i	$0.815702\pi$
$234$	0.500000	−	1.53884i	0.0326860	−	0.100597i
$235$		0			0
$236$	14.4271	−	10.4819i	0.939121	−	0.682311i
$237$	−8.89919	+	6.46564i	−0.578064	+	0.419988i
$238$	0.927051	+	2.85317i	0.0600918	+	0.184944i
$239$	0.809017	−	2.48990i	0.0523310	−	0.161058i	−0.921476	−	0.388436i	$-0.873015\pi$
$239$	0.809017	−	2.48990i	0.0523310	−	0.161058i	0.973807	+	0.227378i	$0.0730154\pi$
$240$		0			0
$241$	21.7082			1.39835			0.699174	−	0.714951i	$-0.253551\pi$
$241$	21.7082			1.39835			0.699174	+	0.714951i	$0.253551\pi$
$242$	−2.01722	+	3.68571i	−0.129672	+	0.236927i
$243$	1.00000			0.0641500
$244$	12.8435	+	9.33132i	0.822218	+	0.597376i
$245$		0			0
$246$	−0.500000	−	1.53884i	−0.0318788	−	0.0981130i
$247$	2.92705	−	2.12663i	0.186244	−	0.135314i
$248$	6.06231	−	4.40452i	0.384957	−	0.279687i
$249$	2.30902	+	7.10642i	0.146328	+	0.450351i
$250$		0			0
$251$	−20.2082	−	14.6821i	−1.27553	−	0.926727i	−0.276122	−	0.961123i	$-0.589049\pi$
$251$	−20.2082	−	14.6821i	−1.27553	−	0.926727i	−0.999408	+	0.0343954i	$0.989049\pi$
$252$	−1.85410			−0.116797
$253$	−9.28115	+	10.5474i	−0.583501	+	0.663108i
$254$	2.18034			0.136807
$255$		0			0
$256$	1.71885	−	5.29007i	0.107428	−	0.330629i
$257$	3.93769	+	12.1190i	0.245627	+	0.755961i	0.995533	+	0.0944167i	$0.0300986\pi$
$257$	3.93769	+	12.1190i	0.245627	+	0.755961i	−0.749906	+	0.661544i	$0.769901\pi$
$258$	2.07295	−	1.50609i	0.129056	−	0.0937648i
$259$	−1.42705	+	1.03681i	−0.0886726	+	0.0644244i
$260$		0			0
$261$	−1.85410	+	5.70634i	−0.114766	+	0.353214i
$262$	−3.95492	−	2.87341i	−0.244335	−	0.177520i
$263$	−18.2705			−1.12661			−0.563304	−	0.826250i	$-0.690470\pi$
$263$	−18.2705			−1.12661			−0.563304	+	0.826250i	$0.690470\pi$
$264$	−4.76393	+	1.06957i	−0.293200	+	0.0658274i
$265$		0			0
$266$	0.263932	+	0.191758i	0.0161827	+	0.0117574i
$267$	−1.16312	+	3.57971i	−0.0711817	+	0.219075i
$268$	−2.78115	−	8.55951i	−0.169886	−	0.522855i
$269$	−1.14590	+	0.832544i	−0.0698666	+	0.0507611i	−0.622170	−	0.782882i	$-0.713749\pi$
$269$	−1.14590	+	0.832544i	−0.0698666	+	0.0507611i	0.552304	+	0.833643i	$0.313749\pi$
$270$		0			0
$271$	5.06231	+	15.5802i	0.307513	+	0.946428i	0.978727	+	0.205165i	$0.0657731\pi$
$271$	5.06231	+	15.5802i	0.307513	+	0.946428i	−0.671214	+	0.741263i	$0.734227\pi$
$272$	7.63525	−	23.4989i	0.462955	−	1.42483i
$273$	−3.42705	−	2.48990i	−0.207415	−	0.150695i
$274$	−5.43769			−0.328503
$275$		0			0
$276$	−7.85410			−0.472761
$277$	17.9721	+	13.0575i	1.07984	+	0.784550i	0.977655	−	0.210215i	$-0.0674164\pi$
$277$	17.9721	+	13.0575i	1.07984	+	0.784550i	0.102186	+	0.994765i	$0.467416\pi$
$278$	−0.656541	+	2.02063i	−0.0393767	+	0.121189i
$279$	1.57295	+	4.84104i	0.0941700	+	0.289825i
$280$		0			0
$281$	−23.6525	+	17.1845i	−1.41099	+	1.02514i	−0.417811	+	0.908534i	$0.637202\pi$
$281$	−23.6525	+	17.1845i	−1.41099	+	1.02514i	−0.993178	+	0.116609i	$0.962798\pi$
$282$	−0.128677	−	0.396027i	−0.00766261	−	0.0235831i
$283$	−2.38197	+	7.33094i	−0.141593	+	0.435779i	−0.996557	−	0.0829083i	$-0.973579\pi$
$283$	−2.38197	+	7.33094i	−0.141593	+	0.435779i	0.854964	+	0.518687i	$0.173579\pi$
$284$	−7.98936	−	5.80461i	−0.474081	−	0.344440i
$285$		0			0
$286$	−4.92705	−	2.12663i	−0.291343	−	0.125750i
$287$	−4.23607			−0.250047
$288$	−3.35410	−	2.43690i	−0.197642	−	0.143596i
$289$	13.8090	−	42.4998i	0.812295	−	2.49999i
$290$		0			0
$291$	0.927051	−	0.673542i	0.0543447	−	0.0394837i
$292$	−11.5623	+	8.40051i	−0.676633	+	0.491602i
$293$	−2.98278	−	9.18005i	−0.174256	−	0.536304i	0.825343	−	0.564632i	$-0.190982\pi$
$293$	−2.98278	−	9.18005i	−0.174256	−	0.536304i	−0.999599	+	0.0283276i	$0.990982\pi$
$294$	−0.708204	+	2.17963i	−0.0413033	+	0.127118i
$295$		0			0
$296$	−2.59675			−0.150933
$297$	0.309017	−	3.30220i	0.0179310	−	0.191613i
$298$	0.0901699			0.00522340
$299$	−14.5172	−	10.5474i	−0.839553	−	0.609971i
$300$		0			0
$301$	−2.07295	−	6.37988i	−0.119483	−	0.367730i
$302$	−5.85410	+	4.25325i	−0.336866	+	0.244747i
$303$	4.66312	−	3.38795i	0.267889	−	0.194633i
$304$	−0.830303	−	2.55541i	−0.0476212	−	0.146563i
$305$		0			0
$306$	−2.42705	−	1.76336i	−0.138745	−	0.100804i
$307$	18.9787			1.08317			0.541586	−	0.840645i	$-0.317824\pi$
$307$	18.9787			1.08317			0.541586	+	0.840645i	$0.317824\pi$
$308$	−0.572949	+	6.12261i	−0.0326468	+	0.348868i
$309$	−6.94427			−0.395046
$310$		0			0
$311$	−6.07295	+	18.6906i	−0.344365	+	1.05985i	0.617557	+	0.786526i	$0.288122\pi$
$311$	−6.07295	+	18.6906i	−0.344365	+	1.05985i	−0.961923	+	0.273322i	$0.911878\pi$
$312$	−1.92705	−	5.93085i	−0.109098	−	0.335768i
$313$	−9.28115	+	6.74315i	−0.524602	+	0.381146i	−0.818335	−	0.574742i	$-0.805102\pi$
$313$	−9.28115	+	6.74315i	−0.524602	+	0.381146i	0.293733	+	0.955888i	$0.405102\pi$
$314$	0.708204	−	0.514540i	0.0399663	−	0.0290372i
$315$		0			0
$316$	−6.30244	+	19.3969i	−0.354540	+	1.09116i
$317$	−23.6074	−	17.1518i	−1.32592	−	0.963340i	−0.999838	−	0.0179992i	$-0.994270\pi$
$317$	−23.6074	−	17.1518i	−1.32592	−	0.963340i	−0.326085	−	0.945340i	$-0.605730\pi$
$318$	1.00000			0.0560772
$319$	18.2705	+	7.88597i	1.02295	+	0.441529i
$320$		0			0
$321$	−2.04508	−	1.48584i	−0.114146	−	0.0829316i
$322$	0.500000	−	1.53884i	0.0278639	−	0.0857563i
$323$	−2.07295	−	6.37988i	−0.115342	−	0.354986i
$324$	1.50000	−	1.08981i	0.0833333	−	0.0605452i
$325$		0			0
$326$	1.39919	+	4.30625i	0.0774938	+	0.238501i
$327$	−3.70820	+	11.4127i	−0.205064	+	0.631123i
$328$	−5.04508	−	3.66547i	−0.278568	−	0.202392i
$329$	−1.09017			−0.0601030
$330$		0			0
$331$	3.29180			0.180933			0.0904667	−	0.995899i	$-0.471164\pi$
$331$	3.29180			0.180933			0.0904667	+	0.995899i	$0.471164\pi$
$332$	11.2082	+	8.14324i	0.615130	+	0.446918i
$333$	0.545085	−	1.67760i	0.0298705	−	0.0919319i
$334$	2.01064	+	6.18812i	0.110017	+	0.338599i
$335$		0			0
$336$	−2.54508	+	1.84911i	−0.138846	+	0.100877i
$337$	−1.29180	−	3.97574i	−0.0703686	−	0.216572i	0.909687	−	0.415294i	$-0.136321\pi$
$337$	−1.29180	−	3.97574i	−0.0703686	−	0.216572i	−0.980056	+	0.198721i	$0.936321\pi$
$338$	0.583592	−	1.79611i	0.0317432	−	0.0976956i
$339$	3.66312	+	2.66141i	0.198953	+	0.144548i
$340$		0			0
$341$	16.4721	−	3.69822i	0.892016	−	0.200270i
$342$	−0.326238			−0.0176409
