LMFDB - Embedded newform 375.2.g.a.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, 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:	$4$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	375.301
Dual form			375.2.g.a.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -4.47214 q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -4.47214 q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.61803 + 1.90211i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(2.73607 + 1.98787i) q^{13} +(-3.61803 + 2.62866i) q^{14} +(0.809017 + 0.587785i) q^{16} +(0.881966 + 2.71441i) q^{17} -1.00000 q^{18} +(-1.00000 - 3.07768i) q^{19} +(1.38197 - 4.25325i) q^{21} +(-1.00000 + 3.07768i) q^{22} +(-3.61803 + 2.62866i) q^{23} -3.00000 q^{24} +3.38197 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.38197 - 4.25325i) q^{28} +(1.35410 - 4.16750i) q^{29} +(2.23607 + 6.88191i) q^{31} -5.00000 q^{32} +(-1.00000 - 3.07768i) q^{33} +(2.30902 + 1.67760i) q^{34} +(0.809017 - 0.587785i) q^{36} +(6.54508 + 4.75528i) q^{37} +(-2.61803 - 1.90211i) q^{38} +(-2.73607 + 1.98787i) q^{39} +(1.11803 + 0.812299i) q^{41} +(-1.38197 - 4.25325i) q^{42} +5.70820 q^{43} +(-1.00000 - 3.07768i) q^{44} +(-1.38197 + 4.25325i) q^{46} +(1.61803 - 4.97980i) q^{47} +(-0.809017 + 0.587785i) q^{48} +13.0000 q^{49} -2.85410 q^{51} +(-2.73607 + 1.98787i) q^{52} +(-0.427051 + 1.31433i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-4.14590 - 12.7598i) q^{56} +3.23607 q^{57} +(-1.35410 - 4.16750i) q^{58} +(3.23607 + 2.35114i) q^{59} +(0.500000 - 0.363271i) q^{61} +(5.85410 + 4.25325i) q^{62} +(3.61803 + 2.62866i) q^{63} +(-5.66312 + 4.11450i) q^{64} +(-2.61803 - 1.90211i) q^{66} +(-1.61803 - 4.97980i) q^{67} -2.85410 q^{68} +(-1.38197 - 4.25325i) q^{69} +(-0.236068 + 0.726543i) q^{71} +(0.927051 - 2.85317i) q^{72} +(2.50000 - 1.81636i) q^{73} +8.09017 q^{74} +3.23607 q^{76} +(11.7082 - 8.50651i) q^{77} +(-1.04508 + 3.21644i) q^{78} +(0.309017 + 0.951057i) q^{81} +1.38197 q^{82} +(-1.09017 - 3.35520i) q^{83} +(3.61803 + 2.62866i) q^{84} +(4.61803 - 3.35520i) q^{86} +(3.54508 + 2.57565i) q^{87} +(-7.85410 - 5.70634i) q^{88} +(-6.16312 + 4.47777i) q^{89} +(-12.2361 - 8.89002i) q^{91} +(-1.38197 - 4.25325i) q^{92} -7.23607 q^{93} +(-1.61803 - 4.97980i) q^{94} +(1.54508 - 4.75528i) q^{96} +(-2.73607 + 8.42075i) q^{97} +(10.5172 - 7.64121i) q^{98} +3.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 + q^4 - q^6 - 3 * q^8 - q^9	$ 4 q + q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{8} - q^{9} - 6 q^{11} - q^{12} + 2 q^{13} - 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 10 q^{21} - 4 q^{22} - 10 q^{23} - 12 q^{24} + 18 q^{26} + q^{27} + 10 q^{28} - 8 q^{29} - 20 q^{32} - 4 q^{33} + 7 q^{34} + q^{36} + 15 q^{37} - 6 q^{38} - 2 q^{39} - 10 q^{42} - 4 q^{43} - 4 q^{44} - 10 q^{46} + 2 q^{47} - q^{48} + 52 q^{49} + 2 q^{51} - 2 q^{52} + 5 q^{53} - q^{54} - 30 q^{56} + 4 q^{57} + 8 q^{58} + 4 q^{59} + 2 q^{61} + 10 q^{62} + 10 q^{63} - 7 q^{64} - 6 q^{66} - 2 q^{67} + 2 q^{68} - 10 q^{69} + 8 q^{71} - 3 q^{72} + 10 q^{73} + 10 q^{74} + 4 q^{76} + 20 q^{77} + 7 q^{78} - q^{81} + 10 q^{82} + 18 q^{83} + 10 q^{84} + 14 q^{86} + 3 q^{87} - 18 q^{88} - 9 q^{89} - 40 q^{91} - 10 q^{92} - 20 q^{93} - 2 q^{94} - 5 q^{96} - 2 q^{97} + 13 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 + q^4 - q^6 - 3 * q^8 - q^9 - 6 * q^11 - q^12 + 2 * q^13 - 10 * q^14 + q^16 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 10 * q^21 - 4 * q^22 - 10 * q^23 - 12 * q^24 + 18 * q^26 + q^27 + 10 * q^28 - 8 * q^29 - 20 * q^32 - 4 * q^33 + 7 * q^34 + q^36 + 15 * q^37 - 6 * q^38 - 2 * q^39 - 10 * q^42 - 4 * q^43 - 4 * q^44 - 10 * q^46 + 2 * q^47 - q^48 + 52 * q^49 + 2 * q^51 - 2 * q^52 + 5 * q^53 - q^54 - 30 * q^56 + 4 * q^57 + 8 * q^58 + 4 * q^59 + 2 * q^61 + 10 * q^62 + 10 * q^63 - 7 * q^64 - 6 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^69 + 8 * q^71 - 3 * q^72 + 10 * q^73 + 10 * q^74 + 4 * q^76 + 20 * q^77 + 7 * q^78 - q^81 + 10 * q^82 + 18 * q^83 + 10 * q^84 + 14 * q^86 + 3 * q^87 - 18 * q^88 - 9 * q^89 - 40 * q^91 - 10 * q^92 - 20 * q^93 - 2 * q^94 - 5 * q^96 - 2 * q^97 + 13 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i	−0.263792	−	0.964580i	$-0.584973\pi$
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i	0.835853	+	0.548953i	$0.184973\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	−4.47214			−1.69031			−0.845154	−	0.534522i	$-0.820491\pi$
$7$	−4.47214			−1.69031			−0.845154	+	0.534522i	$0.820491\pi$
$8$	0.927051	+	2.85317i	0.327762	+	1.00875i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−2.61803	+	1.90211i	−0.789367	+	0.573509i	−0.907776	−	0.419456i	$-0.862221\pi$
$11$	−2.61803	+	1.90211i	−0.789367	+	0.573509i	0.118409	+	0.992965i	$0.462221\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	2.73607	+	1.98787i	0.758849	+	0.551336i	0.898557	−	0.438857i	$-0.144616\pi$
$13$	2.73607	+	1.98787i	0.758849	+	0.551336i	−0.139708	+	0.990193i	$0.544616\pi$
$14$	−3.61803	+	2.62866i	−0.966960	+	0.702538i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	0.881966	+	2.71441i	0.213908	+	0.658342i	0.999229	+	0.0392530i	$0.0124978\pi$
$17$	0.881966	+	2.71441i	0.213908	+	0.658342i	−0.785321	+	0.619089i	$0.787502\pi$
$18$	−1.00000			−0.235702
$19$	−1.00000	−	3.07768i	−0.229416	−	0.706069i	−0.997813	−	0.0660962i	$-0.978946\pi$
$19$	−1.00000	−	3.07768i	−0.229416	−	0.706069i	0.768398	−	0.639973i	$-0.221054\pi$
$20$		0			0
$21$	1.38197	−	4.25325i	0.301570	−	0.928136i
$22$	−1.00000	+	3.07768i	−0.213201	+	0.656164i
$23$	−3.61803	+	2.62866i	−0.754412	+	0.548113i	−0.897191	−	0.441642i	$-0.854396\pi$
$23$	−3.61803	+	2.62866i	−0.754412	+	0.548113i	0.142779	+	0.989755i	$0.454396\pi$
$24$	−3.00000			−0.612372
$25$		0			0
$26$	3.38197			0.663258
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	1.38197	−	4.25325i	0.261167	−	0.803789i
$29$	1.35410	−	4.16750i	0.251450	−	0.773885i	−0.743058	−	0.669227i	$-0.766625\pi$
$29$	1.35410	−	4.16750i	0.251450	−	0.773885i	0.994508	−	0.104658i	$-0.0333747\pi$
$30$		0			0
$31$	2.23607	+	6.88191i	0.401610	+	1.23603i	0.923693	+	0.383133i	$0.125155\pi$
$31$	2.23607	+	6.88191i	0.401610	+	1.23603i	−0.522083	+	0.852894i	$0.674845\pi$
$32$	−5.00000			−0.883883
$33$	−1.00000	−	3.07768i	−0.174078	−	0.535756i
$34$	2.30902	+	1.67760i	0.395993	+	0.287706i
$35$		0			0
$36$	0.809017	−	0.587785i	0.134836	−	0.0979642i
$37$	6.54508	+	4.75528i	1.07601	+	0.781764i	0.976982	−	0.213321i	$-0.0684282\pi$
$37$	6.54508	+	4.75528i	1.07601	+	0.781764i	0.0990233	+	0.995085i	$0.468428\pi$
$38$	−2.61803	−	1.90211i	−0.424701	−	0.308563i
$39$	−2.73607	+	1.98787i	−0.438122	+	0.318314i
$40$		0			0
$41$	1.11803	+	0.812299i	0.174608	+	0.126860i	0.671657	−	0.740863i	$-0.265583\pi$
$41$	1.11803	+	0.812299i	0.174608	+	0.126860i	−0.497049	+	0.867722i	$0.665583\pi$
$42$	−1.38197	−	4.25325i	−0.213242	−	0.656291i
$43$	5.70820			0.870493			0.435246	−	0.900311i	$-0.356661\pi$
$43$	5.70820			0.870493			0.435246	+	0.900311i	$0.356661\pi$
$44$	−1.00000	−	3.07768i	−0.150756	−	0.463978i
$45$		0			0
$46$	−1.38197	+	4.25325i	−0.203760	+	0.627108i
$47$	1.61803	−	4.97980i	0.236015	−	0.726378i	−0.760971	−	0.648786i	$-0.775277\pi$
$47$	1.61803	−	4.97980i	0.236015	−	0.726378i	0.996985	−	0.0775917i	$-0.0247231\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	13.0000			1.85714
$50$		0			0
$51$	−2.85410			−0.399654
$52$	−2.73607	+	1.98787i	−0.379424	+	0.275668i
$53$	−0.427051	+	1.31433i	−0.0586600	+	0.180537i	−0.976093	−	0.217354i	$-0.930258\pi$
$53$	−0.427051	+	1.31433i	−0.0586600	+	0.180537i	0.917433	+	0.397890i	$0.130258\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$		0			0
$56$	−4.14590	−	12.7598i	−0.554019	−	1.70509i
$57$	3.23607			0.428628
$58$	−1.35410	−	4.16750i	−0.177802	−	0.547219i
$59$	3.23607	+	2.35114i	0.421300	+	0.306092i	0.778161	−	0.628065i	$-0.216153\pi$
$59$	3.23607	+	2.35114i	0.421300	+	0.306092i	−0.356861	+	0.934158i	$0.616153\pi$
$60$		0			0
$61$	0.500000	−	0.363271i	0.0640184	−	0.0465121i	−0.555316	−	0.831640i	$-0.687403\pi$
$61$	0.500000	−	0.363271i	0.0640184	−	0.0465121i	0.619334	+	0.785127i	$0.287403\pi$
$62$	5.85410	+	4.25325i	0.743472	+	0.540164i
