LMFDB - Embedded newform 225.4.e.d.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.4
Root			$0.112625 + 0.195072i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.d.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.112625 + 0.195072i) q^{2} +(-2.06755 + 4.76710i) q^{3} +(3.97463 + 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(-15.5970 + 27.0148i) q^{7} -3.59257 q^{8} +(-18.4505 - 19.7124i) q^{9} +O(q^{10})$	\(q+(-0.112625 + 0.195072i) q^{2} +(-2.06755 + 4.76710i) q^{3} +(3.97463 + 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(-15.5970 + 27.0148i) q^{7} -3.59257 q^{8} +(-18.4505 - 19.7124i) q^{9} +(-9.06424 + 15.6997i) q^{11} +(-41.0357 + 4.71394i) q^{12} +(-25.0781 - 43.4366i) q^{13} +(-3.51322 - 6.08508i) q^{14} +(-31.3924 + 54.3733i) q^{16} +131.631 q^{17} +(5.92333 - 1.37907i) q^{18} +23.2428 q^{19} +(-96.5348 - 130.207i) q^{21} +(-2.04172 - 3.53636i) q^{22} +(-16.4928 - 28.5664i) q^{23} +(7.42780 - 17.1261i) q^{24} +11.2977 q^{26} +(132.118 - 47.1991i) q^{27} -247.969 q^{28} +(-62.9087 + 108.961i) q^{29} +(-62.5563 - 108.351i) q^{31} +(-21.4414 - 37.1376i) q^{32} +(-56.1014 - 75.6700i) q^{33} +(-14.8249 + 25.6775i) q^{34} +(62.3714 - 205.368i) q^{36} -99.9894 q^{37} +(-2.61772 + 4.53402i) q^{38} +(258.917 - 29.7428i) q^{39} +(-122.663 - 212.458i) q^{41} +(36.2720 - 4.16670i) q^{42} +(69.5882 - 120.530i) q^{43} -144.108 q^{44} +7.43001 q^{46} +(-236.480 + 409.596i) q^{47} +(-194.298 - 262.070i) q^{48} +(-315.033 - 545.654i) q^{49} +(-272.153 + 627.498i) q^{51} +(199.352 - 345.289i) q^{52} -421.529 q^{53} +(-5.67258 + 31.0884i) q^{54} +(56.0333 - 97.0526i) q^{56} +(-48.0556 + 110.801i) q^{57} +(-14.1702 - 24.5435i) q^{58} +(371.207 + 642.949i) q^{59} +(-4.48868 + 7.77462i) q^{61} +28.1816 q^{62} +(820.300 - 190.982i) q^{63} -492.620 q^{64} +(21.0795 - 2.42149i) q^{66} +(294.453 + 510.008i) q^{67} +(523.185 + 906.182i) q^{68} +(170.279 - 19.5606i) q^{69} -48.5526 q^{71} +(66.2847 + 70.8182i) q^{72} -409.800 q^{73} +(11.2613 - 19.5051i) q^{74} +(92.3816 + 160.010i) q^{76} +(-282.750 - 489.737i) q^{77} +(-23.3585 + 53.8572i) q^{78} +(-265.263 + 459.449i) q^{79} +(-48.1577 + 727.408i) q^{81} +55.2595 q^{82} +(-147.295 + 255.122i) q^{83} +(512.688 - 1182.10i) q^{84} +(15.6747 + 27.1494i) q^{86} +(-389.362 - 525.174i) q^{87} +(32.5639 - 56.4023i) q^{88} +852.817 q^{89} +1564.57 q^{91} +(131.106 - 227.082i) q^{92} +(645.857 - 74.1922i) q^{93} +(-53.2672 - 92.2615i) q^{94} +(221.370 - 25.4296i) q^{96} +(-194.045 + 336.096i) q^{97} +141.922 q^{98} +(476.719 - 110.990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9 + 23 * q^11 - 287 * q^12 + 96 * q^13 - 21 * q^14 - 324 * q^16 + 322 * q^17 + 89 * q^18 + 558 * q^19 + 180 * q^21 + 311 * q^22 - 96 * q^23 + 48 * q^24 + 716 * q^26 + 470 * q^27 - 674 * q^28 - 296 * q^29 - 244 * q^31 + 314 * q^32 + 211 * q^33 - 125 * q^34 - 2399 * q^36 - 808 * q^37 - 305 * q^38 + 634 * q^39 - 47 * q^41 - 1941 * q^42 + 525 * q^43 - 110 * q^44 + 1434 * q^46 - 164 * q^47 - 2051 * q^48 - 1225 * q^49 + 1517 * q^51 + 1682 * q^52 + 1012 * q^53 - 4066 * q^54 - 981 * q^56 - 337 * q^57 + 1183 * q^58 - 85 * q^59 - 828 * q^61 - 1572 * q^62 + 828 * q^63 + 4472 * q^64 + 4930 * q^66 + 1093 * q^67 - 2473 * q^68 - 822 * q^69 - 656 * q^71 + 4626 * q^72 - 4170 * q^73 - 1316 * q^74 - 2789 * q^76 - 24 * q^77 + 5314 * q^78 - 2110 * q^79 - 2167 * q^81 + 124 * q^82 - 1290 * q^83 + 5775 * q^84 - 2569 * q^86 - 3604 * q^87 + 2271 * q^88 + 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 696 * q^93 + 517 * q^94 - 593 * q^96 + 1787 * q^97 + 2558 * q^98 + 2320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.112625	+	0.195072i	−0.0398189	+	0.0689684i	−0.885248	−	0.465119i	$-0.846011\pi$