$343$	10.5172	+	7.64121i	0.567877	+	0.412586i
$344$	3.05166	−	9.39205i	0.164535	−	0.506386i
$345$		0			0
$346$	3.40983	−	2.47739i	0.183314	−	0.133185i
$347$	−8.47214	+	6.15537i	−0.454808	+	0.330437i	−0.791491	−	0.611181i	$-0.790695\pi$
$347$	−8.47214	+	6.15537i	−0.454808	+	0.330437i	0.336683	+	0.941618i	$0.390695\pi$
$348$	3.43769	+	10.5801i	0.184280	+	0.567155i
$349$	−0.218847	+	0.673542i	−0.0117146	+	0.0360539i	−0.956743	−	0.290935i	$-0.906034\pi$
$349$	−0.218847	+	0.673542i	−0.0117146	+	0.0360539i	0.945028	+	0.326988i	$0.106034\pi$
$350$		0			0
$351$	4.23607			0.226105
$352$	−9.08359	+	10.3229i	−0.484157	+	0.550211i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$	−2.97214	−	2.15938i	−0.157967	−	0.114770i
$355$		0			0
$356$	2.15654	+	6.63715i	0.114296	+	0.351768i
$357$	−6.35410	+	4.61653i	−0.336295	+	0.244332i
$358$	5.39919	−	3.92274i	0.285356	−	0.207323i
$359$	1.14590	+	3.52671i	0.0604782	+	0.186133i	0.976731	−	0.214468i	$-0.0688016\pi$
$359$	1.14590	+	3.52671i	0.0604782	+	0.186133i	−0.916253	+	0.400600i	$0.868802\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	4.38197			0.230311
$363$	−10.8090	−	2.04087i	−0.567326	−	0.107118i
$364$	−7.85410			−0.411667
$365$		0			0
$366$	1.01064	−	3.11044i	0.0528272	−	0.162585i
$367$	−8.91641	−	27.4419i	−0.465433	−	1.43245i	−0.858438	−	0.512918i	$-0.828564\pi$
$367$	−8.91641	−	27.4419i	−0.465433	−	1.43245i	0.393005	−	0.919536i	$-0.371436\pi$
$368$	−10.7812	+	7.83297i	−0.562006	+	0.408322i
$369$	3.42705	−	2.48990i	0.178405	−	0.129619i
$370$		0			0
$371$	0.809017	−	2.48990i	0.0420021	−	0.129269i
$372$	7.63525	+	5.54734i	0.395870	+	0.287616i
$373$	34.8885			1.80646			0.903230	−	0.429156i	$-0.141189\pi$
$373$	34.8885			1.80646			0.903230	+	0.429156i	$0.141189\pi$
$374$	−6.57295	+	7.46969i	−0.339879	+	0.386249i
$375$		0			0
$376$	−1.29837	−	0.943324i	−0.0669585	−	0.0486482i
$377$	−7.85410	+	24.1724i	−0.404507	+	1.24494i
$378$	0.118034	+	0.363271i	0.00607101	+	0.0186847i
$379$	−8.80902	+	6.40013i	−0.452489	+	0.328752i	−0.790578	−	0.612362i	$-0.790220\pi$
$379$	−8.80902	+	6.40013i	−0.452489	+	0.328752i	0.338089	+	0.941114i	$0.390220\pi$
$380$		0			0
$381$	1.76393	+	5.42882i	0.0903690	+	0.278127i
$382$	−2.73607	+	8.42075i	−0.139989	+	0.430843i
$383$	0.572949	+	0.416272i	0.0292763	+	0.0212705i	0.602327	−	0.798249i	$-0.294240\pi$
$383$	0.572949	+	0.416272i	0.0292763	+	0.0212705i	−0.573051	+	0.819520i	$0.694240\pi$
$384$	−10.0902			−0.514912
$385$		0			0
$386$	3.76393			0.191579
$387$	5.42705	+	3.94298i	0.275873	+	0.200433i
$388$	0.656541	−	2.02063i	0.0333308	−	0.102582i
$389$	1.77458	+	5.46158i	0.0899745	+	0.276913i	0.985911	−	0.167268i	$-0.0534946\pi$
$389$	1.77458	+	5.46158i	0.0899745	+	0.276913i	−0.895937	+	0.444181i	$0.853495\pi$
$390$		0			0
$391$	−26.9164	+	19.5559i	−1.36122	+	0.988985i
$392$	2.72949	+	8.40051i	0.137860	+	0.424290i
$393$	3.95492	−	12.1720i	0.199499	−	0.613995i
$394$	−4.95492	−	3.59996i	−0.249625	−	0.181363i
$395$		0			0
$396$	−3.13525	−	5.29007i	−0.157552	−	0.265836i
$397$	5.29180			0.265588			0.132794	−	0.991144i	$-0.457605\pi$
$397$	5.29180			0.265588			0.132794	+	0.991144i	$0.457605\pi$
$398$	2.07295	+	1.50609i	0.103908	+	0.0754933i
$399$	−0.263932	+	0.812299i	−0.0132131	+	0.0406658i
$400$		0			0
$401$	−23.2082	+	16.8617i	−1.15896	+	0.842035i	−0.989646	−	0.143526i	$-0.954156\pi$
$401$	−23.2082	+	16.8617i	−1.15896	+	0.842035i	−0.169316	+	0.985562i	$0.554156\pi$
$402$	−1.50000	+	1.08981i	−0.0748132	+	0.0543550i
$403$	6.66312	+	20.5070i	0.331914	+	1.02153i
$404$	3.30244	−	10.1639i	0.164302	−	0.505671i
$405$		0			0
$406$	−2.29180			−0.113740
$407$	−5.37132	−	2.31838i	−0.266247	−	0.114918i
$408$	−11.5623			−0.572419
$409$	−2.00000	−	1.45309i	−0.0988936	−	0.0718504i	0.537240	−	0.843430i	$-0.319467\pi$
$409$	−2.00000	−	1.45309i	−0.0988936	−	0.0718504i	−0.636133	+	0.771579i	$0.719467\pi$
$410$		0			0
$411$	−4.39919	−	13.5393i	−0.216996	−	0.667845i
$412$	−10.4164	+	7.56796i	−0.513180	+	0.372847i
$413$	−7.78115	+	5.65334i	−0.382886	+	0.278183i
$414$	0.500000	+	1.53884i	0.0245737	+	0.0756299i
$415$		0			0
$416$	−14.2082	−	10.3229i	−0.696615	−	0.506120i
$417$	−5.56231			−0.272387
$418$	−0.100813	+	1.07730i	−0.00493093	+	0.0526926i
$419$	−24.4508			−1.19450			−0.597251	−	0.802054i	$-0.703740\pi$
$419$	−24.4508			−1.19450			−0.597251	+	0.802054i	$0.703740\pi$
$420$		0			0
$421$	−8.50000	+	26.1603i	−0.414265	+	1.27498i	0.498642	+	0.866808i	$0.333832\pi$
$421$	−8.50000	+	26.1603i	−0.414265	+	1.27498i	−0.912907	+	0.408168i	$0.866168\pi$
$422$	0.163119	+	0.502029i	0.00794051	+	0.0244384i
$423$	0.881966	−	0.640786i	0.0428827	−	0.0311561i
$424$	3.11803	−	2.26538i	0.151425	−	0.110017i
$425$		0			0
$426$	−0.628677	+	1.93487i	−0.0304595	+	0.0937447i
$427$	−6.92705	−	5.03280i	−0.335223	−	0.243554i
$428$	−4.68692			−0.226551
$429$	1.30902	−	13.9883i	0.0631999	−	0.675363i
$430$		0			0
$431$	13.8262	+	10.0453i	0.665986	+	0.483867i	0.868679	−	0.495375i	$-0.164969\pi$
$431$	13.8262	+	10.0453i	0.665986	+	0.483867i	−0.202693	+	0.979242i	$0.564969\pi$
$432$	0.972136	−	2.99193i	0.0467719	−	0.143949i
$433$	8.43769	+	25.9686i	0.405490	+	1.24797i	0.920486	+	0.390776i	$0.127793\pi$
$433$	8.43769	+	25.9686i	0.405490	+	1.24797i	−0.514996	+	0.857193i	$0.672207\pi$
$434$	−1.57295	+	1.14281i	−0.0755040	+	0.0548568i
$435$		0			0
$436$	6.87539	+	21.1603i	0.329271	+	1.01339i
$437$	−1.11803	+	3.44095i	−0.0534828	+	0.164603i
$438$	2.38197	+	1.73060i	0.113815	+	0.0826912i
$439$	36.7082			1.75199			0.875993	−	0.482323i	$-0.160207\pi$
$439$	36.7082			1.75199			0.875993	+	0.482323i	$0.160207\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	−10.2812	−	7.46969i	−0.489025	−	0.355297i
$443$	−5.43769	+	16.7355i	−0.258353	+	0.795128i	0.734798	+	0.678286i	$0.237277\pi$
$443$	−5.43769	+	16.7355i	−0.258353	+	0.795128i	−0.993151	+	0.116842i	$0.962723\pi$
$444$	−1.01064	−	3.11044i	−0.0479630	−	0.147615i
$445$		0			0
$446$	−4.69098	+	3.40820i	−0.222124	+	0.161383i
$447$	0.0729490	+	0.224514i	0.00345037	+	0.0106191i
$448$	−1.45492	+	4.47777i	−0.0687383	+	0.211555i
$449$	21.7984	+	15.8374i	1.02873	+	0.747415i	0.968054	−	0.250742i	$-0.0806747\pi$