$63$	3.61803	+	2.62866i	0.455829	+	0.331179i
$64$	−5.66312	+	4.11450i	−0.707890	+	0.514312i
$65$		0			0
$66$	−2.61803	−	1.90211i	−0.322258	−	0.234134i
$67$	−1.61803	−	4.97980i	−0.197674	−	0.608379i	−0.999935	−	0.0114051i	$-0.996370\pi$
$67$	−1.61803	−	4.97980i	−0.197674	−	0.608379i	0.802261	−	0.596974i	$-0.203630\pi$
$68$	−2.85410			−0.346111
$69$	−1.38197	−	4.25325i	−0.166369	−	0.512032i
$70$		0			0
$71$	−0.236068	+	0.726543i	−0.0280161	+	0.0862247i	−0.964087	−	0.265587i	$-0.914434\pi$
$71$	−0.236068	+	0.726543i	−0.0280161	+	0.0862247i	0.936071	+	0.351812i	$0.114434\pi$
$72$	0.927051	−	2.85317i	0.109254	−	0.336249i
$73$	2.50000	−	1.81636i	0.292603	−	0.212588i	−0.431793	−	0.901973i	$-0.642119\pi$
$73$	2.50000	−	1.81636i	0.292603	−	0.212588i	0.724396	+	0.689384i	$0.242119\pi$
$74$	8.09017			0.940463
$75$		0			0
$76$	3.23607			0.371202
$77$	11.7082	−	8.50651i	1.33427	−	0.969407i
$78$	−1.04508	+	3.21644i	−0.118333	+	0.364190i
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.38197			0.152613
$83$	−1.09017	−	3.35520i	−0.119662	−	0.368281i	0.873229	−	0.487310i	$-0.162022\pi$
$83$	−1.09017	−	3.35520i	−0.119662	−	0.368281i	−0.992891	+	0.119029i	$0.962022\pi$
$84$	3.61803	+	2.62866i	0.394760	+	0.286810i
$85$		0			0
$86$	4.61803	−	3.35520i	0.497975	−	0.361800i
$87$	3.54508	+	2.57565i	0.380073	+	0.276139i
$88$	−7.85410	−	5.70634i	−0.837250	−	0.608298i
$89$	−6.16312	+	4.47777i	−0.653289	+	0.474642i	−0.864390	−	0.502822i	$-0.832295\pi$
$89$	−6.16312	+	4.47777i	−0.653289	+	0.474642i	0.211101	+	0.977464i	$0.432295\pi$
$90$		0			0
$91$	−12.2361	−	8.89002i	−1.28269	−	0.931928i
$92$	−1.38197	−	4.25325i	−0.144080	−	0.443432i
$93$	−7.23607			−0.750345
$94$	−1.61803	−	4.97980i	−0.166887	−	0.513627i
$95$		0			0
$96$	1.54508	−	4.75528i	0.157695	−	0.485334i
$97$	−2.73607	+	8.42075i	−0.277806	+	0.854998i	0.710658	+	0.703538i	$0.248397\pi$
$97$	−2.73607	+	8.42075i	−0.277806	+	0.854998i	−0.988463	+	0.151460i	$0.951603\pi$
$98$	10.5172	−	7.64121i	1.06240	−	0.771879i
$99$	3.23607			0.325237
$100$		0			0
$101$	−16.5623			−1.64801			−0.824006	−	0.566582i	$-0.808266\pi$
$101$	−16.5623			−1.64801			−0.824006	+	0.566582i	$0.808266\pi$
$102$	−2.30902	+	1.67760i	−0.228627	+	0.166107i
$103$	0.381966	−	1.17557i	0.0376362	−	0.115832i	−0.930473	−	0.366360i	$-0.880604\pi$
$103$	0.381966	−	1.17557i	0.0376362	−	0.115832i	0.968110	+	0.250527i	$0.0806040\pi$
$104$	−3.13525	+	9.64932i	−0.307437	+	0.946194i
$105$		0			0
$106$	0.427051	+	1.31433i	0.0414789	+	0.127659i
$107$	−16.4721			−1.59242			−0.796211	−	0.605019i	$-0.793165\pi$
$107$	−16.4721			−1.59242			−0.796211	+	0.605019i	$0.793165\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	15.4443	+	11.2209i	1.47929	+	1.07477i	0.977784	+	0.209617i	$0.0672217\pi$
$109$	15.4443	+	11.2209i	1.47929	+	1.07477i	0.501509	+	0.865152i	$0.332778\pi$
$110$		0			0
$111$	−6.54508	+	4.75528i	−0.621232	+	0.451351i
$112$	−3.61803	−	2.62866i	−0.341872	−	0.248385i
$113$	2.16312	+	1.57160i	0.203489	+	0.147843i	0.684863	−	0.728672i	$-0.259862\pi$
$113$	2.16312	+	1.57160i	0.203489	+	0.147843i	−0.481374	+	0.876515i	$0.659862\pi$
$114$	2.61803	−	1.90211i	0.245201	−	0.178149i
$115$		0			0
$116$	3.54508	+	2.57565i	0.329153	+	0.239144i
$117$	−1.04508	−	3.21644i	−0.0966181	−	0.297360i
$118$	4.00000			0.368230
$119$	−3.94427	−	12.1392i	−0.361571	−	1.11280i
$120$		0			0
$121$	−0.163119	+	0.502029i	−0.0148290	+	0.0456390i
$122$	0.190983	−	0.587785i	0.0172908	−	0.0532156i
$123$	−1.11803	+	0.812299i	−0.100810	+	0.0732426i
$124$	−7.23607			−0.649818
$125$		0			0
$126$	4.47214			0.398410
$127$	7.85410	−	5.70634i	0.696939	−	0.506356i	−0.181995	−	0.983299i	$-0.558255\pi$
$127$	7.85410	−	5.70634i	0.696939	−	0.506356i	0.878934	+	0.476944i	$0.158255\pi$
$128$	0.927051	−	2.85317i	0.0819405	−	0.252187i
$129$	−1.76393	+	5.42882i	−0.155306	+	0.477981i
$130$		0			0
$131$	4.38197	+	13.4863i	0.382854	+	1.17830i	0.938025	+	0.346568i	$0.112653\pi$
$131$	4.38197	+	13.4863i	0.382854	+	1.17830i	−0.555171	+	0.831736i	$0.687347\pi$
$132$	3.23607			0.281664
$133$	4.47214	+	13.7638i	0.387783	+	1.19347i
$134$	−4.23607	−	3.07768i	−0.365941	−	0.265871i
$135$		0			0
$136$	−6.92705	+	5.03280i	−0.593990	+	0.431559i
$137$	−4.35410	−	3.16344i	−0.371996	−	0.270271i	0.386042	−	0.922481i	$-0.373842\pi$
$137$	−4.35410	−	3.16344i	−0.371996	−	0.270271i	−0.758038	+	0.652210i	$0.773842\pi$
$138$	−3.61803	−	2.62866i	−0.307988	−	0.223766i
$139$	4.09017	−	2.97168i	0.346924	−	0.252055i	−0.400654	−	0.916230i	$-0.631217\pi$
$139$	4.09017	−	2.97168i	0.346924	−	0.252055i	0.747577	+	0.664175i	$0.231217\pi$
$140$		0			0
$141$	4.23607	+	3.07768i	0.356741	+	0.259188i
$142$	0.236068	+	0.726543i	0.0198104	+	0.0609701i
$143$	−10.9443			−0.915206
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$		0			0
$146$	0.954915	−	2.93893i	0.0790293	−	0.243227i
$147$	−4.01722	+	12.3637i	−0.331335	+	1.01974i
$148$	−6.54508	+	4.75528i	−0.538003	+	0.390882i
$149$	−12.1459			−0.995031			−0.497515	−	0.867455i	$-0.665754\pi$
$149$	−12.1459			−0.995031			−0.497515	+	0.867455i	$0.665754\pi$
$150$		0			0
$151$	16.4721			1.34048			0.670242	−	0.742143i	$-0.266190\pi$
$151$	16.4721			1.34048			0.670242	+	0.742143i	$0.266190\pi$
$152$	7.85410	−	5.70634i	0.637052	−	0.462845i
$153$	0.881966	−	2.71441i	0.0713027	−	0.219447i
$154$	4.47214	−	13.7638i	0.360375	−	1.10912i
$155$		0			0
$156$	−1.04508	−	3.21644i	−0.0836738	−	0.257521i
$157$	13.7984			1.10123			0.550615	−	0.834759i	$-0.314393\pi$
$157$	13.7984			1.10123			0.550615	+	0.834759i	$0.314393\pi$
$158$		0			0
$159$	−1.11803	−	0.812299i	−0.0886659	−	0.0644195i
$160$		0			0
$161$	16.1803	−	11.7557i	1.27519	−	0.926479i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	2.38197	+	1.73060i	0.186570	+	0.135551i	0.677150	−	0.735845i	$-0.263215\pi$
$163$	2.38197	+	1.73060i	0.186570	+	0.135551i	−0.490580	+	0.871396i	$0.663215\pi$
$164$	−1.11803	+	0.812299i	−0.0873038	+	0.0634299i
$165$		0			0
$166$	−2.85410	−	2.07363i	−0.221521	−	0.160945i
$167$	7.23607	+	22.2703i	0.559944	+	1.72333i	0.682517	+	0.730870i	$0.260886\pi$
$167$	7.23607	+	22.2703i	0.559944	+	1.72333i	−0.122573	+	0.992460i	$0.539114\pi$
$168$	13.4164			1.03510
$169$	−0.482779	−	1.48584i	−0.0371369	−	0.114295i
$170$		0			0
$171$	−1.00000	+	3.07768i	−0.0764719	+	0.235356i
$172$	−1.76393	+	5.42882i	−0.134499	+	0.413944i
$173$	8.01722	−	5.82485i	0.609538	−	0.442855i	−0.239714	−	0.970844i	$-0.577054\pi$
$173$	8.01722	−	5.82485i	0.609538	−	0.442855i	0.849252	+	0.527988i	$0.177054\pi$
$174$	4.38197			0.332196
$175$		0			0
$176$	−3.23607			−0.243928
$177$	−3.23607	+	2.35114i	−0.243238	+	0.176723i
$178$	−2.35410	+	7.24518i	−0.176447	+	0.543049i
$179$	1.90983	−	5.87785i	0.142747	−	0.439331i	−0.853967	−	0.520327i	$-0.825810\pi$
$179$	1.90983	−	5.87785i	0.142747	−	0.439331i	0.996714	+	0.0809958i	$0.0258100\pi$
$180$		0			0
$181$	−3.02786	−	9.31881i	−0.225059	−	0.692661i	−0.998286	−	0.0585312i	$-0.981358\pi$
$181$	−3.02786	−	9.31881i	−0.225059	−	0.692661i	0.773226	−	0.634130i	$-0.218642\pi$
$182$	−15.1246			−1.12111
$183$	0.190983	+	0.587785i	0.0141179	+	0.0434503i
$184$	−10.8541	−	7.88597i	−0.800175	−	0.581361i
$185$		0			0
$186$	−5.85410	+	4.25325i	−0.429244	+	0.311864i
$187$	−7.47214	−	5.42882i	−0.546417	−	0.396995i
$188$	4.23607	+	3.07768i	0.308947	+	0.224463i
$189$	−3.61803	+	2.62866i	−0.263173	+	0.191207i
$190$		0			0
$191$	19.9443	+	14.4904i	1.44312	+	1.04849i	0.987380	+	0.158371i	$0.0506243\pi$
$191$	19.9443	+	14.4904i	1.44312	+	1.04849i	0.455737	+	0.890114i	$0.349376\pi$
$192$	−2.16312	−	6.65740i	−0.156110	−	0.480456i
$193$	−7.67376			−0.552369			−0.276185	−	0.961105i	$-0.589070\pi$
$193$	−7.67376			−0.552369			−0.276185	+	0.961105i	$0.589070\pi$
$194$	2.73607	+	8.42075i	0.196438	+	0.604575i
$195$		0			0
$196$	−4.01722	+	12.3637i	−0.286944	+	0.883124i
$197$	−1.66312	+	5.11855i	−0.118492	+	0.364682i	−0.992659	−	0.120943i	$-0.961408\pi$
$197$	−1.66312	+	5.11855i	−0.118492	+	0.364682i	0.874167	+	0.485625i	$0.161408\pi$
$198$	2.61803	−	1.90211i	0.186056	−	0.135177i
$199$	−18.6525			−1.32224			−0.661119	−	0.750281i	$-0.729918\pi$
$199$	−18.6525			−1.32224			−0.661119	+	0.750281i	$0.729918\pi$
$200$		0			0
$201$	5.23607			0.369324
$202$	−13.3992	+	9.73508i	−0.942764	+	0.684958i