$2$	−0.112625	+	0.195072i	−0.0398189	+	0.0689684i	0.845429	+	0.534088i	$0.179345\pi$
$3$	−2.06755	+	4.76710i	−0.397899	+	0.917429i
$3$	−2.06755	+	4.76710i	−0.397899	+	0.917429i
$4$	3.97463	+	6.88426i	0.496829	+	0.860533i
$5$		0			0
$5$		0			0
$6$	−0.697071	−	0.940215i	−0.0474297	−	0.0639735i
$7$	−15.5970	+	27.0148i	−0.842159	+	1.45866i	0.0459062	+	0.998946i	$0.485382\pi$
$7$	−15.5970	+	27.0148i	−0.842159	+	1.45866i	−0.888066	+	0.459717i	$0.847951\pi$
$8$	−3.59257			−0.158771
$9$	−18.4505	−	19.7124i	−0.683352	−	0.730089i
$10$		0			0
$11$	−9.06424	+	15.6997i	−0.248452	+	0.430331i	−0.963096	−	0.269156i	$-0.913255\pi$
$11$	−9.06424	+	15.6997i	−0.248452	+	0.430331i	0.714645	+	0.699488i	$0.246588\pi$
$12$	−41.0357	+	4.71394i	−0.987166	+	0.113400i
$13$	−25.0781	−	43.4366i	−0.535032	−	0.926702i	−0.999162	−	0.0409353i	$-0.986966\pi$
$13$	−25.0781	−	43.4366i	−0.535032	−	0.926702i	0.464130	−	0.885767i	$-0.346367\pi$
$14$	−3.51322	−	6.08508i	−0.0670678	−	0.116165i
$15$		0			0
$16$	−31.3924	+	54.3733i	−0.490507	+	0.849583i
$17$	131.631			1.87795			0.938977	−	0.343981i	$-0.111776\pi$
$17$	131.631			1.87795			0.938977	+	0.343981i	$0.111776\pi$
$18$	5.92333	−	1.37907i	0.0775634	−	0.0180583i
$19$	23.2428			0.280646			0.140323	−	0.990106i	$-0.455186\pi$
$19$	23.2428			0.280646			0.140323	+	0.990106i	$0.455186\pi$
$20$		0			0
$21$	−96.5348	−	130.207i	−1.00312	−	1.35302i
$22$	−2.04172	−	3.53636i	−0.0197862	−	0.0342707i
$23$	−16.4928	−	28.5664i	−0.149521	−	0.258978i	0.781529	−	0.623868i	$-0.214440\pi$
$23$	−16.4928	−	28.5664i	−0.149521	−	0.258978i	−0.931051	+	0.364890i	$0.881107\pi$
$24$	7.42780	−	17.1261i	0.0631747	−	0.145661i
$25$		0			0
$26$	11.2977			0.0852176
$27$	132.118	−	47.1991i	0.941710	−	0.336425i
$28$	−247.969			−1.67364
$29$	−62.9087	+	108.961i	−0.402823	+	0.697709i	−0.994065	−	0.108784i	$-0.965304\pi$
$29$	−62.9087	+	108.961i	−0.402823	+	0.697709i	0.591243	+	0.806494i	$0.298637\pi$
$30$		0			0
$31$	−62.5563	−	108.351i	−0.362434	−	0.627754i	0.625927	−	0.779882i	$-0.284721\pi$
$31$	−62.5563	−	108.351i	−0.362434	−	0.627754i	−0.988361	+	0.152128i	$0.951387\pi$
$32$	−21.4414	−	37.1376i	−0.118448	−	0.205158i
$33$	−56.1014	−	75.6700i	−0.295940	−	0.399166i
$34$	−14.8249	+	25.6775i	−0.0747781	+	0.129519i
$35$		0			0
$36$	62.3714	−	205.368i	0.288757	−	0.950776i
$37$	−99.9894			−0.444274			−0.222137	−	0.975015i	$-0.571303\pi$
$37$	−99.9894			−0.444274			−0.222137	+	0.975015i	$0.571303\pi$
$38$	−2.61772	+	4.53402i	−0.0111750	+	0.0193557i
$39$	258.917	−	29.7428i	1.06307	−	0.122119i
$40$		0			0
$41$	−122.663	−	212.458i	−0.467237	−	0.809278i	0.532063	−	0.846705i	$-0.321417\pi$
$41$	−122.663	−	212.458i	−0.467237	−	0.809278i	−0.999299	+	0.0374272i	$0.988084\pi$
$42$	36.2720	−	4.16670i	0.133259	−	0.0153080i
$43$	69.5882	−	120.530i	0.246793	−	0.427458i	−0.715841	−	0.698263i	$-0.753957\pi$
$43$	69.5882	−	120.530i	0.246793	−	0.427458i	0.962634	+	0.270805i	$0.0872899\pi$
$44$	−144.108			−0.493752
$45$		0			0
$46$	7.43001			0.0238151