$449$	21.7984	+	15.8374i	1.02873	+	0.747415i	0.0606750	+	0.998158i	$0.480675\pi$
$450$		0			0
$451$	−7.16312	−	12.0862i	−0.337298	−	0.569118i
$452$	8.39512			0.394873
$453$	−15.3262	−	11.1352i	−0.720089	−	0.523176i
$454$	1.08359	−	3.33495i	0.0508555	−	0.156517i
$455$		0			0
$456$	−1.01722	+	0.739054i	−0.0476357	+	0.0346094i
$457$	−18.5902	+	13.5065i	−0.869611	+	0.631810i	−0.930483	−	0.366336i	$-0.880612\pi$
$457$	−18.5902	+	13.5065i	−0.869611	+	0.631810i	0.0608712	+	0.998146i	$0.480612\pi$
$458$	−1.00000	−	3.07768i	−0.0467269	−	0.143811i
$459$	2.42705	−	7.46969i	0.113285	−	0.348655i
$460$		0			0
$461$	−24.2705			−1.13039			−0.565195	−	0.824957i	$-0.691199\pi$
$461$	−24.2705			−1.13039			−0.565195	+	0.824957i	$0.691199\pi$
$462$	1.23607	−	0.277515i	0.0575071	−	0.0129111i
$463$	−35.2705			−1.63916			−0.819580	−	0.572965i	$-0.805793\pi$
$463$	−35.2705			−1.63916			−0.819580	+	0.572965i	$0.805793\pi$
$464$	15.2705	+	11.0947i	0.708916	+	0.515057i
$465$		0			0
$466$	1.28115	+	3.94298i	0.0593483	+	0.182655i
$467$	−12.0451	+	8.75127i	−0.557380	+	0.404960i	−0.830499	−	0.557020i	$-0.811945\pi$
$467$	−12.0451	+	8.75127i	−0.557380	+	0.404960i	0.273119	+	0.961980i	$0.411945\pi$
$468$	6.35410	−	4.61653i	0.293718	−	0.213399i
$469$	1.50000	+	4.61653i	0.0692636	+	0.213171i
$470$		0			0
$471$	1.85410	+	1.34708i	0.0854325	+	0.0620704i
$472$	−14.1591			−0.651723
$473$	14.6976	−	16.7027i	0.675795	−	0.767993i
$474$	4.20163			0.192987
$475$		0			0
$476$	−4.50000	+	13.8496i	−0.206257	+	0.634794i
$477$	0.809017	+	2.48990i	0.0370423	+	0.114005i
$478$	−0.809017	+	0.587785i	−0.0370036	+	0.0268847i
$479$	24.7705	−	17.9968i	1.13179	−	0.822296i	0.145839	−	0.989308i	$-0.453412\pi$
$479$	24.7705	−	17.9968i	1.13179	−	0.822296i	0.985955	+	0.167012i	$0.0534120\pi$
$480$		0			0
$481$	2.30902	−	7.10642i	0.105282	−	0.324025i
$482$	−6.70820	−	4.87380i	−0.305550	−	0.221995i
$483$	4.23607			0.192748
$484$	−18.4377	+	8.71851i	−0.838077	+	0.396296i
$485$		0			0
$486$	−0.309017	−	0.224514i	−0.0140173	−	0.0101842i
$487$	−0.218847	+	0.673542i	−0.00991691	+	0.0305211i	−0.955893	−	0.293717i	$-0.905108\pi$
$487$	−0.218847	+	0.673542i	−0.00991691	+	0.0305211i	0.945976	+	0.324238i	$0.105108\pi$
$488$	−3.89512	−	11.9880i	−0.176324	−	0.542669i
$489$	−9.59017	+	6.96767i	−0.433682	+	0.315089i
$490$		0			0
$491$	−8.98936	−	27.6664i	−0.405684	−	1.24857i	−0.920323	−	0.391160i	$-0.872074\pi$
$491$	−8.98936	−	27.6664i	−0.405684	−	1.24857i	0.514639	−	0.857407i	$-0.327926\pi$
$492$	2.42705	−	7.46969i	0.109420	−	0.336760i
$493$	38.1246	+	27.6992i	1.71705	+	1.24751i
$494$	−1.38197			−0.0621776
$495$		0			0
$496$	16.0132			0.719012
$497$	4.30902	+	3.13068i	0.193286	+	0.140430i
$498$	0.881966	−	2.71441i	0.0395218	−	0.121636i
$499$	−7.68034	−	23.6377i	−0.343819	−	1.05817i	−0.962213	−	0.272298i	$-0.912216\pi$
$499$	−7.68034	−	23.6377i	−0.343819	−	1.05817i	0.618394	−	0.785868i	$-0.287784\pi$
$500$		0			0
$501$	−13.7812	+	10.0126i	−0.615697	+	0.447330i
$502$	2.94834	+	9.07405i	0.131591	+	0.404995i
$503$	7.00000	−	21.5438i	0.312115	−	0.960590i	−0.664811	−	0.747011i	$-0.731488\pi$
$503$	7.00000	−	21.5438i	0.312115	−	0.960590i	0.976926	−	0.213579i	$-0.0685119\pi$
$504$	1.19098	+	0.865300i	0.0530506	+	0.0385435i
$505$		0			0
$506$	5.23607	−	1.17557i	0.232772	−	0.0522605i
$507$	4.94427			0.219583
$508$	8.56231	+	6.22088i	0.379891	+	0.276007i
$509$	−1.15654	+	3.55947i	−0.0512628	+	0.157771i	−0.973411	−	0.229067i	$-0.926433\pi$
$509$	−1.15654	+	3.55947i	−0.0512628	+	0.157771i	0.922148	+	0.386837i	$0.126433\pi$
$510$		0			0
$511$	6.23607	−	4.53077i	0.275867	−	0.200429i
$512$	−18.0451	+	13.1105i	−0.797488	+	0.579409i
$513$	−0.263932	−	0.812299i	−0.0116529	−	0.0358639i
$514$	1.50407	−	4.62904i	0.0663415	−	0.204178i
$515$		0			0
$516$	12.4377			0.547539
$517$	−1.84346	−	3.11044i	−0.0810752	−	0.136797i
$518$	0.673762			0.0296034
$519$	8.92705	+	6.48588i	0.391854	+	0.284699i
$520$		0			0
$521$	−2.76393	−	8.50651i	−0.121090	−	0.372677i	0.872078	−	0.489366i	$-0.162772\pi$
$521$	−2.76393	−	8.50651i	−0.121090	−	0.372677i	−0.993168	+	0.116689i	$0.962772\pi$
$522$	1.85410	−	1.34708i	0.0811518	−	0.0589603i
$523$	−12.3541	+	8.97578i	−0.540207	+	0.392483i	−0.824162	−	0.566354i	$-0.808353\pi$
$523$	−12.3541	+	8.97578i	−0.540207	+	0.392483i	0.283955	+	0.958838i	$0.408353\pi$
$524$	−7.33282	−	22.5681i	−0.320336	−	0.985891i
$525$		0			0
$526$	5.64590	+	4.10199i	0.246173	+	0.178855i
$527$	39.9787			1.74150
$528$	−9.57953	−	4.13474i	−0.416895	−	0.179942i
$529$	−5.05573			−0.219814
$530$		0			0
$531$	2.97214	−	9.14729i	0.128980	−	0.396959i
$532$	0.489357	+	1.50609i	0.0212163	+	0.0652971i
$533$	14.5172	−	10.5474i	0.628811	−	0.456858i
$534$	1.16312	−	0.845055i	0.0503331	−	0.0365691i
$535$		0			0
$536$	−2.20820	+	6.79615i	−0.0953799	+	0.293549i
$537$	14.1353	+	10.2699i	0.609981	+	0.443177i
$538$	0.541020			0.0233250
$539$	−1.85410	+	19.8132i	−0.0798618	+	0.853414i
$540$		0			0
$541$	36.8156	+	26.7481i	1.58283	+	1.14999i	0.913364	+	0.407144i	$0.133475\pi$
$541$	36.8156	+	26.7481i	1.58283	+	1.14999i	0.669462	+	0.742846i	$0.266525\pi$
$542$	1.93363	−	5.95110i	0.0830565	−	0.255622i
$543$	3.54508	+	10.9106i	0.152134	+	0.468221i
$544$	−26.3435	+	19.1396i	−1.12947	+	0.820605i
$545$		0			0
$546$	0.500000	+	1.53884i	0.0213980	+	0.0658563i
$547$	−3.62868	+	11.1679i	−0.155151	+	0.477506i	−0.998176	−	0.0603684i	$-0.980772\pi$
$547$	−3.62868	+	11.1679i	−0.155151	+	0.477506i	0.843025	+	0.537874i	$0.180772\pi$
$548$	−21.3541	−	15.5147i	−0.912202	−	0.662754i
$549$	8.56231			0.365430
$550$		0			0
$551$	5.12461			0.218316
$552$	5.04508	+	3.66547i	0.214733	+	0.156013i
$553$	3.39919	−	10.4616i	0.144548	−	0.444873i
$554$	−2.62210	−	8.06999i	−0.111402	−	0.342861i
$555$		0			0
$556$	−8.34346	+	6.06188i	−0.353841	+	0.257081i
$557$	12.5557	+	38.6426i	0.532003	+	1.63734i	0.750037	+	0.661396i	$0.230036\pi$
$557$	12.5557	+	38.6426i	0.532003	+	1.63734i	−0.218033	+	0.975941i	$0.569964\pi$
$558$	0.600813	−	1.84911i	0.0254344	−	0.0782792i
$559$	22.9894	+	16.7027i	0.972346	+	0.706451i
$560$		0			0
$561$	−23.9164	−	10.3229i	−1.00975	−	0.435832i
$562$	11.1672			0.471059
$563$	−6.95492	−	5.05304i	−0.293115	−	0.212960i	0.431503	−	0.902112i	$-0.357984\pi$