$203$	−6.05573	+	18.6376i	−0.425029	+	1.30810i
$204$	0.881966	−	2.71441i	0.0617500	−	0.190047i
$205$		0			0
$206$	−0.381966	−	1.17557i	−0.0266128	−	0.0819059i
$207$	4.47214			0.310835
$208$	1.04508	+	3.21644i	0.0724636	+	0.223020i
$209$	8.47214	+	6.15537i	0.586030	+	0.425776i
$210$		0			0
$211$	14.4721	−	10.5146i	0.996303	−	0.723856i	0.0350106	−	0.999387i	$-0.488854\pi$
$211$	14.4721	−	10.5146i	0.996303	−	0.723856i	0.961292	+	0.275530i	$0.0888535\pi$
$212$	−1.11803	−	0.812299i	−0.0767869	−	0.0557889i
$213$	−0.618034	−	0.449028i	−0.0423470	−	0.0307669i
$214$	−13.3262	+	9.68208i	−0.910963	+	0.661853i
$215$		0			0
$216$	2.42705	+	1.76336i	0.165140	+	0.119981i
$217$	−10.0000	−	30.7768i	−0.678844	−	2.08927i
$218$	19.0902			1.29295
$219$	0.954915	+	2.93893i	0.0645272	+	0.198594i
$220$		0			0
$221$	−2.98278	+	9.18005i	−0.200643	+	0.617517i
$222$	−2.50000	+	7.69421i	−0.167789	+	0.516401i
$223$	−11.4721	+	8.33499i	−0.768231	+	0.558153i	−0.901424	−	0.432938i	$-0.857477\pi$
$223$	−11.4721	+	8.33499i	−0.768231	+	0.558153i	0.133193	+	0.991090i	$0.457477\pi$
$224$	22.3607			1.49404
$225$		0			0
$226$	2.67376			0.177856
$227$	−16.1803	+	11.7557i	−1.07393	+	0.780254i	−0.976614	−	0.215000i	$-0.931025\pi$
$227$	−16.1803	+	11.7557i	−1.07393	+	0.780254i	−0.0973129	+	0.995254i	$0.531025\pi$
$228$	−1.00000	+	3.07768i	−0.0662266	+	0.203825i
$229$	−7.71885	+	23.7562i	−0.510076	+	1.56985i	0.281991	+	0.959417i	$0.409005\pi$
$229$	−7.71885	+	23.7562i	−0.510076	+	1.56985i	−0.792067	+	0.610435i	$0.790995\pi$
$230$		0			0
$231$	4.47214	+	13.7638i	0.294245	+	0.905593i
$232$	13.1459			0.863070
$233$	−4.51722	−	13.9026i	−0.295933	−	0.910788i	−0.982906	−	0.184106i	$-0.941061\pi$
$233$	−4.51722	−	13.9026i	−0.295933	−	0.910788i	0.686973	−	0.726682i	$-0.258939\pi$
$234$	−2.73607	−	1.98787i	−0.178862	−	0.129951i
$235$		0			0
$236$	−3.23607	+	2.35114i	−0.210650	+	0.153046i
$237$		0			0
$238$	−10.3262	−	7.50245i	−0.669351	−	0.486312i
$239$	5.70820	−	4.14725i	0.369233	−	0.268263i	−0.387660	−	0.921803i	$-0.626716\pi$
$239$	5.70820	−	4.14725i	0.369233	−	0.268263i	0.756893	+	0.653539i	$0.226716\pi$
$240$		0			0
$241$	0.836881	+	0.608030i	0.0539082	+	0.0391666i	0.614413	−	0.788985i	$-0.289393\pi$
$241$	0.836881	+	0.608030i	0.0539082	+	0.0391666i	−0.560505	+	0.828151i	$0.689393\pi$
$242$	0.163119	+	0.502029i	0.0104857	+	0.0322716i
$243$	−1.00000			−0.0641500
$244$	0.190983	+	0.587785i	0.0122264	+	0.0376291i
$245$		0			0
$246$	−0.427051	+	1.31433i	−0.0272278	+	0.0837985i
$247$	3.38197	−	10.4086i	0.215189	−	0.662285i
$248$	−17.5623	+	12.7598i	−1.11521	+	0.810246i
$249$	3.52786			0.223569
$250$		0			0
$251$	−26.9443			−1.70071			−0.850354	−	0.526212i	$-0.823612\pi$
$251$	−26.9443			−1.70071			−0.850354	+	0.526212i	$0.823612\pi$
$252$	−3.61803	+	2.62866i	−0.227915	+	0.165590i
$253$	4.47214	−	13.7638i	0.281161	−	0.865324i
$254$	3.00000	−	9.23305i	0.188237	−	0.579333i
$255$		0			0
$256$	−5.25329	−	16.1680i	−0.328331	−	1.01050i
$257$	12.7984			0.798341			0.399170	−	0.916877i	$-0.369298\pi$
$257$	12.7984			0.798341			0.399170	+	0.916877i	$0.369298\pi$
$258$	1.76393	+	5.42882i	0.109818	+	0.337984i
$259$	−29.2705	−	21.2663i	−1.81878	−	1.32142i
$260$		0			0
$261$	−3.54508	+	2.57565i	−0.219435	+	0.159429i
$262$	11.4721	+	8.33499i	0.708751	+	0.514938i
$263$	9.61803	+	6.98791i	0.593073	+	0.430893i	0.843414	−	0.537265i	$-0.180542\pi$
$263$	9.61803	+	6.98791i	0.593073	+	0.430893i	−0.250340	+	0.968158i	$0.580542\pi$
$264$	7.85410	−	5.70634i	0.483387	−	0.351201i
$265$		0			0
$266$	11.7082	+	8.50651i	0.717876	+	0.521567i
$267$	−2.35410	−	7.24518i	−0.144069	−	0.443398i
$268$	5.23607			0.319844
$269$	−0.0450850	−	0.138757i	−0.00274888	−	0.00846018i	0.949673	−	0.313244i	$-0.101416\pi$
$269$	−0.0450850	−	0.138757i	−0.00274888	−	0.00846018i	−0.952422	+	0.304784i	$0.901416\pi$
$270$		0			0
$271$	6.85410	−	21.0948i	0.416357	−	1.28142i	−0.494674	−	0.869078i	$-0.664713\pi$
$271$	6.85410	−	21.0948i	0.416357	−	1.28142i	0.911031	−	0.412337i	$-0.135287\pi$
$272$	−0.881966	+	2.71441i	−0.0534770	+	0.164585i
$273$	12.2361	−	8.89002i	0.740561	−	0.538049i
$274$	−5.38197			−0.325136
$275$		0			0
$276$	4.47214			0.269191
$277$	−4.69098	+	3.40820i	−0.281854	+	0.204779i	−0.719726	−	0.694259i	$-0.755732\pi$
$277$	−4.69098	+	3.40820i	−0.281854	+	0.204779i	0.437872	+	0.899037i	$0.355732\pi$
$278$	1.56231	−	4.80828i	0.0937009	−	0.288382i
$279$	2.23607	−	6.88191i	0.133870	−	0.412009i
$280$		0			0
$281$	−5.37132	−	16.5312i	−0.320426	−	0.986171i	−0.973463	−	0.228844i	$-0.926505\pi$
$281$	−5.37132	−	16.5312i	−0.320426	−	0.986171i	0.653037	−	0.757326i	$-0.273495\pi$
$282$	5.23607			0.311803
$283$	−0.0901699	−	0.277515i	−0.00536005	−	0.0164965i	0.948341	−	0.317254i	$-0.102761\pi$
$283$	−0.0901699	−	0.277515i	−0.00536005	−	0.0164965i	−0.953701	+	0.300757i	$0.902761\pi$
$284$	−0.618034	−	0.449028i	−0.0366736	−	0.0266449i
$285$		0			0
$286$	−8.85410	+	6.43288i	−0.523554	+	0.380384i
$287$	−5.00000	−	3.63271i	−0.295141	−	0.214432i
$288$	4.04508	+	2.93893i	0.238359	+	0.173178i
$289$	7.16312	−	5.20431i	0.421360	−	0.306136i
$290$		0			0
$291$	−7.16312	−	5.20431i	−0.419909	−	0.305082i
$292$	0.954915	+	2.93893i	0.0558822	+	0.171988i
$293$	−3.79837			−0.221903			−0.110952	−	0.993826i	$-0.535390\pi$
$293$	−3.79837			−0.221903			−0.110952	+	0.993826i	$0.535390\pi$
$294$	4.01722	+	12.3637i	0.234289	+	0.721068i
$295$		0			0
$296$	−7.50000	+	23.0826i	−0.435929	+	1.34165i
$297$	−1.00000	+	3.07768i	−0.0580259	+	0.178585i
$298$	−9.82624	+	7.13918i	−0.569219	+	0.413562i
$299$	−15.1246			−0.874679
$300$		0			0
$301$	−25.5279			−1.47140
$302$	13.3262	−	9.68208i	0.766839	−	0.557141i
$303$	5.11803	−	15.7517i	0.294023	−	0.904911i
$304$	1.00000	−	3.07768i	0.0573539	−	0.176517i
$305$		0			0
$306$	−0.881966	−	2.71441i	−0.0504186	−	0.155173i
$307$	−1.34752			−0.0769073			−0.0384536	−	0.999260i	$-0.512243\pi$
$307$	−1.34752			−0.0769073			−0.0384536	+	0.999260i	$0.512243\pi$
$308$	4.47214	+	13.7638i	0.254824	+	0.784266i
$309$	1.00000	+	0.726543i	0.0568880	+	0.0413316i
$310$		0			0
$311$	−3.47214	+	2.52265i	−0.196887	+	0.143047i	−0.681861	−	0.731482i	$-0.738829\pi$
$311$	−3.47214	+	2.52265i	−0.196887	+	0.143047i	0.484974	+	0.874529i	$0.338829\pi$
$312$	−8.20820	−	5.96361i	−0.464698	−	0.337623i
$313$	6.85410	+	4.97980i	0.387417	+	0.281475i	0.764396	−	0.644747i	$-0.223037\pi$
$313$	6.85410	+	4.97980i	0.387417	+	0.281475i	−0.376979	+	0.926222i	$0.623037\pi$
$314$	11.1631	−	8.11048i	0.629971	−	0.457701i
$315$		0			0
$316$		0			0
$317$	7.67376	+	23.6174i	0.431001	+	1.32649i	0.897129	+	0.441768i	$0.145649\pi$
$317$	7.67376	+	23.6174i	0.431001	+	1.32649i	−0.466128	+	0.884717i	$0.654351\pi$
$318$	−1.38197			−0.0774968
$319$	4.38197	+	13.4863i	0.245343	+	0.755088i
$320$		0			0
$321$	5.09017	−	15.6659i	0.284106	−	0.874387i
$322$	6.18034	−	19.0211i	0.344417	−	1.06001i
$323$	7.47214	−	5.42882i	0.415761	−	0.302068i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	2.94427			0.163068
$327$	−15.4443	+	11.2209i	−0.854070	+	0.620518i
$328$	−1.28115	+	3.94298i	−0.0707398	+	0.217715i
$329$	−7.23607	+	22.2703i	−0.398937	+	1.22780i
$330$		0			0
$331$	3.38197	+	10.4086i	0.185890	+	0.572110i	0.999963	−	0.00865315i	$-0.00275442\pi$
$331$	3.38197	+	10.4086i	0.185890	+	0.572110i	−0.814073	+	0.580763i	$0.802754\pi$
$332$	3.52786			0.193617
$333$	−2.50000	−	7.69421i	−0.136999	−	0.421640i
$334$	18.9443	+	13.7638i	1.03658	+	0.753123i
$335$		0			0
$336$	3.61803	−	2.62866i	0.197380	−	0.143405i
$337$	−12.0902	−	8.78402i	−0.658594	−	0.478496i	0.207594	−	0.978215i	$-0.433437\pi$
$337$	−12.0902	−	8.78402i	−0.658594	−	0.478496i	−0.866188	+	0.499719i	$0.833437\pi$
$338$	−1.26393	−	0.918300i	−0.0687488	−	0.0499490i
$339$	−2.16312	+	1.57160i	−0.117484	+	0.0853575i
$340$		0			0
$341$	−18.9443	−	13.7638i	−1.02589	−	0.745353i
$342$	1.00000	+	3.07768i	0.0540738	+	0.166422i
$343$	−26.8328			−1.44884
$344$	5.29180	+	16.2865i	0.285315	+	0.878108i
$345$		0			0
$346$	3.06231	−	9.42481i	0.164631	−	0.506681i
$347$	10.4164	−	32.0584i	0.559182	−	1.72099i	−0.125453	−	0.992100i	$-0.540038\pi$
$347$	10.4164	−	32.0584i	0.559182	−	1.72099i	0.684635	−	0.728886i	$-0.259962\pi$
$348$	−3.54508	+	2.57565i	−0.190037	+	0.138070i