$47$	−236.480	+	409.596i	−0.733919	+	1.27119i	0.221276	+	0.975211i	$0.428978\pi$
$47$	−236.480	+	409.596i	−0.733919	+	1.27119i	−0.955196	+	0.295975i	$0.904356\pi$
$48$	−194.298	−	262.070i	−0.584259	−	0.788054i
$49$	−315.033	−	545.654i	−0.918465	−	1.59083i
$50$		0			0
$51$	−272.153	+	627.498i	−0.747237	+	1.72289i
$52$	199.352	−	345.289i	0.531639	−	0.920825i
$53$	−421.529			−1.09248			−0.546240	−	0.837628i	$-0.683941\pi$
$53$	−421.529			−1.09248			−0.546240	+	0.837628i	$0.683941\pi$
$54$	−5.67258	+	31.0884i	−0.0142952	+	0.0783443i
$55$		0			0
$56$	56.0333	−	97.0526i	0.133710	−	0.231593i
$57$	−48.0556	+	110.801i	−0.111669	+	0.257472i
$58$	−14.1702	−	24.5435i	−0.0320799	−	0.0555641i
$59$	371.207	+	642.949i	0.819101	+	1.41873i	0.906345	+	0.422538i	$0.138861\pi$
$59$	371.207	+	642.949i	0.819101	+	1.41873i	−0.0872437	+	0.996187i	$0.527806\pi$
$60$		0			0
$61$	−4.48868	+	7.77462i	−0.00942158	+	0.0163187i	−0.870698	−	0.491818i	$-0.836332\pi$
$61$	−4.48868	+	7.77462i	−0.00942158	+	0.0163187i	0.861276	+	0.508137i	$0.169666\pi$
$62$	28.1816			0.0577269
$63$	820.300	−	190.982i	1.64044	−	0.381929i
$64$	−492.620			−0.962148
$65$		0			0
$66$	21.0795	−	2.42149i	0.0393138	−	0.00451613i
$67$	294.453	+	510.008i	0.536913	+	0.929960i	0.999068	+	0.0431613i	$0.0137429\pi$
$67$	294.453	+	510.008i	0.536913	+	0.929960i	−0.462155	+	0.886799i	$0.652924\pi$
$68$	523.185	+	906.182i	0.933021	+	1.61604i
$69$	170.279	−	19.5606i	0.297089	−	0.0341278i
$70$		0			0
$71$	−48.5526			−0.0811568			−0.0405784	−	0.999176i	$-0.512920\pi$
$71$	−48.5526			−0.0811568			−0.0405784	+	0.999176i	$0.512920\pi$
$72$	66.2847	+	70.8182i	0.108496	+	0.115917i
$73$	−409.800			−0.657034			−0.328517	−	0.944498i	$-0.606549\pi$
$73$	−409.800			−0.657034			−0.328517	+	0.944498i	$0.606549\pi$
$74$	11.2613	−	19.5051i	0.0176905	−	0.0306409i
$75$		0			0
$76$	92.3816	+	160.010i	0.139433	+	0.241505i
$77$	−282.750	−	489.737i	−0.418472	−	0.724815i
$78$	−23.3585	+	53.8572i	−0.0339080	+	0.0781811i
$79$	−265.263	+	459.449i	−0.377778	+	0.654330i	−0.990739	−	0.135783i	$-0.956645\pi$
$79$	−265.263	+	459.449i	−0.377778	+	0.654330i	0.612961	+	0.790113i	$0.289978\pi$
$80$		0			0
$81$	−48.1577	+	727.408i	−0.0660600	+	0.997816i
$82$	55.2595			0.0744195
$83$	−147.295	+	255.122i	−0.194792	+	0.337389i	−0.946832	−	0.321728i	$-0.895736\pi$
$83$	−147.295	+	255.122i	−0.194792	+	0.337389i	0.752040	+	0.659117i	$0.229070\pi$
$84$	512.688	−	1182.10i	0.665939	−	1.53544i
$85$		0			0
$86$	15.6747	+	27.1494i	0.0196541	+	0.0340418i
$87$	−389.362	−	525.174i	−0.479816	−	0.647179i
$88$	32.5639	−	56.4023i	0.0394469	−	0.0683240i
$89$	852.817			1.01571			0.507856	−	0.861442i	$-0.330438\pi$
$89$	852.817			1.01571			0.507856	+	0.861442i	$0.330438\pi$
$90$		0			0
$91$	1564.57			1.80233
$92$	131.106	−	227.082i	0.148573	−	0.257336i
$93$	645.857	−	74.1922i	0.720132	−	0.0827244i
$94$	−53.2672	−	92.2615i	−0.0584478	−	0.101234i
$95$		0			0
$96$	221.370	−	25.4296i	0.235349	−	0.0270354i
$97$	−194.045	+	336.096i	−0.203117	+	0.351808i	−0.949531	−	0.313673i	$-0.898440\pi$
$97$	−194.045	+	336.096i	−0.203117	+	0.351808i	0.746414	+	0.665481i	$0.231774\pi$
$98$	141.922			0.146289
$99$	476.719	−	110.990i	0.483960	−	0.112676i
$100$		0			0
$101$	539.997	−	935.302i	0.531997	−	0.921446i	−0.467305	−	0.884096i	$-0.654775\pi$
$101$	539.997	−	935.302i	0.531997	−	0.921446i	0.999302	−	0.0373500i	$-0.0118916\pi$