$563$	−6.95492	−	5.05304i	−0.293115	−	0.212960i	−0.724617	+	0.689151i	$0.757984\pi$
$564$	0.624612	−	1.92236i	0.0263009	−	0.0809459i
$565$		0			0
$566$	2.38197	−	1.73060i	0.100121	−	0.0727425i
$567$	−0.809017	+	0.587785i	−0.0339755	+	0.0246847i
$568$	2.42299	+	7.45718i	0.101666	+	0.312896i
$569$	3.65248	−	11.2412i	0.153120	−	0.471254i	−0.844846	−	0.535010i	$-0.820308\pi$
$569$	3.65248	−	11.2412i	0.153120	−	0.471254i	0.997966	+	0.0637558i	$0.0203079\pi$
$570$		0			0
$571$	2.09017			0.0874709			0.0437354	−	0.999043i	$-0.486074\pi$
$571$	2.09017			0.0874709			0.0437354	+	0.999043i	$0.486074\pi$
$572$	−13.2812	−	22.4091i	−0.555313	−	0.936971i
$573$	−23.1803			−0.968373
$574$	1.30902	+	0.951057i	0.0546373	+	0.0396963i
$575$		0			0
$576$	−1.45492	−	4.47777i	−0.0606215	−	0.186574i
$577$	14.7984	−	10.7516i	0.616064	−	0.447597i	−0.235480	−	0.971879i	$-0.575666\pi$
$577$	14.7984	−	10.7516i	0.616064	−	0.447597i	0.851545	+	0.524282i	$0.175666\pi$
$578$	−13.8090	+	10.0328i	−0.574379	+	0.417311i
$579$	3.04508	+	9.37181i	0.126549	+	0.389479i
$580$		0			0
$581$	−6.04508	−	4.39201i	−0.250792	−	0.182211i
$582$	−0.437694			−0.0181430
$583$	8.47214	−	1.90211i	0.350880	−	0.0787775i
$584$	11.3475			0.469564
$585$		0			0
$586$	−1.13932	+	3.50647i	−0.0470649	+	0.144851i
$587$	−11.7812	−	36.2587i	−0.486260	−	1.49656i	−0.830147	−	0.557544i	$-0.811744\pi$
$587$	−11.7812	−	36.2587i	−0.486260	−	1.49656i	0.343887	−	0.939011i	$-0.388256\pi$
$588$	−9.00000	+	6.53888i	−0.371154	+	0.269659i
$589$	3.51722	−	2.55541i	0.144925	−	0.105294i
$590$		0			0
$591$	4.95492	−	15.2497i	0.203818	−	0.627287i
$592$	−4.48936	−	3.26171i	−0.184511	−	0.134055i
$593$	−15.0344			−0.617391			−0.308695	−	0.951161i	$-0.599892\pi$
$593$	−15.0344			−0.617391			−0.308695	+	0.951161i	$0.599892\pi$
$594$	−0.836881	+	0.951057i	−0.0343376	+	0.0390223i
$595$		0			0
$596$	0.354102	+	0.257270i	0.0145046	+	0.0105382i
$597$	−2.07295	+	6.37988i	−0.0848402	+	0.261111i
$598$	2.11803	+	6.51864i	0.0866129	+	0.266567i
$599$	15.0902	−	10.9637i	0.616568	−	0.447963i	−0.235153	−	0.971958i	$-0.575559\pi$
$599$	15.0902	−	10.9637i	0.616568	−	0.447963i	0.851721	+	0.523996i	$0.175559\pi$
$600$		0			0
$601$	8.92705	+	27.4746i	0.364142	+	1.12071i	0.950517	+	0.310674i	$0.100555\pi$
$601$	8.92705	+	27.4746i	0.364142	+	1.12071i	−0.586375	+	0.810040i	$0.699445\pi$
$602$	−0.791796	+	2.43690i	−0.0322712	+	0.0993205i
$603$	−3.92705	−	2.85317i	−0.159922	−	0.116190i
$604$	−35.1246			−1.42920
$605$		0			0
$606$	−2.20163			−0.0894349
$607$	2.88197	+	2.09387i	0.116975	+	0.0849876i	0.644735	−	0.764406i	$-0.276968\pi$
$607$	2.88197	+	2.09387i	0.116975	+	0.0849876i	−0.527760	+	0.849394i	$0.676968\pi$
$608$	−1.09424	+	3.36771i	−0.0443771	+	0.136579i
$609$	−1.85410	−	5.70634i	−0.0751320	−	0.231233i
$610$		0			0
$611$	3.73607	−	2.71441i	0.151145	−	0.109813i
$612$	−4.50000	−	13.8496i	−0.181902	−	0.559836i
$613$	8.56231	−	26.3521i	0.345828	−	1.06435i	−0.615311	−	0.788285i	$-0.710969\pi$
$613$	8.56231	−	26.3521i	0.345828	−	1.06435i	0.961139	−	0.276065i	$-0.0890306\pi$
$614$	−5.86475	−	4.26099i	−0.236682	−	0.171959i
$615$		0			0
$616$	3.22542	−	3.66547i	0.129956	−	0.147686i
$617$	11.1803			0.450104			0.225052	−	0.974347i	$-0.427745\pi$
$617$	11.1803			0.450104			0.225052	+	0.974347i	$0.427745\pi$
$618$	2.14590	+	1.55909i	0.0863207	+	0.0627156i
$619$	−4.98278	+	15.3354i	−0.200275	+	0.616382i	0.799600	+	0.600533i	$0.205045\pi$
$619$	−4.98278	+	15.3354i	−0.200275	+	0.616382i	−0.999874	+	0.0158490i	$0.994955\pi$
$620$		0			0
$621$	−3.42705	+	2.48990i	−0.137523	+	0.0999162i
$622$	6.07295	−	4.41226i	0.243503	−	0.176915i
$623$	−1.16312	−	3.57971i	−0.0465994	−	0.143418i
$624$	4.11803	−	12.6740i	0.164853	−	0.507366i
$625$		0			0
$626$	4.38197			0.175139
$627$	−2.76393	+	0.620541i	−0.110381	+	0.0247820i
$628$	4.24922			0.169562
$629$	−11.2082	−	8.14324i	−0.446900	−	0.324692i
$630$		0			0
$631$	−9.95492	−	30.6381i	−0.396299	−	1.21968i	−0.927945	−	0.372716i	$-0.878426\pi$
$631$	−9.95492	−	30.6381i	−0.396299	−	1.21968i	0.531646	−	0.846966i	$-0.321574\pi$
$632$	13.1008	−	9.51830i	0.521122	−	0.378618i
$633$	−1.11803	+	0.812299i	−0.0444379	+	0.0322860i
$634$	3.44427	+	10.6004i	0.136790	+	0.420995i
$635$		0			0
$636$	3.92705	+	2.85317i	0.155718	+	0.113136i
$637$	−25.4164			−1.00703
$638$	−3.87539	−	6.53888i	−0.153428	−	0.258877i
$639$	−5.32624			−0.210703
$640$		0			0
$641$	−4.29837	+	13.2290i	−0.169776	+	0.522515i	−0.999356	−	0.0358711i	$-0.988579\pi$
$641$	−4.29837	+	13.2290i	−0.169776	+	0.522515i	0.829581	+	0.558387i	$0.188579\pi$
$642$	0.298374	+	0.918300i	0.0117759	+	0.0362424i
$643$	11.4443	−	8.31475i	0.451318	−	0.327902i	−0.338798	−	0.940859i	$-0.610020\pi$
$643$	11.4443	−	8.31475i	0.451318	−	0.327902i	0.790116	+	0.612957i	$0.210020\pi$
$644$	6.35410	−	4.61653i	0.250387	−	0.181917i
$645$		0			0
$646$	−0.791796	+	2.43690i	−0.0311528	+	0.0958785i
$647$	12.9164	+	9.38432i	0.507796	+	0.368936i	0.811987	−	0.583676i	$-0.198386\pi$
$647$	12.9164	+	9.38432i	0.507796	+	0.368936i	−0.304191	+	0.952611i	$0.598386\pi$
$648$	−1.47214			−0.0578310
$649$	−29.2877	−	12.6412i	−1.14964	−	0.496212i
$650$		0			0
$651$	−4.11803	−	2.99193i	−0.161398	−	0.117263i
$652$	−6.79180	+	20.9030i	−0.265987	+	0.818625i
$653$	1.04508	+	3.21644i	0.0408973	+	0.125869i	0.969421	−	0.245405i	$-0.0789210\pi$
$653$	1.04508	+	3.21644i	0.0408973	+	0.125869i	−0.928523	+	0.371274i	$0.878921\pi$
$654$	3.70820	−	2.69417i	0.145002	−	0.105350i
$655$		0			0
$656$	−4.11803	−	12.6740i	−0.160782	−	0.494837i
$657$	−2.38197	+	7.33094i	−0.0929293	+	0.286007i
$658$	0.336881	+	0.244758i	0.0131330	+	0.00954168i
$659$	−0.875388			−0.0341003			−0.0170501	−	0.999855i	$-0.505427\pi$
$659$	−0.875388			−0.0341003			−0.0170501	+	0.999855i	$0.505427\pi$
$660$		0			0
$661$	16.4377			0.639352			0.319676	−	0.947527i	$-0.396426\pi$
$661$	16.4377			0.639352			0.319676	+	0.947527i	$0.396426\pi$
$662$	−1.01722	−	0.739054i	−0.0395354	−	0.0287242i
$663$	10.2812	−	31.6421i	0.399287	−	1.22888i
$664$	−3.39919	−	10.4616i	−0.131914	−	0.405990i
$665$		0			0
$666$	−0.545085	+	0.396027i	−0.0211216	+	0.0153458i
$667$	−7.85410	−	24.1724i	−0.304112	−	0.935961i