$349$	25.0344			1.34006			0.670031	−	0.742333i	$-0.266281\pi$
$349$	25.0344			1.34006			0.670031	+	0.742333i	$0.266281\pi$
$350$		0			0
$351$	3.38197			0.180516
$352$	13.0902	−	9.51057i	0.697708	−	0.506915i
$353$	9.38197	−	28.8747i	0.499352	−	1.53685i	−0.310712	−	0.950504i	$-0.600567\pi$
$353$	9.38197	−	28.8747i	0.499352	−	1.53685i	0.810063	−	0.586342i	$-0.199433\pi$
$354$	−1.23607	+	3.80423i	−0.0656963	+	0.202192i
$355$		0			0
$356$	−2.35410	−	7.24518i	−0.124767	−	0.383994i
$357$	12.7639			0.675539
$358$	−1.90983	−	5.87785i	−0.100938	−	0.310654i
$359$	8.56231	+	6.22088i	0.451901	+	0.328325i	0.790346	−	0.612661i	$-0.209901\pi$
$359$	8.56231	+	6.22088i	0.451901	+	0.328325i	−0.338445	+	0.940986i	$0.609901\pi$
$360$		0			0
$361$	6.89919	−	5.01255i	0.363115	−	0.263819i
$362$	−7.92705	−	5.75934i	−0.416637	−	0.302704i
$363$	−0.427051	−	0.310271i	−0.0224144	−	0.0162850i
$364$	12.2361	−	8.89002i	0.641344	−	0.465964i
$365$		0			0
$366$	0.500000	+	0.363271i	0.0261354	+	0.0189885i
$367$	1.85410	+	5.70634i	0.0967833	+	0.297868i	0.987714	−	0.156270i	$-0.0499471\pi$
$367$	1.85410	+	5.70634i	0.0967833	+	0.297868i	−0.890931	+	0.454139i	$0.849947\pi$
$368$	−4.47214			−0.233126
$369$	−0.427051	−	1.31433i	−0.0222314	−	0.0684212i
$370$		0			0
$371$	1.90983	−	5.87785i	0.0991534	−	0.305163i
$372$	2.23607	−	6.88191i	0.115935	−	0.356810i
$373$	23.7984	−	17.2905i	1.23223	−	0.895270i	0.235178	−	0.971952i	$-0.424433\pi$
$373$	23.7984	−	17.2905i	1.23223	−	0.895270i	0.997056	+	0.0766827i	$0.0244328\pi$
$374$	−9.23607			−0.477586
$375$		0			0
$376$	15.7082			0.810089
$377$	11.9894	−	8.71078i	0.617483	−	0.448628i
$378$	−1.38197	+	4.25325i	−0.0710807	+	0.218764i
$379$	7.23607	−	22.2703i	0.371692	−	1.14395i	−0.573992	−	0.818861i	$-0.694606\pi$
$379$	7.23607	−	22.2703i	0.371692	−	1.14395i	0.945684	−	0.325089i	$-0.105394\pi$
$380$		0			0
$381$	3.00000	+	9.23305i	0.153695	+	0.473024i
$382$	24.6525			1.26133
$383$	−6.43769	−	19.8132i	−0.328951	−	1.01241i	−0.969626	−	0.244594i	$-0.921345\pi$
$383$	−6.43769	−	19.8132i	−0.328951	−	1.01241i	0.640675	−	0.767812i	$-0.278655\pi$
$384$	2.42705	+	1.76336i	0.123855	+	0.0899859i
$385$		0			0
$386$	−6.20820	+	4.51052i	−0.315989	+	0.229580i
$387$	−4.61803	−	3.35520i	−0.234748	−	0.170554i
$388$	−7.16312	−	5.20431i	−0.363652	−	0.264209i
$389$	30.0066	−	21.8011i	1.52139	−	1.10536i	0.560603	−	0.828085i	$-0.310570\pi$
$389$	30.0066	−	21.8011i	1.52139	−	1.10536i	0.960791	−	0.277272i	$-0.0894304\pi$
$390$		0			0
$391$	−10.3262	−	7.50245i	−0.522220	−	0.379415i
$392$	12.0517	+	37.0912i	0.608701	+	1.87339i
$393$	−14.1803			−0.715304
$394$	1.66312	+	5.11855i	0.0837867	+	0.257869i
$395$		0			0
$396$	−1.00000	+	3.07768i	−0.0502519	+	0.154659i
$397$	−3.38197	+	10.4086i	−0.169736	+	0.522394i	−0.999354	−	0.0359377i	$-0.988558\pi$
$397$	−3.38197	+	10.4086i	−0.169736	+	0.522394i	0.829618	+	0.558331i	$0.188558\pi$
$398$	−15.0902	+	10.9637i	−0.756402	+	0.549558i
$399$	−14.4721			−0.724513
$400$		0			0
$401$	33.4508			1.67046			0.835228	−	0.549904i	$-0.185336\pi$
$401$	33.4508			1.67046			0.835228	+	0.549904i	$0.185336\pi$
$402$	4.23607	−	3.07768i	0.211276	−	0.153501i
$403$	−7.56231	+	23.2744i	−0.376705	+	1.15938i
$404$	5.11803	−	15.7517i	0.254632	−	0.783676i
$405$		0			0
$406$	6.05573	+	18.6376i	0.300541	+	0.924969i
$407$	−26.1803			−1.29771
$408$	−2.64590	−	8.14324i	−0.130991	−	0.403150i
$409$	−20.8713	−	15.1639i	−1.03202	−	0.749807i	−0.0633084	−	0.997994i	$-0.520165\pi$
$409$	−20.8713	−	15.1639i	−1.03202	−	0.749807i	−0.968712	+	0.248187i	$0.920165\pi$
$410$		0			0
$411$	4.35410	−	3.16344i	0.214772	−	0.156041i
$412$	1.00000	+	0.726543i	0.0492665	+	0.0357942i
$413$	−14.4721	−	10.5146i	−0.712127	−	0.517391i
$414$	3.61803	−	2.62866i	0.177817	−	0.129191i
$415$		0			0
$416$	−13.6803	−	9.93935i	−0.670734	−	0.487317i
$417$	1.56231	+	4.80828i	0.0765064	+	0.235463i
$418$	10.4721			0.512209
$419$	10.1803	+	31.3319i	0.497342	+	1.53066i	0.813275	+	0.581880i	$0.197683\pi$
$419$	10.1803	+	31.3319i	0.497342	+	1.53066i	−0.315932	+	0.948782i	$0.602317\pi$
$420$		0			0
$421$	7.15248	−	22.0131i	0.348590	−	1.07285i	−0.611043	−	0.791597i	$-0.709250\pi$
$421$	7.15248	−	22.0131i	0.348590	−	1.07285i	0.959634	−	0.281253i	$-0.0907502\pi$
$422$	5.52786	−	17.0130i	0.269092	−	0.828181i
$423$	−4.23607	+	3.07768i	−0.205965	+	0.149642i
$424$	−4.14590			−0.201343
$425$		0			0
$426$	−0.763932			−0.0370126
$427$	−2.23607	+	1.62460i	−0.108211	+	0.0786198i
$428$	5.09017	−	15.6659i	0.246043	−	0.757241i
$429$	3.38197	−	10.4086i	0.163283	−	0.502533i
$430$		0			0
$431$	−3.29180	−	10.1311i	−0.158560	−	0.487998i	0.839944	−	0.542673i	$-0.182588\pi$
$431$	−3.29180	−	10.1311i	−0.158560	−	0.487998i	−0.998504	+	0.0546749i	$0.982588\pi$
$432$	1.00000			0.0481125
$433$	−7.71885	−	23.7562i	−0.370944	−	1.14165i	−0.946174	−	0.323657i	$-0.895088\pi$
$433$	−7.71885	−	23.7562i	−0.370944	−	1.14165i	0.575230	−	0.817991i	$-0.304912\pi$
$434$	−26.1803	−	19.0211i	−1.25670	−	0.913043i
$435$		0			0
$436$	−15.4443	+	11.2209i	−0.739646	+	0.537385i
$437$	11.7082	+	8.50651i	0.560079	+	0.406921i
$438$	2.50000	+	1.81636i	0.119455	+	0.0867889i
$439$	5.00000	−	3.63271i	0.238637	−	0.173380i	−0.462039	−	0.886860i	$-0.652882\pi$
$439$	5.00000	−	3.63271i	0.238637	−	0.173380i	0.700676	+	0.713480i	$0.252882\pi$
$440$		0			0
$441$	−10.5172	−	7.64121i	−0.500820	−	0.363867i
$442$	2.98278	+	9.18005i	0.141876	+	0.436650i
$443$	30.7639			1.46164			0.730819	−	0.682571i	$-0.239138\pi$
$443$	30.7639			1.46164			0.730819	+	0.682571i	$0.239138\pi$
$444$	−2.50000	−	7.69421i	−0.118645	−	0.365151i
$445$		0			0
$446$	−4.38197	+	13.4863i	−0.207492	+	0.638595i
$447$	3.75329	−	11.5514i	0.177524	−	0.546364i
$448$	25.3262	−	18.4006i	1.19655	−	0.869346i
$449$	−7.79837			−0.368028			−0.184014	−	0.982924i	$-0.558909\pi$
$449$	−7.79837			−0.368028			−0.184014	+	0.982924i	$0.558909\pi$
$450$		0			0
$451$	−4.47214			−0.210585
$452$	−2.16312	+	1.57160i	−0.101745	+	0.0739217i
$453$	−5.09017	+	15.6659i	−0.239157	+	0.736050i
$454$	−6.18034	+	19.0211i	−0.290058	+	0.892706i
$455$		0			0
$456$	3.00000	+	9.23305i	0.140488	+	0.432377i
$457$	−22.3607			−1.04599			−0.522994	−	0.852336i	$-0.675185\pi$
$457$	−22.3607			−1.04599			−0.522994	+	0.852336i	$0.675185\pi$
$458$	7.71885	+	23.7562i	0.360678	+	1.11005i
$459$	2.30902	+	1.67760i	0.107776	+	0.0783036i
$460$		0			0
$461$	6.63525	−	4.82079i	0.309035	−	0.224527i	−0.422448	−	0.906387i	$-0.638829\pi$
$461$	6.63525	−	4.82079i	0.309035	−	0.224527i	0.731482	+	0.681861i	$0.238829\pi$
$462$	11.7082	+	8.50651i	0.544715	+	0.395759i
$463$	18.7984	+	13.6578i	0.873635	+	0.634733i	0.931560	−	0.363588i	$-0.118448\pi$
$463$	18.7984	+	13.6578i	0.873635	+	0.634733i	−0.0579252	+	0.998321i	$0.518448\pi$
$464$	3.54508	−	2.57565i	0.164576	−	0.119572i
$465$		0			0
$466$	−11.8262	−	8.59226i	−0.547840	−	0.398029i
$467$	−1.79837	−	5.53483i	−0.0832188	−	0.256121i	0.900786	−	0.434263i	$-0.142991\pi$
$467$	−1.79837	−	5.53483i	−0.0832188	−	0.256121i	−0.984005	+	0.178142i	$0.942991\pi$
$468$	3.38197			0.156331
$469$	7.23607	+	22.2703i	0.334131	+	1.02835i
$470$		0			0
$471$	−4.26393	+	13.1230i	−0.196472	+	0.604677i
$472$	−3.70820	+	11.4127i	−0.170684	+	0.525311i
$473$	−14.9443	+	10.8576i	−0.687138	+	0.499235i
$474$		0			0
$475$		0			0
$476$	12.7639			0.585034
$477$	1.11803	−	0.812299i	0.0511913	−	0.0371926i
$478$	2.18034	−	6.71040i	0.0997264	−	0.306926i
$479$	0.326238	−	1.00406i	0.0149062	−	0.0458765i	−0.943327	−	0.331865i	$-0.892322\pi$
$479$	0.326238	−	1.00406i	0.0149062	−	0.0458765i	0.958233	+	0.285989i	$0.0923220\pi$
$480$		0			0
$481$	8.45492	+	26.0216i	0.385511	+	1.18648i
$482$	1.03444			0.0471175
$483$	6.18034	+	19.0211i	0.281215	+	0.865491i
$484$	−0.427051	−	0.310271i	−0.0194114	−	0.0141032i
$485$		0			0
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−3.00000	−	2.17963i	−0.135943	−	0.0987684i	0.517736	−	0.855541i	$-0.326775\pi$
$487$	−3.00000	−	2.17963i	−0.135943	−	0.0987684i	−0.653679	+	0.756772i	$0.726775\pi$
$488$	1.50000	+	1.08981i	0.0679018	+	0.0493336i
$489$	−2.38197	+	1.73060i	−0.107716	+	0.0782604i
$490$		0			0
$491$	24.1803	+	17.5680i	1.09124	+	0.792835i	0.979609	−	0.200915i	$-0.0643914\pi$
$491$	24.1803	+	17.5680i	1.09124	+	0.792835i	0.111635	+	0.993749i	$0.464391\pi$