$102$	−91.7562	−	123.761i	−0.0890707	−	0.120139i
$103$	−297.498	−	515.282i	−0.284596	−	0.492935i	0.687915	−	0.725791i	$-0.258526\pi$
$103$	−297.498	−	515.282i	−0.284596	−	0.492935i	−0.972511	+	0.232856i	$0.925193\pi$
$104$	90.0948	+	156.049i	0.0849473	+	0.147133i
$105$		0			0
$106$	47.4747	−	82.2286i	0.0435014	−	0.0753467i
$107$	498.693			0.450565			0.225282	−	0.974293i	$-0.427670\pi$
$107$	498.693			0.450565			0.225282	+	0.974293i	$0.427670\pi$
$108$	850.053	+	721.938i	0.757374	+	0.643227i
$109$	−959.301			−0.842976			−0.421488	−	0.906834i	$-0.638492\pi$
$109$	−959.301			−0.842976			−0.421488	+	0.906834i	$0.638492\pi$
$110$		0			0
$111$	206.733	−	476.660i	0.176777	−	0.407590i
$112$	−979.256	−	1696.12i	−0.826170	−	1.43097i
$113$	864.396	+	1497.18i	0.719607	+	1.24640i	0.961156	+	0.276007i	$0.0890113\pi$
$113$	864.396	+	1497.18i	0.719607	+	1.24640i	−0.241549	+	0.970389i	$0.577655\pi$
$114$	−16.2019	−	21.8532i	−0.0133109	−	0.0179539i
$115$		0			0
$116$	−1000.16			−0.800536
$117$	−393.535	+	1295.78i	−0.310960	+	1.02388i
$118$	−167.228			−0.130463
$119$	−2053.05	+	3555.99i	−1.58154	+	2.73930i
$120$		0			0
$121$	501.179	+	868.068i	0.376543	+	0.652192i
$122$	−1.01107	−	1.75123i	−0.000750315	−	0.00129958i
$123$	1266.42	−	145.479i	0.928368	−	0.106645i
$124$	497.277	−	861.309i	0.360135	−	0.623773i
$125$		0			0
$126$	−55.1308	+	181.527i	−0.0389797	+	0.128347i
$127$	−1019.95			−0.712647			−0.356324	−	0.934363i	$-0.615970\pi$
$127$	−1019.95			−0.712647			−0.356324	+	0.934363i	$0.615970\pi$
$128$	227.013	−	393.197i	0.156760	−	0.271516i
$129$	430.703	+	580.936i	0.293964	+	0.396500i
$130$		0			0
$131$	851.196	+	1474.31i	0.567705	+	0.983294i	0.996792	+	0.0800308i	$0.0255019\pi$
$131$	851.196	+	1474.31i	0.567705	+	0.983294i	−0.429088	+	0.903263i	$0.641165\pi$
$132$	297.950	−	686.977i	0.196464	−	0.452983i
$133$	−362.518	+	627.900i	−0.236348	+	0.409367i
$134$	−132.651			−0.0855172
$135$		0			0
$136$	−472.893			−0.298164
$137$	−524.839	+	909.049i	−0.327300	+	0.566900i	−0.981975	−	0.189010i	$-0.939472\pi$
$137$	−524.839	+	909.049i	−0.327300	+	0.566900i	0.654675	+	0.755910i	$0.272805\pi$
$138$	−15.3619	+	35.4196i	−0.00947602	+	0.0218487i
$139$	−717.411	−	1242.59i	−0.437770	−	0.758240i	0.559747	−	0.828663i	$-0.310898\pi$
$139$	−717.411	−	1242.59i	−0.437770	−	0.758240i	−0.997517	+	0.0704236i	$0.977565\pi$
$140$		0			0
$141$	−1463.65	−	1974.18i	−0.874197	−	1.17912i
$142$	5.46823	−	9.47126i	0.00323158	−	0.00559726i
$143$	909.256			0.531719
$144$	1651.03	−	384.394i	0.955460	−	0.222450i
$145$		0			0
$146$	46.1537	−	79.9406i	0.0261624	−	0.0453146i
$147$	3252.53	−	373.631i	1.82493	−	0.209637i
$148$	−397.421	−	688.353i	−0.220728	−	0.382313i
$149$	−609.231	−	1055.22i	−0.334968	−	0.580181i	0.648511	−	0.761205i	$-0.275392\pi$
$149$	−609.231	−	1055.22i	−0.334968	−	0.580181i	−0.983479	+	0.181024i	$0.942059\pi$
$150$		0			0
$151$	−804.751	+	1393.87i	−0.433707	+	0.751202i	−0.997189	−	0.0749258i	$-0.976128\pi$
$151$	−804.751	+	1393.87i	−0.433707	+	0.751202i	0.563482	+	0.826128i	$0.309461\pi$
$152$	−83.5014			−0.0445583
$153$	−2428.66	−	2594.76i	−1.28330	−	1.37107i
$154$	127.379			0.0666524
$155$		0			0
$156$	1233.86	+	1664.23i	0.633253	+	0.854137i
$157$	643.168	+	1114.00i	0.326945	+	0.566286i	0.981904	−	0.189379i	$-0.0606474\pi$
$157$	643.168	+	1114.00i	0.326945	+	0.566286i	−0.654959	+	0.755664i	$0.727314\pi$