$668$	−9.75987	+	30.0378i	−0.377621	+	1.16220i
$669$	−12.2812	−	8.92278i	−0.474817	−	0.344975i
$670$		0			0
$671$	2.64590	−	28.2744i	0.102144	−	1.09152i
$672$	4.14590			0.159931
$673$	−14.4271	−	10.4819i	−0.556122	−	0.404046i	0.273916	−	0.961754i	$-0.411681\pi$
$673$	−14.4271	−	10.4819i	−0.556122	−	0.404046i	−0.830038	+	0.557707i	$0.811681\pi$
$674$	−0.493422	+	1.51860i	−0.0190059	+	0.0584942i
$675$		0			0
$676$	7.41641	−	5.38834i	0.285246	−	0.207244i
$677$	18.1803	−	13.2088i	0.698727	−	0.507655i	−0.180790	−	0.983522i	$-0.557866\pi$
$677$	18.1803	−	13.2088i	0.698727	−	0.507655i	0.879517	+	0.475867i	$0.157866\pi$
$678$	−0.534442	−	1.64484i	−0.0205251	−	0.0631698i
$679$	−0.354102	+	1.08981i	−0.0135892	+	0.0418232i
$680$		0			0
$681$	9.18034			0.351791
$682$	−5.92047	−	2.55541i	−0.226707	−	0.0978517i
$683$	49.0689			1.87757			0.938784	−	0.344505i	$-0.111953\pi$
$683$	49.0689			1.87757			0.938784	+	0.344505i	$0.111953\pi$
$684$	−1.28115	−	0.930812i	−0.0489861	−	0.0355905i
$685$		0			0
$686$	−1.53444	−	4.72253i	−0.0585853	−	0.180307i
$687$	6.85410	−	4.97980i	0.261500	−	0.189991i
$688$	17.0729	−	12.4042i	0.650900	−	0.472907i
$689$	3.42705	+	10.5474i	0.130560	+	0.401823i
$690$		0			0
$691$	−26.4164	−	19.1926i	−1.00493	−	0.730123i	−0.0417884	−	0.999126i	$-0.513306\pi$
$691$	−26.4164	−	19.1926i	−1.00493	−	0.730123i	−0.963139	+	0.269004i	$0.913306\pi$
$692$	20.4590			0.777734
$693$	1.69098	+	2.85317i	0.0642351	+	0.108383i
$694$	4.00000			0.151838
$695$		0			0
$696$	2.72949	−	8.40051i	0.103461	−	0.318420i
$697$	−10.2812	−	31.6421i	−0.389426	−	1.19853i
$698$	0.218847	−	0.159002i	0.00828348	−	0.00601830i
$699$	−8.78115	+	6.37988i	−0.332134	+	0.241309i
$700$		0			0
$701$	−3.15248	+	9.70232i	−0.119067	+	0.366452i	−0.992774	−	0.120002i	$-0.961710\pi$
$701$	−3.15248	+	9.70232i	−0.119067	+	0.366452i	0.873706	+	0.486454i	$0.161710\pi$
$702$	−1.30902	−	0.951057i	−0.0494057	−	0.0358953i
$703$	−1.50658			−0.0568217
$704$	−15.2361	+	3.42071i	−0.574231	+	0.128923i
$705$		0			0
$706$	−3.70820	−	2.69417i	−0.139560	−	0.101396i
$707$	−1.78115	+	5.48183i	−0.0669872	+	0.206165i
$708$	−5.51064	−	16.9600i	−0.207103	−	0.637396i
$709$	32.5344	−	23.6377i	1.22186	−	0.887731i	0.225604	−	0.974219i	$-0.427565\pi$
$709$	32.5344	−	23.6377i	1.22186	−	0.887731i	0.996253	+	0.0864884i	$0.0275645\pi$
$710$		0			0
$711$	3.39919	+	10.4616i	0.127479	+	0.392341i
$712$	1.71227	−	5.26982i	0.0641700	−	0.197495i
$713$	−17.4443	−	12.6740i	−0.653293	−	0.474645i
$714$	3.00000			0.112272
$715$		0			0
$716$	32.3951			1.21066
$717$	−2.11803	−	1.53884i	−0.0790994	−	0.0574691i
$718$	0.437694	−	1.34708i	0.0163346	−	0.0502727i
$719$	14.3647	+	44.2101i	0.535715	+	1.64876i	0.742100	+	0.670289i	$0.233830\pi$
$719$	14.3647	+	44.2101i	0.535715	+	1.64876i	−0.206385	+	0.978471i	$0.566170\pi$
$720$		0			0
$721$	5.61803	−	4.08174i	0.209227	−	0.152012i
$722$	−2.15654	−	6.63715i	−0.0802582	−	0.247009i
$723$	6.70820	−	20.6457i	0.249481	−	0.767823i
$724$	17.2082	+	12.5025i	0.639538	+	0.464651i
$725$		0			0
$726$	2.88197	+	3.05744i	0.106960	+	0.113472i
$727$	15.8541			0.587996			0.293998	−	0.955806i	$-0.405014\pi$
$727$	15.8541			0.587996			0.293998	+	0.955806i	$0.405014\pi$
$728$	5.04508	+	3.66547i	0.186983	+	0.135851i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	42.6246	−	30.9686i	1.57653	−	1.14541i
$732$	12.8435	−	9.33132i	0.474708	−	0.344895i
$733$	15.3262	+	47.1693i	0.566088	+	1.74224i	0.664698	+	0.747112i	$0.268560\pi$
$733$	15.3262	+	47.1693i	0.566088	+	1.74224i	−0.0986105	+	0.995126i	$0.531440\pi$
$734$	−3.40576	+	10.4819i	−0.125709	+	0.386893i
$735$		0			0
$736$	17.5623			0.647355
$737$	−10.6353	+	12.0862i	−0.391755	+	0.445202i
$738$	−1.61803			−0.0595607
$739$	−2.42705	−	1.76336i	−0.0892805	−	0.0648661i	0.542250	−	0.840218i	$-0.317573\pi$
$739$	−2.42705	−	1.76336i	−0.0892805	−	0.0648661i	−0.631530	+	0.775351i	$0.717573\pi$
$740$		0			0
$741$	−1.11803	−	3.44095i	−0.0410720	−	0.126407i
$742$	−0.809017	+	0.587785i	−0.0296999	+	0.0215783i
$743$	−5.75329	+	4.18001i	−0.211068	+	0.153350i	−0.688297	−	0.725429i	$-0.741641\pi$
$743$	−5.75329	+	4.18001i	−0.211068	+	0.153350i	0.477229	+	0.878779i	$0.341641\pi$
$744$	−2.31559	−	7.12667i	−0.0848938	−	0.261276i
$745$		0			0
$746$	−10.7812	−	7.83297i	−0.394726	−	0.286785i
$747$	7.47214			0.273391
$748$	−47.1246	+	10.5801i	−1.72305	+	0.386848i
$749$	2.52786			0.0923661
$750$		0			0
$751$	7.06231	−	21.7355i	0.257707	−	0.793141i	−0.735577	−	0.677441i	$-0.763089\pi$
$751$	7.06231	−	21.7355i	0.257707	−	0.793141i	0.993284	−	0.115700i	$-0.0369111\pi$
$752$	−1.05979	−	3.26171i	−0.0386467	−	0.118942i
$753$	−20.2082	+	14.6821i	−0.736428	+	0.535046i
$754$	7.85410	−	5.70634i	0.286030	−	0.207813i
$755$		0			0
$756$	−0.572949	+	1.76336i	−0.0208380	+	0.0641326i
$757$	4.04508	+	2.93893i	0.147021	+	0.106817i	0.658864	−	0.752262i	$-0.271037\pi$
$757$	4.04508	+	2.93893i	0.147021	+	0.106817i	−0.511843	+	0.859079i	$0.671037\pi$
$758$	4.15905			0.151064
$759$	7.16312	+	12.0862i	0.260005	+	0.438702i
$760$		0			0
$761$	−34.5517	−	25.1033i	−1.25250	−	0.909992i	−0.254133	−	0.967169i	$-0.581790\pi$
$761$	−34.5517	−	25.1033i	−1.25250	−	0.909992i	−0.998364	+	0.0571772i	$0.981790\pi$
$762$	0.673762	−	2.07363i	0.0244078	−	0.0751196i
$763$	−3.70820	−	11.4127i	−0.134246	−	0.413167i
$764$	−34.7705	+	25.2623i	−1.25795	+	0.913956i
$765$		0			0
$766$	−0.0835921	−	0.257270i	−0.00302031	−	0.00929555i
$767$	12.5902	−	38.7486i	0.454605	−	1.39913i
$768$	−4.50000	−	3.26944i	−0.162380	−	0.117976i
$769$	3.50658			0.126450			0.0632252	−	0.997999i	$-0.479861\pi$
$769$	3.50658			0.126450			0.0632252	+	0.997999i	$0.479861\pi$
$770$		0			0
$771$	12.7426			0.458915
$772$	14.7812	+	10.7391i	0.531985	+	0.386510i
$773$	−1.48936	+	4.58377i	−0.0535684	+	0.164867i	−0.974262	−	0.225421i	$-0.927624\pi$
$773$	−1.48936	+	4.58377i	−0.0535684	+	0.164867i	0.920693	+	0.390287i	$0.127624\pi$
$774$	−0.791796	−	2.43690i	−0.0284605	−	0.0875925i
$775$		0			0
$776$	−1.36475	+	0.991545i	−0.0489915	+	0.0355944i
$777$	0.545085	+	1.67760i	0.0195548	+	0.0601835i
$778$	0.677827	−	2.08614i	0.0243013	−	0.0747917i
$779$	−2.92705	−	2.12663i	−0.104872	−	0.0761943i