$492$	−0.427051	−	1.31433i	−0.0192529	−	0.0592545i
$493$	12.5066			0.563268
$494$	−3.38197	−	10.4086i	−0.152162	−	0.468306i
$495$		0			0
$496$	−2.23607	+	6.88191i	−0.100402	+	0.309007i
$497$	1.05573	−	3.24920i	0.0473559	−	0.145746i
$498$	2.85410	−	2.07363i	0.127895	−	0.0929214i
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$		0			0
$501$	−23.4164			−1.04617
$502$	−21.7984	+	15.8374i	−0.972909	+	0.706860i
$503$	−10.9443	+	33.6830i	−0.487981	+	1.50185i	0.339636	+	0.940557i	$0.389696\pi$
$503$	−10.9443	+	33.6830i	−0.487981	+	1.50185i	−0.827617	+	0.561294i	$0.810304\pi$
$504$	−4.14590	+	12.7598i	−0.184673	+	0.568365i
$505$		0			0
$506$	−4.47214	−	13.7638i	−0.198811	−	0.611876i
$507$	1.56231			0.0693844
$508$	3.00000	+	9.23305i	0.133103	+	0.409650i
$509$	−21.7254	−	15.7844i	−0.962963	−	0.699633i	−0.00912564	−	0.999958i	$-0.502905\pi$
$509$	−21.7254	−	15.7844i	−0.962963	−	0.699633i	−0.953837	+	0.300325i	$0.902905\pi$
$510$		0			0
$511$	−11.1803	+	8.12299i	−0.494589	+	0.359340i
$512$	−8.89919	−	6.46564i	−0.393292	−	0.285744i
$513$	−2.61803	−	1.90211i	−0.115589	−	0.0839803i
$514$	10.3541	−	7.52270i	0.456700	−	0.331812i
$515$		0			0
$516$	−4.61803	−	3.35520i	−0.203298	−	0.147704i
$517$	5.23607	+	16.1150i	0.230282	+	0.708735i
$518$	−36.1803			−1.58967
$519$	3.06231	+	9.42481i	0.134420	+	0.413703i
$520$		0			0
$521$	0.628677	−	1.93487i	0.0275428	−	0.0847682i	−0.936340	−	0.351094i	$-0.885810\pi$
$521$	0.628677	−	1.93487i	0.0275428	−	0.0847682i	0.963883	+	0.266326i	$0.0858097\pi$
$522$	−1.35410	+	4.16750i	−0.0592674	+	0.182406i
$523$	−9.94427	+	7.22494i	−0.434833	+	0.315924i	−0.783578	−	0.621293i	$-0.786608\pi$
$523$	−9.94427	+	7.22494i	−0.434833	+	0.315924i	0.348746	+	0.937217i	$0.386608\pi$
$524$	−14.1803			−0.619471
$525$		0			0
$526$	11.8885			0.518365
$527$	−16.7082	+	12.1392i	−0.727821	+	0.528793i
$528$	1.00000	−	3.07768i	0.0435194	−	0.133939i
$529$	−0.927051	+	2.85317i	−0.0403066	+	0.124051i
$530$		0			0
$531$	−1.23607	−	3.80423i	−0.0536408	−	0.165089i
$532$	−14.4721			−0.627447
$533$	1.44427	+	4.44501i	0.0625584	+	0.192535i
$534$	−6.16312	−	4.47777i	−0.266704	−	0.193772i
$535$		0			0
$536$	12.7082	−	9.23305i	0.548911	−	0.398807i
$537$	5.00000	+	3.63271i	0.215766	+	0.156763i
$538$	−0.118034	−	0.0857567i	−0.00508881	−	0.00369723i
$539$	−34.0344	+	24.7275i	−1.46597	+	1.06509i
$540$		0			0
$541$	28.5795	+	20.7642i	1.22873	+	0.892724i	0.996794	−	0.0800067i	$-0.0254942\pi$
$541$	28.5795	+	20.7642i	1.22873	+	0.892724i	0.231936	+	0.972731i	$0.425494\pi$
$542$	−6.85410	−	21.0948i	−0.294409	−	0.906097i
$543$	9.79837			0.420488
$544$	−4.40983	−	13.5721i	−0.189070	−	0.581897i
$545$		0			0
$546$	4.67376	−	14.3844i	0.200019	−	0.615594i
$547$	0.729490	−	2.24514i	0.0311907	−	0.0959952i	−0.934249	−	0.356621i	$-0.883929\pi$
$547$	0.729490	−	2.24514i	0.0311907	−	0.0959952i	0.965440	+	0.260626i	$0.0839288\pi$
$548$	4.35410	−	3.16344i	0.185998	−	0.135135i
$549$	−0.618034			−0.0263770
$550$		0			0
$551$	−14.1803			−0.604103
$552$	10.8541	−	7.88597i	0.461981	−	0.335649i
$553$		0			0
$554$	−1.79180	+	5.51458i	−0.0761261	+	0.234292i
$555$		0			0
$556$	1.56231	+	4.80828i	0.0662565	+	0.203917i
$557$	−22.2705			−0.943632			−0.471816	−	0.881697i	$-0.656401\pi$
$557$	−22.2705			−0.943632			−0.471816	+	0.881697i	$0.656401\pi$
$558$	−2.23607	−	6.88191i	−0.0946603	−	0.291334i
$559$	15.6180	+	11.3472i	0.660572	+	0.479934i
$560$		0			0
$561$	7.47214	−	5.42882i	0.315474	−	0.229205i
$562$	−14.0623	−	10.2169i	−0.593183	−	0.430972i
$563$	−14.1803	−	10.3026i	−0.597630	−	0.434204i	0.247407	−	0.968912i	$-0.420422\pi$
$563$	−14.1803	−	10.3026i	−0.597630	−	0.434204i	−0.845037	+	0.534708i	$0.820422\pi$
$564$	−4.23607	+	3.07768i	−0.178371	+	0.129594i
$565$		0			0
$566$	−0.236068	−	0.171513i	−0.00992268	−	0.00720925i
$567$	−1.38197	−	4.25325i	−0.0580371	−	0.178620i
$568$	−2.29180			−0.0961616
$569$	−9.35410	−	28.7890i	−0.392144	−	1.20690i	−0.931163	−	0.364603i	$-0.881205\pi$
$569$	−9.35410	−	28.7890i	−0.392144	−	1.20690i	0.539019	−	0.842294i	$-0.318795\pi$
$570$		0			0
$571$	−6.56231	+	20.1967i	−0.274624	+	0.845206i	0.714695	+	0.699437i	$0.246566\pi$
$571$	−6.56231	+	20.1967i	−0.274624	+	0.845206i	−0.989319	+	0.145769i	$0.953434\pi$
$572$	3.38197	−	10.4086i	0.141407	−	0.435206i
$573$	−19.9443	+	14.4904i	−0.833184	+	0.605344i
$574$	−6.18034			−0.257962
$575$		0			0
$576$	7.00000			0.291667
$577$	−25.0344	+	18.1886i	−1.04220	+	0.757201i	−0.970713	−	0.240241i	$-0.922774\pi$
$577$	−25.0344	+	18.1886i	−1.04220	+	0.757201i	−0.0714842	+	0.997442i	$0.522774\pi$
$578$	2.73607	−	8.42075i	0.113805	−	0.350257i
$579$	2.37132	−	7.29818i	0.0985488	−	0.303302i
$580$		0			0
$581$	4.87539	+	15.0049i	0.202265	+	0.622508i
$582$	−8.85410			−0.367014
$583$	−1.38197	−	4.25325i	−0.0572352	−	0.176152i
$584$	7.50000	+	5.44907i	0.310352	+	0.225484i
$585$		0			0
$586$	−3.07295	+	2.23263i	−0.126942	+	0.0922290i
$587$	−11.7984	−	8.57202i	−0.486971	−	0.353805i	0.317047	−	0.948410i	$-0.397309\pi$
$587$	−11.7984	−	8.57202i	−0.486971	−	0.353805i	−0.804018	+	0.594605i	$0.797309\pi$
$588$	−10.5172	−	7.64121i	−0.433723	−	0.315118i
$589$	18.9443	−	13.7638i	0.780585	−	0.567128i
$590$		0			0
$591$	−4.35410	−	3.16344i	−0.179104	−	0.130127i
$592$	2.50000	+	7.69421i	0.102749	+	0.316230i
$593$	32.7426			1.34458			0.672290	−	0.740288i	$-0.265311\pi$
$593$	32.7426			1.34458			0.672290	+	0.740288i	$0.265311\pi$
$594$	1.00000	+	3.07768i	0.0410305	+	0.126279i
$595$		0			0
$596$	3.75329	−	11.5514i	0.153741	−	0.473165i
$597$	5.76393	−	17.7396i	0.235902	−	0.726032i
$598$	−12.2361	+	8.89002i	−0.500370	+	0.363540i
$599$	−12.4721			−0.509598			−0.254799	−	0.966994i	$-0.582009\pi$
$599$	−12.4721			−0.509598			−0.254799	+	0.966994i	$0.582009\pi$
$600$		0			0
$601$	−24.3262			−0.992288			−0.496144	−	0.868240i	$-0.665251\pi$
$601$	−24.3262			−0.992288			−0.496144	+	0.868240i	$0.665251\pi$
$602$	−20.6525	+	15.0049i	−0.841732	+	0.611554i
$603$	−1.61803	+	4.97980i	−0.0658914	+	0.202793i
$604$	−5.09017	+	15.6659i	−0.207116	+	0.637438i
$605$		0			0
$606$	−5.11803	−	15.7517i	−0.207906	−	0.639869i
$607$	39.2361			1.59254			0.796271	−	0.604940i	$-0.206803\pi$
$607$	39.2361			1.59254			0.796271	+	0.604940i	$0.206803\pi$
$608$	5.00000	+	15.3884i	0.202777	+	0.624083i
$609$	−15.8541	−	11.5187i	−0.642441	−	0.466760i
$610$		0			0
$611$	14.3262	−	10.4086i	0.579578	−	0.421088i
$612$	2.30902	+	1.67760i	0.0933365	+	0.0678129i
$613$	31.9615	+	23.2214i	1.29091	+	0.937903i	0.999823	−	0.0187931i	$-0.00598237\pi$
$613$	31.9615	+	23.2214i	1.29091	+	0.937903i	0.291089	+	0.956696i	$0.405982\pi$
$614$	−1.09017	+	0.792055i	−0.0439957	+	0.0319647i
$615$		0			0
$616$	35.1246	+	25.5195i	1.41521	+	1.02821i
$617$	−8.33688	−	25.6583i	−0.335630	−	1.03296i	−0.966411	−	0.257002i	$-0.917265\pi$
$617$	−8.33688	−	25.6583i	−0.335630	−	1.03296i	0.630781	−	0.775961i	$-0.282735\pi$
$618$	1.23607			0.0497219
$619$	8.76393	+	26.9726i	0.352252	+	1.08412i	0.957586	+	0.288149i	$0.0930398\pi$
$619$	8.76393	+	26.9726i	0.352252	+	1.08412i	−0.605333	+	0.795972i	$0.706960\pi$
$620$		0			0
$621$	−1.38197	+	4.25325i	−0.0554564	+	0.170677i
$622$	−1.32624	+	4.08174i	−0.0531773	+	0.163663i
$623$	27.5623	−	20.0252i	1.10426	−	0.802292i
$624$	−3.38197			−0.135387
$625$		0			0
$626$	8.47214			0.338615
$627$	−8.47214	+	6.15537i	−0.338345	+	0.245822i
$628$	−4.26393	+	13.1230i	−0.170149	+	0.523666i
$629$	−7.13525	+	21.9601i	−0.284501	+	0.875605i
$630$		0			0
$631$	3.18034	+	9.78808i	0.126607	+	0.389657i	0.994190	−	0.107635i	$-0.0343277\pi$
$631$	3.18034	+	9.78808i	0.126607	+	0.389657i	−0.867583	+	0.497292i	$0.834328\pi$
$632$		0			0
$633$	5.52786	+	17.0130i	0.219713	+	0.676207i
$634$	20.0902	+	14.5964i	0.797883	+	0.579696i
$635$		0			0
$636$	1.11803	−	0.812299i	0.0443329	−	0.0322098i
$637$	35.5689	+	25.8423i	1.40929	+	1.02391i
$638$	11.4721	+	8.33499i	0.454186	+	0.329986i
$639$	0.618034	−	0.449028i	0.0244490	−	0.0177633i
$640$		0			0
$641$	−31.5066	−	22.8909i	−1.24444	−	0.904135i	−0.246549	−	0.969130i	$-0.579297\pi$
$641$	−31.5066	−	22.8909i	−1.24444	−	0.904135i	−0.997886	+	0.0649953i	$0.979297\pi$
$642$	−5.09017	−	15.6659i	−0.200893	−	0.618285i
$643$	−13.8885			−0.547711			−0.273855	−	0.961771i	$-0.588299\pi$