$158$	−59.7505	−	103.491i	−0.0300854	−	0.0521095i
$159$	871.531	−	2009.47i	0.434698	−	1.00227i
$160$		0			0
$161$	1028.95			0.503683
$162$	−136.473	−	91.3185i	−0.0661873	−	0.0442880i
$163$	−1416.84			−0.680830			−0.340415	−	0.940275i	$-0.610568\pi$
$163$	−1416.84			−0.680830			−0.340415	+	0.940275i	$0.610568\pi$
$164$	975.079	−	1688.89i	0.464273	−	0.804145i
$165$		0			0
$166$	−33.1782	−	57.4663i	−0.0155128	−	0.0268690i
$167$	447.487	+	775.071i	0.207351	+	0.359142i	0.950879	−	0.309562i	$-0.100182\pi$
$167$	447.487	+	775.071i	0.207351	+	0.359142i	−0.743528	+	0.668704i	$0.766849\pi$
$168$	346.808	+	467.777i	0.159267	+	0.214820i
$169$	−159.323	+	275.955i	−0.0725183	+	0.125605i
$170$		0			0
$171$	−428.842	−	458.172i	−0.191780	−	0.204896i
$172$	1106.35			0.490456
$173$	−867.548	+	1502.64i	−0.381263	+	0.660367i	−0.991243	−	0.132050i	$-0.957844\pi$
$173$	−867.548	+	1502.64i	−0.381263	+	0.660367i	0.609980	+	0.792417i	$0.291177\pi$
$174$	146.299	−	16.8059i	0.0637407	−	0.00732214i
$175$		0			0
$176$	−569.097	−	985.705i	−0.243735	−	0.422161i
$177$	−3832.49	+	440.253i	−1.62750	+	0.186957i
$178$	−96.0485	+	166.361i	−0.0404446	+	0.0700521i
$179$	2133.37			0.890815			0.445408	−	0.895328i	$-0.353059\pi$
$179$	2133.37			0.890815			0.445408	+	0.895328i	$0.353059\pi$
$180$		0			0
$181$	−3611.98			−1.48330			−0.741648	−	0.670789i	$-0.765955\pi$
$181$	−3611.98			−1.48330			−0.741648	+	0.670789i	$0.765955\pi$
$182$	−176.210	+	305.205i	−0.0717668	+	0.124304i
$183$	−27.7819	−	37.4724i	−0.0112224	−	0.0151368i
$184$	59.2516	+	102.627i	0.0237396	+	0.0411182i
$185$		0			0
$186$	−58.2668	+	134.345i	−0.0229695	+	0.0529603i
$187$	−1193.13	+	2066.57i	−0.466581	+	0.808142i
$188$	−3759.69			−1.45853
$189$	−785.575	+	4305.32i	−0.302340	+	1.65696i
$190$		0			0
$191$	298.495	−	517.008i	0.113080	−	0.195861i	−0.803930	−	0.594723i	$-0.797262\pi$
$191$	298.495	−	517.008i	0.113080	−	0.195861i	0.917011	+	0.398863i	$0.130595\pi$
$192$	1018.51	−	2348.37i	0.382838	−	0.882702i
$193$	−603.872	−	1045.94i	−0.225221	−	0.390094i	0.731165	−	0.682201i	$-0.238977\pi$
$193$	−603.872	−	1045.94i	−0.225221	−	0.390094i	−0.956386	+	0.292107i	$0.905644\pi$
$194$	−43.7087	−	75.7056i	−0.0161758	−	0.0280173i
$195$		0			0
$196$	2504.28	−	4337.54i	0.912639	−	1.58074i
$197$	3268.56			1.18211			0.591054	−	0.806632i	$-0.298712\pi$
$197$	3268.56			1.18211			0.591054	+	0.806632i	$0.298712\pi$
$198$	−32.0394	+	105.495i	−0.0114997	+	0.0378646i
$199$	−2109.88			−0.751585			−0.375793	−	0.926704i	$-0.622629\pi$
$199$	−2109.88			−0.751585			−0.375793	+	0.926704i	$0.622629\pi$
$200$		0			0
$201$	−3040.05	+	349.223i	−1.06681	+	0.122549i
$202$	121.634	+	210.677i	0.0423671	+	0.0733820i
$203$	−1962.38	−	3398.93i	−0.678482	−	1.17516i
$204$	−5401.57	+	620.500i	−1.85385	+	0.212959i
$205$		0			0
$206$	134.023			0.0453292
$207$	−258.811	+	852.177i	−0.0869017	+	0.286137i
$208$	3149.05			1.04975
$209$	−210.678	+	364.906i	−0.0697269	+	0.120771i
$210$		0			0
$211$	−329.321	−	570.400i	−0.107447	−	0.186104i	0.807288	−	0.590157i	$-0.200934\pi$
$211$	−329.321	−	570.400i	−0.107447	−	0.186104i	−0.914735	+	0.404053i	$0.867601\pi$
$212$	−1675.42	−	2901.92i	−0.542776	−	0.940116i
$213$	100.385	−	231.455i	0.0322923	−	0.0744556i
$214$	−56.1652	+	97.2810i	−0.0179410	+	0.0310747i
$215$		0			0
$216$	−474.644	+	169.566i	−0.149516	+	0.0534144i
$217$	3902.77			1.22091
$218$	108.041	−	187.133i	0.0335664	−	0.0581387i