$780$		0			0
$781$	−1.64590	+	17.5883i	−0.0588949	+	0.629358i
$782$	12.7082			0.454444
$783$	4.85410	+	3.52671i	0.173471	+	0.126034i
$784$	−5.83282	+	17.9516i	−0.208315	+	0.641127i
$785$		0			0
$786$	−3.95492	+	2.87341i	−0.141067	+	0.102491i
$787$	3.00000	−	2.17963i	0.106938	−	0.0776953i	−0.533031	−	0.846096i	$-0.678947\pi$
$787$	3.00000	−	2.17963i	0.106938	−	0.0776953i	0.639969	+	0.768400i	$0.278947\pi$
$788$	−9.18692	−	28.2744i	−0.327270	−	1.00723i
$789$	−5.64590	+	17.3763i	−0.200999	+	0.618612i
$790$		0			0
$791$	−4.52786			−0.160992
$792$	−0.454915	+	4.86128i	−0.0161647	+	0.172738i
$793$	36.2705			1.28800
$794$	−1.63525	−	1.18808i	−0.0580330	−	0.0421635i
$795$		0			0
$796$	3.84346	+	11.8290i	0.136228	+	0.419266i
$797$	−39.2705	+	28.5317i	−1.39103	+	1.01064i	−0.395282	+	0.918560i	$0.629353\pi$
$797$	−39.2705	+	28.5317i	−1.39103	+	1.01064i	−0.995751	+	0.0920845i	$0.970647\pi$
$798$	0.263932	−	0.191758i	0.00934309	−	0.00678815i
$799$	−2.64590	−	8.14324i	−0.0936051	−	0.288087i
$800$		0			0
$801$	3.04508	+	2.21238i	0.107593	+	0.0781707i
$802$	10.9574			0.386920
$803$	23.4721	+	10.1311i	0.828314	+	0.357519i
$804$	−9.00000			−0.317406
$805$		0			0
$806$	2.54508	−	7.83297i	0.0896468	−	0.275904i
$807$	0.437694	+	1.34708i	0.0154076	+	0.0474196i
$808$	−6.86475	+	4.98753i	−0.241501	+	0.175461i
$809$	−12.8713	+	9.35156i	−0.452532	+	0.328783i	−0.790594	−	0.612340i	$-0.790228\pi$
$809$	−12.8713	+	9.35156i	−0.452532	+	0.328783i	0.338063	+	0.941124i	$0.390228\pi$
$810$		0			0
$811$	5.07953	−	15.6332i	0.178366	−	0.548955i	−0.821405	−	0.570346i	$-0.806809\pi$
$811$	5.07953	−	15.6332i	0.178366	−	0.548955i	0.999771	+	0.0213905i	$0.00680931\pi$
$812$	−9.00000	−	6.53888i	−0.315838	−	0.229470i
$813$	16.3820			0.574541
$814$	1.13932	+	1.92236i	0.0399332	+	0.0673786i
$815$		0			0
$816$	−19.9894	−	14.5231i	−0.699767	−	0.508411i
$817$	1.77051	−	5.44907i	0.0619423	−	0.190639i
$818$	0.291796	+	0.898056i	0.0102024	+	0.0313998i
$819$	−3.42705	+	2.48990i	−0.119751	+	0.0870041i
$820$		0			0
$821$	−2.65654	−	8.17599i	−0.0927139	−	0.285344i	0.893937	−	0.448192i	$-0.147932\pi$
$821$	−2.65654	−	8.17599i	−0.0927139	−	0.285344i	−0.986651	+	0.162848i	$0.947932\pi$
$822$	−1.68034	+	5.17155i	−0.0586086	+	0.180379i
$823$	20.8992	+	15.1841i	0.728500	+	0.529286i	0.889089	−	0.457735i	$-0.151339\pi$
$823$	20.8992	+	15.1841i	0.728500	+	0.529286i	−0.160589	+	0.987021i	$0.551339\pi$
$824$	10.2229			0.356132
$825$		0			0
$826$	3.67376			0.127827
$827$	16.7082	+	12.1392i	0.581001	+	0.422122i	0.839085	−	0.544000i	$-0.183091\pi$
$827$	16.7082	+	12.1392i	0.581001	+	0.422122i	−0.258084	+	0.966123i	$0.583091\pi$
$828$	−2.42705	+	7.46969i	−0.0843459	+	0.259590i
$829$	13.1008	+	40.3202i	0.455010	+	1.40038i	0.871123	+	0.491064i	$0.163392\pi$
$829$	13.1008	+	40.3202i	0.455010	+	1.40038i	−0.416113	+	0.909313i	$0.636608\pi$
$830$		0			0
$831$	17.9721	−	13.0575i	0.623446	−	0.452960i
$832$	−6.16312	−	18.9681i	−0.213668	−	0.657602i
$833$	−14.5623	+	44.8182i	−0.504554	+	1.55286i
$834$	1.71885	+	1.24882i	0.0595188	+	0.0432429i
$835$		0			0
$836$	−3.46962	+	3.94298i	−0.119999	+	0.136371i
$837$	5.09017			0.175942
$838$	7.55573	+	5.48956i	0.261008	+	0.189634i
$839$	11.0729	−	34.0790i	0.382281	−	1.17654i	−0.556153	−	0.831080i	$-0.687723\pi$
$839$	11.0729	−	34.0790i	0.382281	−	1.17654i	0.938434	−	0.345459i	$-0.112277\pi$
$840$		0			0
$841$	−5.66312	+	4.11450i	−0.195280	+	0.141879i
$842$	8.50000	−	6.17561i	0.292929	−	0.212826i
$843$	9.03444	+	27.8052i	0.311163	+	0.957660i
$844$	−0.791796	+	2.43690i	−0.0272547	+	0.0838815i
$845$		0			0
$846$	−0.416408			−0.0143164
$847$	9.94427	−	4.70228i	0.341689	−	0.161572i
$848$	8.23607			0.282828
$849$	6.23607	+	4.53077i	0.214021	+	0.155496i
$850$		0			0
$851$	2.30902	+	7.10642i	0.0791521	+	0.243605i
$852$	−7.98936	+	5.80461i	−0.273711	+	0.198863i
$853$	−1.75329	+	1.27384i	−0.0600315	+	0.0436154i	−0.617396	−	0.786652i	$-0.711812\pi$
$853$	−1.75329	+	1.27384i	−0.0600315	+	0.0436154i	0.557365	+	0.830268i	$0.311812\pi$
$854$	1.01064	+	3.11044i	0.0345835	+	0.106437i
$855$		0			0
$856$	3.01064	+	2.18736i	0.102902	+	0.0747624i
$857$	−32.2361			−1.10116			−0.550582	−	0.834781i	$-0.685594\pi$
$857$	−32.2361			−1.10116			−0.550582	+	0.834781i	$0.685594\pi$
$858$	−3.54508	+	4.02874i	−0.121027	+	0.137539i
$859$	−7.58359			−0.258749			−0.129374	−	0.991596i	$-0.541297\pi$
$859$	−7.58359			−0.258749			−0.129374	+	0.991596i	$0.541297\pi$
$860$		0			0
$861$	−1.30902	+	4.02874i	−0.0446112	+	0.137299i
$862$	−2.01722	−	6.20837i	−0.0687068	−	0.211458i
$863$	29.0344	−	21.0948i	0.988344	−	0.718074i	0.0287861	−	0.999586i	$-0.490836\pi$
$863$	29.0344	−	21.0948i	0.988344	−	0.718074i	0.959558	+	0.281512i	$0.0908358\pi$
$864$	−3.35410	+	2.43690i	−0.114109	+	0.0829049i
$865$		0			0
$866$	3.22291	−	9.91910i	0.109519	−	0.337065i
$867$	−36.1525	−	26.2663i	−1.22780	−	0.892051i
$868$	−9.43769			−0.320336
$869$	35.5967	−	7.99197i	1.20754	−	0.271109i
$870$		0			0
$871$	−16.6353	−	12.0862i	−0.563664	−	0.409526i
$872$	5.45898	−	16.8010i	0.184864	−	0.568954i
$873$	−0.354102	−	1.08981i	−0.0119845	−	0.0368846i
$874$	1.11803	−	0.812299i	0.0378181	−	0.0274764i
$875$		0			0
$876$	4.41641	+	13.5923i	0.149217	+	0.459241i
$877$	12.3779	−	38.0953i	0.417972	−	1.28639i	−0.491593	−	0.870825i	$-0.663585\pi$
$877$	12.3779	−	38.0953i	0.417972	−	1.28639i	0.909565	−	0.415561i	$-0.136415\pi$
$878$	−11.3435	−	8.24151i	−0.382823	−	0.278137i
$879$	−9.65248			−0.325570
$880$		0			0
$881$	30.7984			1.03762			0.518812	−	0.854888i	$-0.326375\pi$
$881$	30.7984			1.03762			0.518812	+	0.854888i	$0.326375\pi$
$882$	1.85410	+	1.34708i	0.0624309	+	0.0453587i
$883$	−5.85410	+	18.0171i	−0.197006	+	0.606323i	0.802941	+	0.596058i	$0.203267\pi$
$883$	−5.85410	+	18.0171i	−0.197006	+	0.606323i	−0.999947	+	0.0102644i	$0.996733\pi$
$884$	−19.0623	−	58.6677i	−0.641135	−	1.97321i
$885$		0			0
$886$	5.43769	−	3.95072i	0.182683	−	0.132727i
$887$	−9.42047	−	28.9932i	−0.316309	−	0.973498i	−0.975212	−	0.221270i	$-0.928980\pi$
$887$	−9.42047	−	28.9932i	−0.316309	−	0.973498i	0.658904	−	0.752227i	$-0.271020\pi$
$888$	−0.802439	+	2.46965i	−0.0269281	+	0.0828762i
$889$	−4.61803	−	3.35520i	−0.154884	−	0.112530i