$643$	−13.8885			−0.547711			−0.273855	+	0.961771i	$0.588299\pi$
$644$	6.18034	+	19.0211i	0.243540	+	0.749538i
$645$		0			0
$646$	2.85410	−	8.78402i	0.112293	−	0.345603i
$647$	−3.20163	+	9.85359i	−0.125869	+	0.387385i	−0.994058	−	0.108848i	$-0.965284\pi$
$647$	−3.20163	+	9.85359i	−0.125869	+	0.387385i	0.868189	+	0.496233i	$0.165284\pi$
$648$	−2.42705	+	1.76336i	−0.0953436	+	0.0692712i
$649$	−12.9443			−0.508107
$650$		0			0
$651$	32.3607			1.26832
$652$	−2.38197	+	1.73060i	−0.0932850	+	0.0677755i
$653$	−13.9377	+	42.8958i	−0.545424	+	1.67864i	0.174555	+	0.984647i	$0.444151\pi$
$653$	−13.9377	+	42.8958i	−0.545424	+	1.67864i	−0.719979	+	0.693995i	$0.755849\pi$
$654$	−5.89919	+	18.1558i	−0.230676	+	0.709949i
$655$		0			0
$656$	0.427051	+	1.31433i	0.0166735	+	0.0513159i
$657$	−3.09017			−0.120559
$658$	7.23607	+	22.2703i	0.282091	+	0.868188i
$659$	5.32624	+	3.86974i	0.207481	+	0.150744i	0.686673	−	0.726966i	$-0.259070\pi$
$659$	5.32624	+	3.86974i	0.207481	+	0.150744i	−0.479192	+	0.877710i	$0.659070\pi$
$660$		0			0
$661$	−20.5623	+	14.9394i	−0.799781	+	0.581075i	−0.910850	−	0.412738i	$-0.864573\pi$
$661$	−20.5623	+	14.9394i	−0.799781	+	0.581075i	0.111069	+	0.993813i	$0.464573\pi$
$662$	8.85410	+	6.43288i	0.344124	+	0.250021i
$663$	−7.80902	−	5.67358i	−0.303277	−	0.220344i
$664$	8.56231	−	6.22088i	0.332282	−	0.241417i
$665$		0			0
$666$	−6.54508	−	4.75528i	−0.253617	−	0.184263i
$667$	6.05573	+	18.6376i	0.234479	+	0.721651i
$668$	−23.4164			−0.906008
$669$	−4.38197	−	13.4863i	−0.169417	−	0.521411i
$670$		0			0
$671$	−0.618034	+	1.90211i	−0.0238589	+	0.0734303i
$672$	−6.90983	+	21.2663i	−0.266552	+	0.820364i
$673$	24.1074	−	17.5150i	0.929272	−	0.675155i	−0.0165428	−	0.999863i	$-0.505266\pi$
$673$	24.1074	−	17.5150i	0.929272	−	0.675155i	0.945814	+	0.324708i	$0.105266\pi$
$674$	−14.9443			−0.575632
$675$		0			0
$676$	1.56231			0.0600887
$677$	30.2705	−	21.9928i	1.16339	−	0.845252i	0.173187	−	0.984889i	$-0.444593\pi$
$677$	30.2705	−	21.9928i	1.16339	−	0.845252i	0.990203	+	0.139636i	$0.0445934\pi$
$678$	−0.826238	+	2.54290i	−0.0317315	+	0.0976594i
$679$	12.2361	−	37.6587i	0.469577	−	1.44521i
$680$		0			0
$681$	−6.18034	−	19.0211i	−0.236831	−	0.728891i
$682$	−23.4164			−0.896661
$683$	−2.29180	−	7.05342i	−0.0876931	−	0.269892i	0.897588	−	0.440836i	$-0.145318\pi$
$683$	−2.29180	−	7.05342i	−0.0876931	−	0.269892i	−0.985281	+	0.170945i	$0.945318\pi$
$684$	−2.61803	−	1.90211i	−0.100103	−	0.0727291i
$685$		0			0
$686$	−21.7082	+	15.7719i	−0.828823	+	0.602175i
$687$	−20.2082	−	14.6821i	−0.770991	−	0.560158i
$688$	4.61803	+	3.35520i	0.176061	+	0.127916i
$689$	−3.78115	+	2.74717i	−0.144050	+	0.104659i
$690$		0			0
$691$	17.1803	+	12.4822i	0.653571	+	0.474847i	0.864486	−	0.502657i	$-0.167644\pi$
$691$	17.1803	+	12.4822i	0.653571	+	0.474847i	−0.210915	+	0.977504i	$0.567644\pi$
$692$	3.06231	+	9.42481i	0.116411	+	0.358277i
$693$	−14.4721			−0.549751
$694$	−10.4164	−	32.0584i	−0.395401	−	1.21692i
$695$		0			0
$696$	−4.06231	+	12.5025i	−0.153981	+	0.473906i
$697$	−1.21885	+	3.75123i	−0.0461671	+	0.142088i
$698$	20.2533	−	14.7149i	0.766598	−	0.556966i
$699$	14.6180			0.552905
$700$		0			0
$701$	0.437694			0.0165315			0.00826574	−	0.999966i	$-0.497369\pi$
$701$	0.437694			0.0165315			0.00826574	+	0.999966i	$0.497369\pi$
$702$	2.73607	−	1.98787i	0.103266	−	0.0750273i
$703$	8.09017	−	24.8990i	0.305127	−	0.939083i
$704$	7.00000	−	21.5438i	0.263822	−	0.811962i
$705$		0			0
$706$	−9.38197	−	28.8747i	−0.353095	−	1.08671i
$707$	74.0689			2.78565
$708$	−1.23607	−	3.80423i	−0.0464543	−	0.142972i
$709$	5.44427	+	3.95550i	0.204464	+	0.148552i	0.685305	−	0.728256i	$-0.259669\pi$
$709$	5.44427	+	3.95550i	0.204464	+	0.148552i	−0.480841	+	0.876808i	$0.659669\pi$
$710$		0			0
$711$		0			0
$712$	−18.4894	−	13.4333i	−0.692918	−	0.503434i
$713$	−26.1803	−	19.0211i	−0.980461	−	0.712347i
$714$	10.3262	−	7.50245i	0.386450	−	0.280772i
$715$		0			0
$716$	5.00000	+	3.63271i	0.186859	+	0.135761i
$717$	2.18034	+	6.71040i	0.0814263	+	0.250604i
$718$	10.5836			0.394976
$719$	−11.0902	−	34.1320i	−0.413594	−	1.27291i	−0.913503	−	0.406832i	$-0.866633\pi$
$719$	−11.0902	−	34.1320i	−0.413594	−	1.27291i	0.499909	−	0.866078i	$-0.333367\pi$
$720$		0			0
$721$	−1.70820	+	5.25731i	−0.0636168	+	0.195792i
$722$	2.63525	−	8.11048i	0.0980740	−	0.301841i
$723$	−0.836881	+	0.608030i	−0.0311239	+	0.0226129i
$724$	9.79837			0.364154
$725$		0			0
$726$	−0.527864			−0.0195909
$727$	12.4164	−	9.02105i	0.460499	−	0.334572i	−0.333228	−	0.942846i	$-0.608138\pi$
$727$	12.4164	−	9.02105i	0.460499	−	0.334572i	0.793727	+	0.608274i	$0.208138\pi$
$728$	14.0213	−	43.1531i	0.519663	−	1.59936i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	5.03444	+	15.4944i	0.186206	+	0.573082i
$732$	−0.618034			−0.0228432
$733$	−0.798374	−	2.45714i	−0.0294886	−	0.0907566i	0.935229	−	0.354043i	$-0.115193\pi$
$733$	−0.798374	−	2.45714i	−0.0294886	−	0.0907566i	−0.964718	+	0.263287i	$0.915193\pi$
$734$	4.85410	+	3.52671i	0.179168	+	0.130173i
$735$		0			0
$736$	18.0902	−	13.1433i	0.666813	−	0.484468i
$737$	13.7082	+	9.95959i	0.504948	+	0.366866i
$738$	−1.11803	−	0.812299i	−0.0411554	−	0.0299011i
$739$	−14.3262	+	10.4086i	−0.526999	+	0.382887i	−0.819234	−	0.573459i	$-0.805601\pi$
$739$	−14.3262	+	10.4086i	−0.526999	+	0.382887i	0.292235	+	0.956347i	$0.405601\pi$
$740$		0			0
$741$	8.85410	+	6.43288i	0.325264	+	0.236318i
$742$	−1.90983	−	5.87785i	−0.0701121	−	0.215783i
$743$	−0.875388			−0.0321149			−0.0160574	−	0.999871i	$-0.505111\pi$
$743$	−0.875388			−0.0321149			−0.0160574	+	0.999871i	$0.505111\pi$
$744$	−6.70820	−	20.6457i	−0.245935	−	0.756909i
$745$		0			0
$746$	9.09017	−	27.9767i	0.332815	−	1.02430i
$747$	−1.09017	+	3.35520i	−0.0398872	+	0.122760i
$748$	7.47214	−	5.42882i	0.273208	−	0.198497i
$749$	73.6656			2.69168
$750$		0			0
$751$	5.34752			0.195134			0.0975670	−	0.995229i	$-0.468894\pi$
$751$	5.34752			0.195134			0.0975670	+	0.995229i	$0.468894\pi$
$752$	4.23607	−	3.07768i	0.154474	−	0.112232i
$753$	8.32624	−	25.6255i	0.303425	−	0.933846i
$754$	4.57953	−	14.0943i	0.166777	−	0.513285i
$755$		0			0
$756$	−1.38197	−	4.25325i	−0.0502616	−	0.154689i
$757$	−27.3820			−0.995214			−0.497607	−	0.867402i	$-0.665788\pi$
$757$	−27.3820			−0.995214			−0.497607	+	0.867402i	$0.665788\pi$
$758$	−7.23607	−	22.2703i	−0.262826	−	0.808895i
$759$	11.7082	+	8.50651i	0.424981	+	0.308767i
$760$		0			0
$761$	7.88197	−	5.72658i	0.285721	−	0.207588i	−0.435688	−	0.900098i	$-0.643495\pi$
$761$	7.88197	−	5.72658i	0.285721	−	0.207588i	0.721409	+	0.692509i	$0.243495\pi$
$762$	7.85410	+	5.70634i	0.284524	+	0.206719i
$763$	−69.0689	−	50.1815i	−2.50046	−	1.81669i
$764$	−19.9443	+	14.4904i	−0.721558	+	0.524243i
$765$		0			0
$766$	−16.8541	−	12.2452i	−0.608963	−	0.442438i
$767$	4.18034	+	12.8658i	0.150943	+	0.464556i
$768$	17.0000			0.613435
$769$	−1.74265	−	5.36331i	−0.0628414	−	0.193406i	0.914707	−	0.404118i	$-0.132422\pi$
$769$	−1.74265	−	5.36331i	−0.0628414	−	0.193406i	−0.977548	+	0.210712i	$0.932422\pi$
$770$		0			0
$771$	−3.95492	+	12.1720i	−0.142433	+	0.438363i
$772$	2.37132	−	7.29818i	0.0853458	−	0.262667i
$773$	−29.0623	+	21.1150i	−1.04530	+	0.759454i	−0.971313	−	0.237805i	$-0.923572\pi$
$773$	−29.0623	+	21.1150i	−1.04530	+	0.759454i	−0.0739857	+	0.997259i	$0.523572\pi$
$774$	−5.70820			−0.205177
$775$		0			0
$776$	−26.5623			−0.953531
$777$	29.2705	−	21.2663i	1.05007	−	0.762923i
$778$	11.4615	−	35.2748i	0.410914	−	1.26466i
$779$	1.38197	−	4.25325i	0.0495141	−	0.152389i
$780$		0			0
$781$	−0.763932	−	2.35114i	−0.0273356	−	0.0841304i
$782$	−12.7639			−0.456437
$783$	−1.35410	−	4.16750i	−0.0483917	−	0.148934i
$784$	10.5172	+	7.64121i	0.375615	+	0.272900i
$785$		0			0
$786$	−11.4721	+	8.33499i	−0.409198	+	0.297299i
$787$	6.61803	+	4.80828i	0.235907	+	0.171397i	0.699458	−	0.714674i	$-0.253425\pi$
$787$	6.61803	+	4.80828i	0.235907	+	0.171397i	−0.463551	+	0.886070i	$0.653425\pi$
$788$	−4.35410	−	3.16344i	−0.155108	−	0.112693i
$789$	−9.61803	+	6.98791i	−0.342411	+	0.248776i
$790$		0			0
$791$	−9.67376	−	7.02840i	−0.343959	−	0.249901i
$792$	3.00000	+	9.23305i	0.106600	+	0.328082i
$793$	2.09017			0.0742241
$794$	3.38197	+	10.4086i	0.120021	+	0.369388i