$219$	847.281	−	1953.56i	0.261434	−	0.602783i
$220$		0			0
$221$	−3301.06	−	5717.60i	−1.00476	−	1.74030i
$222$	69.6997	+	94.0115i	0.0210718	+	0.0284218i
$223$	609.397	−	1055.51i	0.182997	−	0.316959i	−0.759903	−	0.650036i	$-0.774754\pi$
$223$	609.397	−	1055.51i	0.182997	−	0.316959i	0.942900	+	0.333077i	$0.108087\pi$
$224$	1337.69			0.399009
$225$		0			0
$226$	−389.410			−0.114616
$227$	−762.785	+	1321.18i	−0.223030	+	0.386299i	−0.955727	−	0.294256i	$-0.904928\pi$
$227$	−762.785	+	1321.18i	−0.223030	+	0.386299i	0.732697	+	0.680555i	$0.238261\pi$
$228$	−953.785	+	109.565i	−0.277044	+	0.0318251i
$229$	3091.33	+	5354.33i	0.892055	+	1.54508i	0.837408	+	0.546578i	$0.184070\pi$
$229$	3091.33	+	5354.33i	0.892055	+	1.54508i	0.0546469	+	0.998506i	$0.482597\pi$
$230$		0			0
$231$	2919.23	−	335.343i	0.831476	−	0.0955150i
$232$	226.004	−	391.450i	0.0639564	−	0.110776i
$233$	2013.82			0.566222			0.283111	−	0.959087i	$-0.408633\pi$
$233$	2013.82			0.566222			0.283111	+	0.959087i	$0.408633\pi$
$234$	−208.448	−	222.704i	−0.0582336	−	0.0622164i
$235$		0			0
$236$	−2950.82	+	5110.97i	−0.813906	+	1.40973i
$237$	−1641.80	−	2214.47i	−0.449984	−	0.606942i
$238$	−462.449	−	800.985i	−0.125950	−	0.218152i
$239$	−2543.15	−	4404.87i	−0.688297	−	1.19216i	−0.972389	−	0.233368i	$-0.925025\pi$
$239$	−2543.15	−	4404.87i	−0.688297	−	1.19216i	0.284092	−	0.958797i	$-0.408308\pi$
$240$		0			0
$241$	−1643.41	+	2846.47i	−0.439259	+	0.760820i	−0.997633	−	0.0687703i	$-0.978092\pi$
$241$	−1643.41	+	2846.47i	−0.439259	+	0.760820i	0.558373	+	0.829590i	$0.311426\pi$
$242$	−225.781			−0.0599742
$243$	−3368.06	−	1733.52i	−0.889140	−	0.457636i
$244$	−71.3634			−0.0187237
$245$		0			0
$246$	−114.252	+	263.428i	−0.0296115	+	0.0682746i
$247$	−582.886	−	1009.59i	−0.150154	−	0.260075i
$248$	224.738	+	389.258i	0.0575439	+	0.0996689i
$249$	−911.655	−	1229.65i	−0.232023	−	0.312955i
$250$		0			0
$251$	3480.55			0.875260			0.437630	−	0.899155i	$-0.355818\pi$
$251$	3480.55			0.875260			0.437630	+	0.899155i	$0.355818\pi$
$252$	4575.16	+	4888.07i	1.14368	+	1.22190i
$253$	597.979			0.148595
$254$	114.872	−	198.964i	0.0283768	−	0.0491501i
$255$		0			0
$256$	−1919.34	−	3324.40i	−0.468590	−	0.811621i
$257$	−3397.49	−	5884.62i	−0.824628	−	1.42830i	−0.902203	−	0.431312i	$-0.858051\pi$
$257$	−3397.49	−	5884.62i	−0.824628	−	1.42830i	0.0775746	−	0.996987i	$-0.475282\pi$
$258$	−161.832	+	18.5903i	−0.0390513	+	0.00448598i
$259$	1559.54	−	2701.19i	0.374150	−	0.648047i
$260$		0			0
$261$	3308.58	−	770.305i	0.784659	−	0.182685i
$262$	−383.464			−0.0904216
$263$	2682.12	−	4645.56i	0.628846	−	1.08919i	−0.358938	−	0.933362i	$-0.616861\pi$
$263$	2682.12	−	4645.56i	0.628846	−	1.08919i	0.987784	−	0.155832i	$-0.0498057\pi$
$264$	201.548	+	271.850i	0.0469865	+	0.0633758i
$265$		0			0
$266$	−81.6572	−	141.434i	−0.0188223	−	0.0326011i
$267$	−1763.24	+	4065.47i	−0.404152	+	0.931845i
$268$	−2340.68	+	4054.18i	−0.533508	+	0.924062i
$269$	48.4985			0.0109926			0.00549629	−	0.999985i	$-0.498250\pi$
$269$	48.4985			0.0109926			0.00549629	+	0.999985i	$0.498250\pi$
$270$		0			0
$271$	7643.16			1.71324			0.856622	−	0.515945i	$-0.172559\pi$
$271$	7643.16			1.71324			0.856622	+	0.515945i	$0.172559\pi$
$272$	−4132.22	+	7157.21i	−0.921149	+	1.59548i
$273$	−3234.83	+	7458.48i	−0.717145	+	1.65351i
$274$	−118.220	−	204.763i	−0.0260654	−	0.0451467i
$275$		0			0