$890$		0			0
$891$	−3.04508	−	1.31433i	−0.102014	−	0.0440316i
$892$	−28.1459			−0.942394
$893$	−0.753289	−	0.547296i	−0.0252079	−	0.0183146i
$894$	0.0278640	−	0.0857567i	0.000931913	−	0.00286813i
$895$		0			0
$896$	8.16312	−	5.93085i	0.272711	−	0.198136i
$897$	−14.5172	+	10.5474i	−0.484716	+	0.352167i
$898$	−3.18034	−	9.78808i	−0.106129	−	0.326632i
$899$	−9.43769	+	29.0462i	−0.314765	+	0.968746i
$900$		0			0
$901$	20.5623			0.685030
$902$	−0.500000	+	5.34307i	−0.0166482	+	0.177905i
$903$	−6.70820			−0.223235
$904$	−5.39261	−	3.91796i	−0.179356	−	0.130309i
$905$		0			0
$906$	2.23607	+	6.88191i	0.0742884	+	0.228636i
$907$	25.3992	−	18.4536i	0.843366	−	0.612741i	−0.0799428	−	0.996799i	$-0.525474\pi$
$907$	25.3992	−	18.4536i	0.843366	−	0.612741i	0.923309	+	0.384058i	$0.125474\pi$
$908$	13.7705	−	10.0049i	0.456990	−	0.332023i
$909$	−1.78115	−	5.48183i	−0.0590771	−	0.181821i
$910$		0			0
$911$	8.57295	+	6.22861i	0.284034	+	0.206363i	0.720675	−	0.693273i	$-0.243832\pi$
$911$	8.57295	+	6.22861i	0.284034	+	0.206363i	−0.436641	+	0.899636i	$0.643832\pi$
$912$	−2.68692			−0.0889727
$913$	2.30902	−	24.6745i	0.0764173	−	0.816606i
$914$	8.77709			0.290320
$915$		0			0
$916$	4.85410	−	14.9394i	0.160384	−	0.493611i
$917$	3.95492	+	12.1720i	0.130603	+	0.401954i
$918$	−2.42705	+	1.76336i	−0.0801046	+	0.0581994i
$919$	4.57295	−	3.32244i	0.150848	−	0.109597i	−0.509801	−	0.860292i	$-0.670281\pi$
$919$	4.57295	−	3.32244i	0.150848	−	0.109597i	0.660649	+	0.750695i	$0.270281\pi$
$920$		0			0
$921$	5.86475	−	18.0498i	0.193250	−	0.594762i
$922$	7.50000	+	5.44907i	0.246999	+	0.179456i
$923$	−22.5623			−0.742647
$924$	5.64590	+	2.43690i	0.185736	+	0.0801680i
$925$		0			0
$926$	10.8992	+	7.91872i	0.358170	+	0.260225i
$927$	−2.14590	+	6.60440i	−0.0704805	+	0.216917i
$928$	−7.68692	−	23.6579i	−0.252335	−	0.776609i
$929$	−0.572949	+	0.416272i	−0.0187978	+	0.0136574i	−0.597145	−	0.802134i	$-0.703698\pi$
$929$	−0.572949	+	0.416272i	−0.0187978	+	0.0136574i	0.578347	+	0.815791i	$0.303698\pi$
$930$		0			0
$931$	1.58359	+	4.87380i	0.0519001	+	0.159732i
$932$	−6.21885	+	19.1396i	−0.203705	+	0.626940i
$933$	15.8992	+	11.5514i	0.520516	+	0.378177i
$934$	5.68692			0.186082
$935$		0			0
$936$	−6.23607			−0.203832
$937$	8.37132	+	6.08212i	0.273479	+	0.198694i	0.716068	−	0.698030i	$-0.245940\pi$
$937$	8.37132	+	6.08212i	0.273479	+	0.198694i	−0.442589	+	0.896725i	$0.645940\pi$
$938$	0.572949	−	1.76336i	0.0187074	−	0.0575756i
$939$	3.54508	+	10.9106i	0.115689	+	0.356056i
$940$		0			0
$941$	−33.5344	+	24.3642i	−1.09319	+	0.794250i	−0.979935	−	0.199316i	$-0.936128\pi$
$941$	−33.5344	+	24.3642i	−1.09319	+	0.794250i	−0.113256	+	0.993566i	$0.536128\pi$
$942$	−0.270510	−	0.832544i	−0.00881369	−	0.0271257i
$943$	−5.54508	+	17.0660i	−0.180573	+	0.555746i
$944$	−24.4787	−	17.7848i	−0.796714	−	0.578847i
$945$		0			0
$946$	−8.29180	+	1.86162i	−0.269590	+	0.0605266i
$947$	−41.3951			−1.34516			−0.672580	−	0.740024i	$-0.734814\pi$
$947$	−41.3951			−1.34516			−0.672580	+	0.740024i	$0.734814\pi$
$948$	16.5000	+	11.9880i	0.535895	+	0.389351i
$949$	−10.0902	+	31.0543i	−0.327541	+	1.00807i
$950$		0			0
$951$	−23.6074	+	17.1518i	−0.765522	+	0.556184i
$952$	9.35410	−	6.79615i	0.303168	−	0.220265i
$953$	−13.1803	−	40.5649i	−0.426953	−	1.31403i	−0.901112	−	0.433587i	$-0.857248\pi$
$953$	−13.1803	−	40.5649i	−0.426953	−	1.31403i	0.474159	−	0.880439i	$-0.342752\pi$
$954$	0.309017	−	0.951057i	0.0100048	−	0.0307916i
$955$		0			0
$956$	−4.85410			−0.156993
$957$	13.1459	−	14.9394i	0.424947	−	0.482922i
$958$	−11.6950			−0.377850
$959$	11.5172	+	8.36775i	0.371910	+	0.270209i
$960$		0			0
$961$	−1.57295	−	4.84104i	−0.0507403	−	0.156163i
$962$	−2.30902	+	1.67760i	−0.0744457	+	0.0540880i
$963$	−2.04508	+	1.48584i	−0.0659019	+	0.0478806i
$964$	−12.4377	−	38.2793i	−0.400591	−	1.23289i
$965$		0			0
$966$	−1.30902	−	0.951057i	−0.0421169	−	0.0305997i
$967$	20.9230			0.672838			0.336419	−	0.941712i	$-0.390784\pi$
$967$	20.9230			0.672838			0.336419	+	0.941712i	$0.390784\pi$
$968$	15.9123	+	3.00444i	0.511442	+	0.0965663i
$969$	−6.70820			−0.215499
$970$		0			0
$971$	−12.9787	+	39.9444i	−0.416507	+	1.28188i	0.494389	+	0.869240i	$0.335392\pi$
$971$	−12.9787	+	39.9444i	−0.416507	+	1.28188i	−0.910896	+	0.412635i	$0.864608\pi$
$972$	−0.572949	−	1.76336i	−0.0183773	−	0.0565597i
$973$	4.50000	−	3.26944i	0.144263	−	0.104813i
$974$	0.218847	−	0.159002i	0.00701231	−	0.00509474i
$975$		0			0
$976$	8.32373	−	25.6178i	0.266436	−	0.820006i
$977$	39.3156	+	28.5645i	1.25782	+	0.913858i	0.998648	−	0.0519742i	$-0.0165514\pi$
$977$	39.3156	+	28.5645i	1.25782	+	0.913858i	0.259169	+	0.965832i	$0.416551\pi$
$978$	4.52786			0.144785
$979$	8.24671	−	9.37181i	0.263566	−	0.299524i
$980$		0			0
$981$	9.70820	+	7.05342i	0.309959	+	0.225198i
$982$	−3.43363	+	10.5676i	−0.109571	+	0.337226i
$983$	13.5623	+	41.7405i	0.432570	+	1.33131i	0.895556	+	0.444949i	$0.146778\pi$
$983$	13.5623	+	41.7405i	0.432570	+	1.33131i	−0.462986	+	0.886366i	$0.653222\pi$
$984$	−5.04508	+	3.66547i	−0.160831	+	0.116851i
$985$		0			0
$986$	−5.56231	−	17.1190i	−0.177140	−	0.545181i
$987$	−0.336881	+	1.03681i	−0.0107230	+	0.0330021i
$988$	−5.42705	−	3.94298i	−0.172657	−	0.125443i
$989$	−28.4164			−0.903589
$990$		0			0
$991$	−38.7426			−1.23070			−0.615350	−	0.788254i	$-0.710985\pi$
$991$	−38.7426			−1.23070			−0.615350	+	0.788254i	$0.710985\pi$
$992$	−17.0729	−	12.4042i	−0.542067	−	0.393834i
$993$	1.01722	−	3.13068i	0.0322805	−	0.0993493i
$994$	−0.628677	−	1.93487i	−0.0199404	−	0.0613703i
$995$		0			0
$996$	11.2082	−	8.14324i	0.355146	−	0.258028i
$997$	14.1525	+	43.5568i	0.448213	+	1.37946i	0.878921	+	0.476967i	$0.158264\pi$
$997$	14.1525	+	43.5568i	0.448213	+	1.37946i	−0.430708	+	0.902492i	$0.641736\pi$
$998$	−2.93363	+	9.02878i	−0.0928624	+	0.285801i
$999$	−1.42705	−	1.03681i	−0.0451499	−	0.0328033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.c.301.1		4
5.2	odd	4		825.2.bx.d.499.2		8
5.3	odd	4		825.2.bx.d.499.1		8
5.4	even	2		33.2.e.b.4.1	✓	4
11.3	even	5	inner	825.2.n.c.751.1		4
11.5	even	5		9075.2.a.cb.1.1		2
11.6	odd	10		9075.2.a.u.1.2		2
15.14	odd	2		99.2.f.a.37.1		4
20.19	odd	2		528.2.y.b.433.1		4