$795$		0			0
$796$	5.76393	−	17.7396i	0.204297	−	0.628762i
$797$	−11.7746	+	36.2384i	−0.417077	+	1.28363i	0.493303	+	0.869857i	$0.335789\pi$
$797$	−11.7746	+	36.2384i	−0.417077	+	1.28363i	−0.910380	+	0.413773i	$0.864211\pi$
$798$	−11.7082	+	8.50651i	−0.414466	+	0.301127i
$799$	14.9443			0.528690
$800$		0			0
$801$	7.61803			0.269170
$802$	27.0623	−	19.6619i	0.955603	−	0.694286i
$803$	−3.09017	+	9.51057i	−0.109050	+	0.335621i
$804$	−1.61803	+	4.97980i	−0.0570637	+	0.175624i
$805$		0			0
$806$	7.56231	+	23.2744i	0.266371	+	0.819805i
$807$	0.145898			0.00513585
$808$	−15.3541	−	47.2551i	−0.540155	−	1.66243i
$809$	18.7812	+	13.6453i	0.660310	+	0.479743i	0.866768	−	0.498712i	$-0.166194\pi$
$809$	18.7812	+	13.6453i	0.660310	+	0.479743i	−0.206457	+	0.978456i	$0.566194\pi$
$810$		0			0
$811$	−7.47214	+	5.42882i	−0.262382	+	0.190632i	−0.711197	−	0.702993i	$-0.751846\pi$
$811$	−7.47214	+	5.42882i	−0.262382	+	0.190632i	0.448814	+	0.893625i	$0.351846\pi$
$812$	−15.8541	−	11.5187i	−0.556370	−	0.404226i
$813$	17.9443	+	13.0373i	0.629333	+	0.457237i
$814$	−21.1803	+	15.3884i	−0.742371	+	0.539364i
$815$		0			0
$816$	−2.30902	−	1.67760i	−0.0808318	−	0.0587277i
$817$	−5.70820	−	17.5680i	−0.199705	−	0.614628i
$818$	−25.7984			−0.902019
$819$	4.67376	+	14.3844i	0.163314	+	0.502630i
$820$		0			0
$821$	1.56231	−	4.80828i	0.0545249	−	0.167810i	−0.920086	−	0.391717i	$-0.871881\pi$
$821$	1.56231	−	4.80828i	0.0545249	−	0.167810i	0.974611	+	0.223907i	$0.0718812\pi$
$822$	1.66312	−	5.11855i	0.0580079	−	0.178530i
$823$	−11.9443	+	8.67802i	−0.416351	+	0.302497i	−0.776168	−	0.630526i	$-0.782839\pi$
$823$	−11.9443	+	8.67802i	−0.416351	+	0.302497i	0.359817	+	0.933023i	$0.382839\pi$
$824$	3.70820			0.129181
$825$		0			0
$826$	−17.8885			−0.622422
$827$	17.8541	−	12.9718i	0.620848	−	0.451072i	−0.232370	−	0.972628i	$-0.574648\pi$
$827$	17.8541	−	12.9718i	0.620848	−	0.451072i	0.853218	+	0.521555i	$0.174648\pi$
$828$	−1.38197	+	4.25325i	−0.0480266	+	0.147811i
$829$	−8.19098	+	25.2093i	−0.284485	+	0.875554i	0.702068	+	0.712110i	$0.252260\pi$
$829$	−8.19098	+	25.2093i	−0.284485	+	0.875554i	−0.986553	+	0.163444i	$0.947740\pi$
$830$		0			0
$831$	−1.79180	−	5.51458i	−0.0621567	−	0.191299i
$832$	−23.6738			−0.820740
$833$	11.4656	+	35.2874i	0.397258	+	1.22263i
$834$	4.09017	+	2.97168i	0.141631	+	0.102901i
$835$		0			0
$836$	−8.47214	+	6.15537i	−0.293015	+	0.212888i
$837$	5.85410	+	4.25325i	0.202347	+	0.147014i
$838$	26.6525	+	19.3642i	0.920695	+	0.668924i
$839$	35.6525	−	25.9030i	1.23086	−	0.894272i	0.233906	−	0.972259i	$-0.424849\pi$
$839$	35.6525	−	25.9030i	1.23086	−	0.894272i	0.996954	+	0.0779870i	$0.0248493\pi$
$840$		0			0
$841$	7.92705	+	5.75934i	0.273347	+	0.198598i
$842$	−7.15248	−	22.0131i	−0.246491	−	0.758620i
$843$	17.3820			0.598667
$844$	5.52786	+	17.0130i	0.190277	+	0.585612i
$845$		0			0
$846$	−1.61803	+	4.97980i	−0.0556292	+	0.171209i
$847$	0.729490	−	2.24514i	0.0250656	−	0.0771439i
$848$	−1.11803	+	0.812299i	−0.0383934	+	0.0278945i
$849$	0.291796			0.0100144
$850$		0			0
$851$	−36.1803			−1.24025
$852$	0.618034	−	0.449028i	0.0211735	−	0.0153834i
$853$	−9.22542	+	28.3929i	−0.315873	+	0.972156i	0.659521	+	0.751686i	$0.270759\pi$
$853$	−9.22542	+	28.3929i	−0.315873	+	0.972156i	−0.975394	+	0.220470i	$0.929241\pi$
$854$	−0.854102	+	2.62866i	−0.0292268	+	0.0899507i
$855$		0			0
$856$	−15.2705	−	46.9978i	−0.521935	−	1.60635i
$857$	3.52786			0.120510			0.0602548	−	0.998183i	$-0.480809\pi$
$857$	3.52786			0.120510			0.0602548	+	0.998183i	$0.480809\pi$
$858$	−3.38197	−	10.4086i	−0.115458	−	0.355344i
$859$	−2.76393	−	2.00811i	−0.0943041	−	0.0685160i	0.539634	−	0.841900i	$-0.318563\pi$
$859$	−2.76393	−	2.00811i	−0.0943041	−	0.0685160i	−0.633938	+	0.773384i	$0.718563\pi$
$860$		0			0
$861$	5.00000	−	3.63271i	0.170400	−	0.123803i
$862$	−8.61803	−	6.26137i	−0.293531	−	0.213263i
$863$	41.3607	+	30.0503i	1.40793	+	1.02292i	0.993619	+	0.112790i	$0.0359788\pi$
$863$	41.3607	+	30.0503i	1.40793	+	1.02292i	0.414315	+	0.910134i	$0.364021\pi$
$864$	−4.04508	+	2.93893i	−0.137617	+	0.0999843i
$865$		0			0
$866$	−20.2082	−	14.6821i	−0.686703	−	0.498919i
$867$	2.73607	+	8.42075i	0.0929217	+	0.285984i
$868$	32.3607			1.09839
$869$		0			0
$870$		0			0
$871$	5.47214	−	16.8415i	0.185416	−	0.570653i
$872$	−17.6976	+	54.4675i	−0.599315	+	1.84450i
$873$	7.16312	−	5.20431i	0.242435	−	0.176139i
$874$	14.4721			0.489527
$875$		0			0
$876$	−3.09017			−0.104407
$877$	14.7361	−	10.7064i	0.497602	−	0.361529i	−0.310499	−	0.950574i	$-0.600496\pi$
$877$	14.7361	−	10.7064i	0.497602	−	0.361529i	0.808100	+	0.589045i	$0.200496\pi$
$878$	1.90983	−	5.87785i	0.0644536	−	0.198368i
$879$	1.17376	−	3.61247i	0.0395900	−	0.121846i
$880$		0			0
$881$	7.74265	+	23.8294i	0.260856	+	0.802833i	0.992619	+	0.121274i	$0.0386979\pi$
$881$	7.74265	+	23.8294i	0.260856	+	0.802833i	−0.731763	+	0.681559i	$0.761302\pi$
$882$	−13.0000			−0.437733
$883$	0.0557281	+	0.171513i	0.00187540	+	0.00577189i	0.951990	−	0.306130i	$-0.0990341\pi$
$883$	0.0557281	+	0.171513i	0.00187540	+	0.00577189i	−0.950114	+	0.311902i	$0.899034\pi$
$884$	−7.80902	−	5.67358i	−0.262646	−	0.190823i
$885$		0			0
$886$	24.8885	−	18.0826i	0.836147	−	0.607496i
$887$	13.8541	+	10.0656i	0.465175	+	0.337970i	0.795558	−	0.605877i	$-0.207178\pi$
$887$	13.8541	+	10.0656i	0.465175	+	0.337970i	−0.330383	+	0.943847i	$0.607178\pi$
$888$	−19.6353	−	14.2658i	−0.658916	−	0.478731i
$889$	−35.1246	+	25.5195i	−1.17804	+	0.855897i
$890$		0			0
$891$	−2.61803	−	1.90211i	−0.0877074	−	0.0637232i
$892$	−4.38197	−	13.4863i	−0.146719	−	0.451555i
$893$	−16.9443			−0.567018
$894$	−3.75329	−	11.5514i	−0.125529	−	0.386338i
$895$		0			0
$896$	−4.14590	+	12.7598i	−0.138505	+	0.426274i
$897$	4.67376	−	14.3844i	0.156052	−	0.480280i
$898$	−6.30902	+	4.58377i	−0.210535	+	0.152962i
$899$	31.7082			1.05753
$900$		0			0
$901$	−3.94427			−0.131403
$902$	−3.61803	+	2.62866i	−0.120467	+	0.0875247i
$903$	7.88854	−	24.2784i	0.262514	−	0.807936i
$904$	−2.47871	+	7.62870i	−0.0824408	+	0.253727i
$905$		0			0
$906$	5.09017	+	15.6659i	0.169110	+	0.520466i
$907$	33.1246			1.09988			0.549942	−	0.835203i	$-0.314650\pi$
$907$	33.1246			1.09988			0.549942	+	0.835203i	$0.314650\pi$
$908$	−6.18034	−	19.0211i	−0.205102	−	0.631238i
$909$	13.3992	+	9.73508i	0.444423	+	0.322892i
$910$		0			0
$911$	3.38197	−	2.45714i	0.112050	−	0.0814088i	−0.530349	−	0.847779i	$-0.677939\pi$
$911$	3.38197	−	2.45714i	0.112050	−	0.0814088i	0.642399	+	0.766370i	$0.277939\pi$
$912$	2.61803	+	1.90211i	0.0866918	+	0.0629853i
$913$	9.23607	+	6.71040i	0.305669	+	0.222082i
$914$	−18.0902	+	13.1433i	−0.598370	+	0.434741i
$915$		0			0
$916$	−20.2082	−	14.6821i	−0.667698	−	0.485111i
$917$	−19.5967	−	60.3126i	−0.647142	−	1.99170i
$918$	2.85410			0.0941994
$919$	−15.2016	−	46.7858i	−0.501455	−	1.54332i	−0.806649	−	0.591031i	$-0.798721\pi$
$919$	−15.2016	−	46.7858i	−0.501455	−	1.54332i	0.305194	−	0.952290i	$-0.401279\pi$
$920$		0			0
$921$	0.416408	−	1.28157i	0.0137211	−	0.0422292i
$922$	2.53444	−	7.80021i	0.0834674	−	0.256886i
$923$	−2.09017	+	1.51860i	−0.0687988	+	0.0499852i
$924$	−14.4721			−0.476098
$925$		0			0
$926$	23.2361			0.763585
$927$	−1.00000	+	0.726543i	−0.0328443	+	0.0238628i
$928$	−6.77051	+	20.8375i	−0.222253	+	0.684024i
$929$	0.645898	−	1.98787i	0.0211912	−	0.0652199i	−0.939902	−	0.341445i	$-0.889084\pi$
$929$	0.645898	−	1.98787i	0.0211912	−	0.0652199i	0.961093	+	0.276225i	$0.0890836\pi$
$930$		0			0
$931$	−13.0000	−	40.0099i	−0.426058	−	1.31127i
$932$	14.6180			0.478830
$933$	−1.32624	−	4.08174i	−0.0434191	−	0.133630i
$934$	−4.70820	−	3.42071i	−0.154057	−	0.111929i
$935$		0			0
$936$	8.20820	−	5.96361i	0.268294	−	0.194927i
$937$	9.45492	+	6.86940i	0.308879	+	0.224413i	0.731415	−	0.681932i	$-0.238860\pi$
$937$	9.45492	+	6.86940i	0.308879	+	0.224413i	−0.422537	+	0.906346i	$0.638860\pi$
$938$	18.9443	+	13.7638i	0.618552	+	0.449405i
$939$	−6.85410	+	4.97980i	−0.223675	+	0.162510i
$940$		0			0
$941$	−4.30902	−	3.13068i	−0.140470	−	0.102057i	0.515331	−	0.856991i	$-0.327669\pi$
$941$	−4.30902	−	3.13068i	−0.140470	−	0.102057i	−0.655801	+	0.754934i	$0.727669\pi$
$942$	4.26393	+	13.1230i	0.138926	+	0.427572i
$943$	−6.18034			−0.201260
$944$	1.23607	+	3.80423i	0.0402306	+	0.123817i