$276$	811.454	+	1094.50i	0.176970	+	0.238699i
$277$	2573.01	−	4456.59i	0.558113	−	0.966680i	−0.439541	−	0.898223i	$-0.644859\pi$
$277$	2573.01	−	4456.59i	0.558113	−	0.966680i	0.997654	−	0.0684576i	$-0.0218078\pi$
$278$	323.193			0.0697261
$279$	−981.658	+	3232.26i	−0.210646	+	0.693586i
$280$		0			0
$281$	−2927.37	+	5070.35i	−0.621467	+	1.07641i	0.367746	+	0.929926i	$0.380130\pi$
$281$	−2927.37	+	5070.35i	−0.621467	+	1.07641i	−0.989213	+	0.146486i	$0.953204\pi$
$282$	549.952	−	63.1752i	0.116132	−	0.0133405i
$283$	4696.92	+	8135.31i	0.986583	+	1.70881i	0.634679	+	0.772776i	$0.281132\pi$
$283$	4696.92	+	8135.31i	0.986583	+	1.70881i	0.351904	+	0.936036i	$0.385534\pi$
$284$	−192.979	−	334.249i	−0.0403211	−	0.0698381i
$285$		0			0
$286$	−102.405	+	177.370i	−0.0211725	+	0.0366718i
$287$	7652.69			1.57395
$288$	−336.467	+	1107.87i	−0.0688420	+	0.226673i
$289$	12413.7			2.52671
$290$		0			0
$291$	−1201.01	−	1619.93i	−0.241939	−	0.326329i
$292$	−1628.81	−	2821.17i	−0.326434	−	0.565400i
$293$	−890.291	−	1542.03i	−0.177513	−	0.307462i	0.763515	−	0.645790i	$-0.223472\pi$
$293$	−890.291	−	1542.03i	−0.177513	−	0.307462i	−0.941028	+	0.338328i	$0.890139\pi$
$294$	−293.431	+	676.559i	−0.0582083	+	0.134210i
$295$		0			0
$296$	359.219			0.0705377
$297$	−456.539	+	2502.04i	−0.0891955	+	0.488833i
$298$	274.458			0.0533522
$299$	−827.217	+	1432.78i	−0.159997	+	0.277123i
$300$		0			0
$301$	2170.74	+	3759.82i	0.415678	+	0.719976i
$302$	−181.270	−	313.969i	−0.0345395	−	0.0598241i
$303$	3342.21	+	4508.00i	0.633680	+	0.854713i
$304$	−729.649	+	1263.79i	−0.137659	+	0.238432i
$305$		0			0
$306$	779.693	−	181.528i	0.145660	−	0.0339127i
$307$	−8480.18			−1.57651			−0.788256	−	0.615347i	$-0.789016\pi$
$307$	−8480.18			−1.57651			−0.788256	+	0.615347i	$0.789016\pi$
$308$	2247.65	−	3893.05i	0.415818	−	0.720218i
$309$	3071.50	−	352.835i	0.565473	−	0.0649582i
$310$		0			0
$311$	3405.40	+	5898.32i	0.620908	+	1.07544i	0.989317	+	0.145780i	$0.0465692\pi$
$311$	3405.40	+	5898.32i	0.620908	+	1.07544i	−0.368409	+	0.929664i	$0.620097\pi$
$312$	−930.176	+	106.853i	−0.168785	+	0.0193890i
$313$	4023.41	−	6968.74i	0.726570	−	1.25846i	−0.231755	−	0.972774i	$-0.574447\pi$
$313$	4023.41	−	6968.74i	0.726570	−	1.25846i	0.958325	−	0.285682i	$-0.0922200\pi$
$314$	−289.747			−0.0520744
$315$		0			0
$316$	−4217.30			−0.750764
$317$	783.112	−	1356.39i	0.138751	−	0.240323i	−0.788273	−	0.615325i	$-0.789025\pi$
$317$	783.112	−	1356.39i	0.138751	−	0.240323i	0.927024	+	0.375002i	$0.122358\pi$
$318$	293.836	+	396.328i	0.0518160	+	0.0698898i
$319$	−1140.44	−	1975.30i	−0.200164	−	0.346694i
$320$		0			0
$321$	−1031.07	+	2377.32i	−0.179280	+	0.413361i
$322$	−115.886	+	200.720i	−0.0200561	+	0.0347382i
$323$	3059.47			0.527039
$324$	−5199.07	+	2559.65i	−0.891474	+	0.438897i
$325$		0			0
$326$	159.571	−	276.385i	0.0271099	−	0.0469557i
$327$	1983.40	−	4573.08i	0.335420	−	0.773371i
$328$	440.674	+	763.271i	0.0741835	+	0.128490i
$329$	−7376.77	−	12776.9i	−1.23615	−	2.14108i
$330$		0			0
$331$	−1221.28	+	2115.32i	−0.202802	+	0.351264i	−0.949430	−	0.313978i	$-0.898338\pi$
$331$	−1221.28	+	2115.32i	−0.202802	+	0.351264i	0.746628	+	0.665242i	$0.231672\pi$
$332$	−2341.77			−0.387113
$333$	1844.85	+	1971.03i	0.303596	+	0.324360i
$334$	−201.593			−0.0330260
$335$		0			0
$336$	10110.2	−	1161.40i	1.64154	−	0.188571i