45.4	even	6		891.2.n.c.136.1		8
45.14	odd	6		891.2.n.b.136.1		8
45.29	odd	6		891.2.n.b.433.1		8
45.34	even	6		891.2.n.c.433.1		8
55.3	odd	20		825.2.bx.d.124.2		8
55.4	even	10		363.2.e.k.130.1		4
55.9	even	10		363.2.e.k.148.1		4
55.14	even	10		33.2.e.b.25.1	yes	4
55.19	odd	10		363.2.e.f.124.1		4
55.24	odd	10		363.2.e.b.148.1		4
55.29	odd	10		363.2.e.b.130.1		4
55.39	odd	10		363.2.a.i.1.1		2
55.47	odd	20		825.2.bx.d.124.1		8
55.49	even	10		363.2.a.d.1.2		2
55.54	odd	2		363.2.e.f.202.1		4
165.14	odd	10		99.2.f.a.91.1		4
165.104	odd	10		1089.2.a.t.1.1		2
165.149	even	10		1089.2.a.l.1.2		2
220.39	even	10		5808.2.a.ci.1.2		2
220.159	odd	10		5808.2.a.cj.1.2		2
220.179	odd	10		528.2.y.b.289.1		4
495.14	odd	30		891.2.n.b.784.1		8
495.124	even	30		891.2.n.c.190.1		8
495.344	odd	30		891.2.n.b.190.1		8
495.454	even	30		891.2.n.c.784.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.4.1	✓	4	5.4	even	2
33.2.e.b.25.1	yes	4	55.14	even	10
99.2.f.a.37.1		4	15.14	odd	2
99.2.f.a.91.1		4	165.14	odd	10
363.2.a.d.1.2		2	55.49	even	10
363.2.a.i.1.1		2	55.39	odd	10
363.2.e.b.130.1		4	55.29	odd	10
363.2.e.b.148.1		4	55.24	odd	10
363.2.e.f.124.1		4	55.19	odd	10
363.2.e.f.202.1		4	55.54	odd	2
363.2.e.k.130.1		4	55.4	even	10
363.2.e.k.148.1		4	55.9	even	10
528.2.y.b.289.1		4	220.179	odd	10
528.2.y.b.433.1		4	20.19	odd	2
825.2.n.c.301.1		4	1.1	even	1	trivial
825.2.n.c.751.1		4	11.3	even	5	inner
825.2.bx.d.124.1		8	55.47	odd	20
825.2.bx.d.124.2		8	55.3	odd	20
825.2.bx.d.499.1		8	5.3	odd	4
825.2.bx.d.499.2		8	5.2	odd	4
891.2.n.b.136.1		8	45.14	odd	6
891.2.n.b.190.1		8	495.344	odd	30
891.2.n.b.433.1		8	45.29	odd	6
891.2.n.b.784.1		8	495.14	odd	30
891.2.n.c.136.1		8	45.4	even	6
891.2.n.c.190.1		8	495.124	even	30
891.2.n.c.433.1		8	45.34	even	6
891.2.n.c.784.1		8	495.454	even	30
1089.2.a.l.1.2		2	165.149	even	10
1089.2.a.t.1.1		2	165.104	odd	10
5808.2.a.ci.1.2		2	220.39	even	10
5808.2.a.cj.1.2		2	220.159	odd	10
9075.2.a.u.1.2		2	11.6	odd	10
9075.2.a.cb.1.1		2	11.5	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.224514i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.224514i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.19098 + 2.48990i) q^{11} -1.85410 q^{12} +(-3.42705 - 2.48990i) q^{13} +(0.118034 - 0.363271i) q^{14} +(-2.54508 + 1.84911i) q^{16} +(-6.35410 + 4.61653i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.263932 + 0.812299i) q^{19} +1.00000 q^{21} +(1.23607 - 0.277515i) q^{22} +4.23607 q^{23} +(1.19098 + 0.865300i) q^{24} +(0.500000 + 1.53884i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.50000 - 1.08981i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-4.11803 - 2.99193i) q^{31} +4.14590 q^{32} +(1.69098 + 2.85317i) q^{33} +3.00000 q^{34} +(-0.572949 + 1.76336i) q^{36} +(0.545085 + 1.67760i) q^{37} +(0.263932 - 0.191758i) q^{38} +(-3.42705 + 2.48990i) q^{39} +(-1.30902 + 4.02874i) q^{41} +(-0.309017 - 0.224514i) q^{42} -6.70820 q^{43} +(5.64590 + 2.43690i) q^{44} +(-1.30902 - 0.951057i) q^{46} +(-0.336881 + 1.03681i) q^{47} +(0.972136 + 2.99193i) q^{48} +(4.85410 - 3.52671i) q^{49} +(2.42705 + 7.46969i) q^{51} +(-2.42705 + 7.46969i) q^{52} +(-2.11803 - 1.53884i) q^{53} +0.381966 q^{54} -1.47214 q^{56} +(0.690983 + 0.502029i) q^{57} +(-0.708204 + 2.17963i) q^{58} +(2.97214 + 9.14729i) q^{59} +(-6.92705 + 5.03280i) q^{61} +(0.600813 + 1.84911i) q^{62} +(0.309017 - 0.951057i) q^{63} +(3.80902 + 2.76741i) q^{64} +(0.118034 - 1.26133i) q^{66} +4.85410 q^{67} +(11.7812 + 8.55951i) q^{68} +(1.30902 - 4.02874i) q^{69} +(4.30902 - 3.13068i) q^{71} +(1.19098 - 0.865300i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(0.208204 - 0.640786i) q^{74} +1.58359 q^{76} +(-3.04508 - 1.31433i) q^{77} +1.61803 q^{78} +(-8.89919 - 6.46564i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.30902 - 0.951057i) q^{82} +(-6.04508 + 4.39201i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(2.07295 + 1.50609i) q^{86} -6.00000 q^{87} +(-2.48936 - 4.20025i) q^{88} -3.76393 q^{89} +(1.30902 - 4.02874i) q^{91} +(-2.42705 - 7.46969i) q^{92} +(-4.11803 + 2.99193i) q^{93} +(0.336881 - 0.244758i) q^{94} +(1.28115 - 3.94298i) q^{96} +(0.927051 + 0.673542i) q^{97} -2.29180 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - 9 * q^4 + q^6 - q^7 - 13 * q^8 - q^9	\( 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9} - 11 q^{11} + 6 q^{12} - 7 q^{13} - 4 q^{14} + q^{16} - 12 q^{17} - 4 q^{18} - 10 q^{19} + 4 q^{21} - 4 q^{22} + 8 q^{23} + 7 q^{24} + 2 q^{26} - q^{27} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 30 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} - 9 q^{37} + 10 q^{38} - 7 q^{39} - 3 q^{41} + q^{42} + 36 q^{44} - 3 q^{46} - 17 q^{47} - 14 q^{48} + 6 q^{49} + 3 q^{51} - 3 q^{52} - 4 q^{53} + 6 q^{54} + 12 q^{56} + 5 q^{57} + 24 q^{58} - 6 q^{59} - 21 q^{61} + 27 q^{62} - q^{63} + 13 q^{64} - 4 q^{66} + 6 q^{67} + 27 q^{68} + 3 q^{69} + 15 q^{71} + 7 q^{72} - 14 q^{73} - 26 q^{74} + 60 q^{76} - q^{77} + 2 q^{78} - 11 q^{79} - q^{81} + 3 q^{82} - 13 q^{83} - 9 q^{84} + 15 q^{86} - 24 q^{87} + 37 q^{88} - 24 q^{89} + 3 q^{91} - 3 q^{92} - 12 q^{93} + 17 q^{94} - 15 q^{96} - 3 q^{97} - 36 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - 9 * q^4 + q^6 - q^7 - 13 * q^8 - q^9 - 11 * q^11 + 6 * q^12 - 7 * q^13 - 4 * q^14 + q^16 - 12 * q^17 - 4 * q^18 - 10 * q^19 + 4 * q^21 - 4 * q^22 + 8 * q^23 + 7 * q^24 + 2 * q^26 - q^27 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 30 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 - 9 * q^37 + 10 * q^38 - 7 * q^39 - 3 * q^41 + q^42 + 36 * q^44 - 3 * q^46 - 17 * q^47 - 14 * q^48 + 6 * q^49 + 3 * q^51 - 3 * q^52 - 4 * q^53 + 6 * q^54 + 12 * q^56 + 5 * q^57 + 24 * q^58 - 6 * q^59 - 21 * q^61 + 27 * q^62 - q^63 + 13 * q^64 - 4 * q^66 + 6 * q^67 + 27 * q^68 + 3 * q^69 + 15 * q^71 + 7 * q^72 - 14 * q^73 - 26 * q^74 + 60 * q^76 - q^77 + 2 * q^78 - 11 * q^79 - q^81 + 3 * q^82 - 13 * q^83 - 9 * q^84 + 15 * q^86 - 24 * q^87 + 37 * q^88 - 24 * q^89 + 3 * q^91 - 3 * q^92 - 12 * q^93 + 17 * q^94 - 15 * q^96 - 3 * q^97 - 36 * q^98 + 4 * q^99

Introduction

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