$945$		0			0
$946$	−5.70820	+	17.5680i	−0.185590	+	0.571186i
$947$	−9.09017	+	27.9767i	−0.295391	+	0.909120i	0.687699	+	0.725996i	$0.258621\pi$
$947$	−9.09017	+	27.9767i	−0.295391	+	0.909120i	−0.983090	+	0.183124i	$0.941379\pi$
$948$		0			0
$949$	10.4508			0.339249
$950$		0			0
$951$	−24.8328			−0.805259
$952$	30.9787	−	22.5074i	1.00403	−	0.729468i
$953$	−3.11803	+	9.59632i	−0.101003	+	0.310855i	−0.988772	−	0.149435i	$-0.952255\pi$
$953$	−3.11803	+	9.59632i	−0.101003	+	0.310855i	0.887769	+	0.460290i	$0.152255\pi$
$954$	0.427051	−	1.31433i	0.0138263	−	0.0425529i
$955$		0			0
$956$	2.18034	+	6.71040i	0.0705172	+	0.217030i
$957$	−14.1803			−0.458385
$958$	−0.326238	−	1.00406i	−0.0105403	−	0.0324396i
$959$	19.4721	+	14.1473i	0.628788	+	0.456841i
$960$		0			0
$961$	−17.2812	+	12.5555i	−0.557457	+	0.405016i
$962$	22.1353	+	16.0822i	0.713669	+	0.518511i
$963$	13.3262	+	9.68208i	0.429432	+	0.312001i
$964$	−0.836881	+	0.608030i	−0.0269541	+	0.0195833i
$965$		0			0
$966$	16.1803	+	11.7557i	0.520594	+	0.378234i
$967$	−10.7639	−	33.1280i	−0.346145	−	1.06532i	−0.960968	−	0.276659i	$-0.910773\pi$
$967$	−10.7639	−	33.1280i	−0.346145	−	1.06532i	0.614823	−	0.788665i	$-0.289227\pi$
$968$	−1.58359			−0.0508986
$969$	2.85410	+	8.78402i	0.0916870	+	0.282183i
$970$		0			0
$971$	−2.03444	+	6.26137i	−0.0652883	+	0.200937i	−0.978379	−	0.206819i	$-0.933689\pi$
$971$	−2.03444	+	6.26137i	−0.0652883	+	0.200937i	0.913091	+	0.407756i	$0.133689\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−18.2918	+	13.2898i	−0.586408	+	0.426050i
$974$	−3.70820			−0.118819
$975$		0			0
$976$	0.618034			0.0197828
$977$	−37.0066	+	26.8869i	−1.18395	+	0.860187i	−0.992611	−	0.121338i	$-0.961281\pi$
$977$	−37.0066	+	26.8869i	−1.18395	+	0.860187i	−0.191334	+	0.981525i	$0.561281\pi$
$978$	−0.909830	+	2.80017i	−0.0290932	+	0.0895395i
$979$	7.61803	−	23.4459i	0.243473	−	0.749334i
$980$		0			0
$981$	−5.89919	−	18.1558i	−0.188347	−	0.579671i
$982$	29.8885			0.953782
$983$	−6.70820	−	20.6457i	−0.213958	−	0.658496i	−0.999226	−	0.0393397i	$-0.987475\pi$
$983$	−6.70820	−	20.6457i	−0.213958	−	0.658496i	0.785267	−	0.619157i	$-0.212525\pi$
$984$	−3.35410	−	2.43690i	−0.106925	−	0.0776855i
$985$		0			0
$986$	10.1180	−	7.35118i	0.322224	−	0.234109i
$987$	−18.9443	−	13.7638i	−0.603003	−	0.438107i
$988$	8.85410	+	6.43288i	0.281687	+	0.204657i
$989$	−20.6525	+	15.0049i	−0.656711	+	0.477128i
$990$		0			0
$991$	2.52786	+	1.83660i	0.0803002	+	0.0583415i	0.627211	−	0.778849i	$-0.284196\pi$
$991$	2.52786	+	1.83660i	0.0803002	+	0.0583415i	−0.546911	+	0.837191i	$0.684196\pi$
$992$	−11.1803	−	34.4095i	−0.354976	−	1.09250i
$993$	−10.9443			−0.347306
$994$	−1.05573	−	3.24920i	−0.0334857	−	0.103058i
$995$		0			0
$996$	−1.09017	+	3.35520i	−0.0345434	+	0.106314i
$997$	−2.90983	+	8.95554i	−0.0921552	+	0.283625i	−0.986502	−	0.163750i	$-0.947641\pi$
$997$	−2.90983	+	8.95554i	−0.0921552	+	0.283625i	0.894347	+	0.447375i	$0.147641\pi$
$998$	−4.85410	+	3.52671i	−0.153654	+	0.111636i
$999$	8.09017			0.255962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.a.301.1		4
5.2	odd	4		375.2.i.a.199.2		8
5.3	odd	4		375.2.i.a.199.1		8
5.4	even	2		75.2.g.a.61.1	yes	4
15.14	odd	2		225.2.h.a.136.1		4
25.3	odd	20		1875.2.b.b.1249.4		4
25.4	even	10		1875.2.a.d.1.2		2
25.9	even	10		75.2.g.a.16.1	✓	4
25.12	odd	20		375.2.i.a.49.1		8
25.13	odd	20		375.2.i.a.49.2		8
25.16	even	5	inner	375.2.g.a.76.1		4
25.21	even	5		1875.2.a.a.1.1		2
25.22	odd	20		1875.2.b.b.1249.1		4
75.29	odd	10		5625.2.a.a.1.2		2
75.59	odd	10		225.2.h.a.91.1		4
75.71	odd	10		5625.2.a.h.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.a.16.1	✓	4	25.9	even	10
75.2.g.a.61.1	yes	4	5.4	even	2
225.2.h.a.91.1		4	75.59	odd	10
225.2.h.a.136.1		4	15.14	odd	2
375.2.g.a.76.1		4	25.16	even	5	inner
375.2.g.a.301.1		4	1.1	even	1	trivial
375.2.i.a.49.1		8	25.12	odd	20
375.2.i.a.49.2		8	25.13	odd	20
375.2.i.a.199.1		8	5.3	odd	4
375.2.i.a.199.2		8	5.2	odd	4
1875.2.a.a.1.1		2	25.21	even	5
1875.2.a.d.1.2		2	25.4	even	10
1875.2.b.b.1249.1		4	25.22	odd	20
1875.2.b.b.1249.4		4	25.3	odd	20
5625.2.a.a.1.2		2	75.29	odd	10
5625.2.a.h.1.1		2	75.71	odd	10

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.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -4.47214 q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -4.47214 q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.61803 + 1.90211i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(2.73607 + 1.98787i) q^{13} +(-3.61803 + 2.62866i) q^{14} +(0.809017 + 0.587785i) q^{16} +(0.881966 + 2.71441i) q^{17} -1.00000 q^{18} +(-1.00000 - 3.07768i) q^{19} +(1.38197 - 4.25325i) q^{21} +(-1.00000 + 3.07768i) q^{22} +(-3.61803 + 2.62866i) q^{23} -3.00000 q^{24} +3.38197 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.38197 - 4.25325i) q^{28} +(1.35410 - 4.16750i) q^{29} +(2.23607 + 6.88191i) q^{31} -5.00000 q^{32} +(-1.00000 - 3.07768i) q^{33} +(2.30902 + 1.67760i) q^{34} +(0.809017 - 0.587785i) q^{36} +(6.54508 + 4.75528i) q^{37} +(-2.61803 - 1.90211i) q^{38} +(-2.73607 + 1.98787i) q^{39} +(1.11803 + 0.812299i) q^{41} +(-1.38197 - 4.25325i) q^{42} +5.70820 q^{43} +(-1.00000 - 3.07768i) q^{44} +(-1.38197 + 4.25325i) q^{46} +(1.61803 - 4.97980i) q^{47} +(-0.809017 + 0.587785i) q^{48} +13.0000 q^{49} -2.85410 q^{51} +(-2.73607 + 1.98787i) q^{52} +(-0.427051 + 1.31433i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-4.14590 - 12.7598i) q^{56} +3.23607 q^{57} +(-1.35410 - 4.16750i) q^{58} +(3.23607 + 2.35114i) q^{59} +(0.500000 - 0.363271i) q^{61} +(5.85410 + 4.25325i) q^{62} +(3.61803 + 2.62866i) q^{63} +(-5.66312 + 4.11450i) q^{64} +(-2.61803 - 1.90211i) q^{66} +(-1.61803 - 4.97980i) q^{67} -2.85410 q^{68} +(-1.38197 - 4.25325i) q^{69} +(-0.236068 + 0.726543i) q^{71} +(0.927051 - 2.85317i) q^{72} +(2.50000 - 1.81636i) q^{73} +8.09017 q^{74} +3.23607 q^{76} +(11.7082 - 8.50651i) q^{77} +(-1.04508 + 3.21644i) q^{78} +(0.309017 + 0.951057i) q^{81} +1.38197 q^{82} +(-1.09017 - 3.35520i) q^{83} +(3.61803 + 2.62866i) q^{84} +(4.61803 - 3.35520i) q^{86} +(3.54508 + 2.57565i) q^{87} +(-7.85410 - 5.70634i) q^{88} +(-6.16312 + 4.47777i) q^{89} +(-12.2361 - 8.89002i) q^{91} +(-1.38197 - 4.25325i) q^{92} -7.23607 q^{93} +(-1.61803 - 4.97980i) q^{94} +(1.54508 - 4.75528i) q^{96} +(-2.73607 + 8.42075i) q^{97} +(10.5172 - 7.64121i) q^{98} +3.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 + q^4 - q^6 - 3 * q^8 - q^9	\( 4 q + q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{8} - q^{9} - 6 q^{11} - q^{12} + 2 q^{13} - 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 10 q^{21} - 4 q^{22} - 10 q^{23} - 12 q^{24} + 18 q^{26} + q^{27} + 10 q^{28} - 8 q^{29} - 20 q^{32} - 4 q^{33} + 7 q^{34} + q^{36} + 15 q^{37} - 6 q^{38} - 2 q^{39} - 10 q^{42} - 4 q^{43} - 4 q^{44} - 10 q^{46} + 2 q^{47} - q^{48} + 52 q^{49} + 2 q^{51} - 2 q^{52} + 5 q^{53} - q^{54} - 30 q^{56} + 4 q^{57} + 8 q^{58} + 4 q^{59} + 2 q^{61} + 10 q^{62} + 10 q^{63} - 7 q^{64} - 6 q^{66} - 2 q^{67} + 2 q^{68} - 10 q^{69} + 8 q^{71} - 3 q^{72} + 10 q^{73} + 10 q^{74} + 4 q^{76} + 20 q^{77} + 7 q^{78} - q^{81} + 10 q^{82} + 18 q^{83} + 10 q^{84} + 14 q^{86} + 3 q^{87} - 18 q^{88} - 9 q^{89} - 40 q^{91} - 10 q^{92} - 20 q^{93} - 2 q^{94} - 5 q^{96} - 2 q^{97} + 13 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + q^4 - q^6 - 3 * q^8 - q^9 - 6 * q^11 - q^12 + 2 * q^13 - 10 * q^14 + q^16 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 10 * q^21 - 4 * q^22 - 10 * q^23 - 12 * q^24 + 18 * q^26 + q^27 + 10 * q^28 - 8 * q^29 - 20 * q^32 - 4 * q^33 + 7 * q^34 + q^36 + 15 * q^37 - 6 * q^38 - 2 * q^39 - 10 * q^42 - 4 * q^43 - 4 * q^44 - 10 * q^46 + 2 * q^47 - q^48 + 52 * q^49 + 2 * q^51 - 2 * q^52 + 5 * q^53 - q^54 - 30 * q^56 + 4 * q^57 + 8 * q^58 + 4 * q^59 + 2 * q^61 + 10 * q^62 + 10 * q^63 - 7 * q^64 - 6 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^69 + 8 * q^71 - 3 * q^72 + 10 * q^73 + 10 * q^74 + 4 * q^76 + 20 * q^77 + 7 * q^78 - q^81 + 10 * q^82 + 18 * q^83 + 10 * q^84 + 14 * q^86 + 3 * q^87 - 18 * q^88 - 9 * q^89 - 40 * q^91 - 10 * q^92 - 20 * q^93 - 2 * q^94 - 5 * q^96 - 2 * q^97 + 13 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more