$337$	4736.49	+	8203.84i	0.765617	+	1.32609i	0.939920	+	0.341396i	$0.110900\pi$
$337$	4736.49	+	8203.84i	0.765617	+	1.32609i	−0.174302	+	0.984692i	$0.555767\pi$
$338$	−35.8874	−	62.1588i	−0.00577520	−	0.0100029i
$339$	−8924.38	+	1025.18i	−1.42981	+	0.164248i
$340$		0			0
$341$	2268.10			0.360190
$342$	137.675	−	32.0535i	0.0217678	−	0.00506799i
$343$	8954.76			1.40966
$344$	−250.000	+	433.013i	−0.0391835	+	0.0678678i
$345$		0			0
$346$	−195.415	−	338.469i	−0.0303630	−	0.0525902i
$347$	−1656.23	−	2868.68i	−0.256229	−	0.443801i	0.709000	−	0.705209i	$-0.249147\pi$
$347$	−1656.23	−	2868.68i	−0.256229	−	0.443801i	−0.965229	+	0.261408i	$0.915813\pi$
$348$	2067.87	−	4767.84i	0.318533	−	0.734435i
$349$	−2834.48	+	4909.46i	−0.434745	+	0.753001i	−0.997275	−	0.0737765i	$-0.976495\pi$
$349$	−2834.48	+	4909.46i	−0.434745	+	0.753001i	0.562530	+	0.826777i	$0.309828\pi$
$350$		0			0
$351$	−5363.44	−	4555.10i	−0.815611	−	0.692687i
$352$	777.400			0.117715
$353$	−869.541	+	1506.09i	−0.131108	+	0.227085i	−0.924104	−	0.382142i	$-0.875187\pi$
$353$	−869.541	+	1506.09i	−0.131108	+	0.227085i	0.792996	+	0.609227i	$0.208520\pi$
$354$	345.753	−	797.195i	0.0519111	−	0.119690i
$355$		0			0
$356$	3389.63	+	5871.02i	0.504636	+	0.874054i
$357$	−12707.0	−	17139.3i	−1.88382	−	2.54091i
$358$	−240.271	+	416.162i	−0.0354713	+	0.0614381i
$359$	8624.58			1.26793			0.633966	−	0.773361i	$-0.281426\pi$
$359$	8624.58			1.26793			0.633966	+	0.773361i	$0.281426\pi$
$360$		0			0
$361$	−6318.77			−0.921238
$362$	406.799	−	704.597i	0.0590632	−	0.102301i
$363$	−5174.38	+	594.401i	−0.748166	+	0.0859449i
$364$	6218.60	+	10770.9i	0.895449	+	1.55096i
$365$		0			0
$366$	10.4387	−	1.19914i	0.00149083	−	0.000171257i
$367$	−3054.59	+	5290.70i	−0.434463	+	0.752513i	−0.997252	−	0.0740883i	$-0.976395\pi$
$367$	−3054.59	+	5290.70i	−0.434463	+	0.752513i	0.562788	+	0.826601i	$0.309729\pi$
$368$	2071.00			0.293365
$369$	−1924.87	+	6337.94i	−0.271558	+	0.894146i
$370$		0			0
$371$	6574.59	−	11387.5i	0.920043	−	1.59356i
$372$	3077.80	+	4151.36i	0.428969	+	0.578597i
$373$	3277.67	+	5677.08i	0.454990	+	0.788065i	0.998688	−	0.0512159i	$-0.0163097\pi$
$373$	3277.67	+	5677.08i	0.454990	+	0.788065i	−0.543698	+	0.839281i	$0.682976\pi$
$374$	−268.753	−	465.494i	−0.0371575	−	0.0643587i
$375$		0			0
$376$	849.572	−	1471.50i	0.116525	−	0.201827i
$377$	6310.52			0.862092
$378$	−751.372	−	638.130i	−0.102239	−	0.0868303i
$379$	5032.40			0.682050			0.341025	−	0.940054i	$-0.389226\pi$
$379$	5032.40			0.682050			0.341025	+	0.940054i	$0.389226\pi$
$380$		0			0
$381$	2108.80	−	4862.22i	0.283562	−	0.653803i
$382$	67.2359	+	116.456i	0.00900547	+	0.0155979i
$383$	1831.49	+	3172.24i	0.244347	+	0.423222i	0.961948	−	0.273233i	$-0.0880930\pi$
$383$	1831.49	+	3172.24i	0.244347	+	0.423222i	−0.717601	+	0.696455i	$0.754760\pi$
$384$	1405.05	+	1895.15i	0.186722	+	0.251852i
$385$		0			0
$386$	272.044			0.0358722
$387$	−3659.88	+	852.094i	−0.480729	+	0.111923i
$388$	−3085.03			−0.403657
$389$	2435.48	−	4218.37i	0.317439	−	0.549820i	−0.662514	−	0.749049i	$-0.730511\pi$
$389$	2435.48	−	4218.37i	0.317439	−	0.549820i	0.979953	+	0.199229i	$0.0638438\pi$
$390$		0			0
$391$	−2170.97	−	3760.22i	−0.280794	−	0.486349i
$392$	1131.78	+	1960.30i	0.145825	+	0.252577i
$393$	−8788.09	+	1009.52i	−1.12799	+	0.129577i
$394$	−368.121	+	637.605i	−0.0470703	+	0.0815281i
$395$		0			0
$396$	2658.87	+	2840.72i	0.337407	+	0.360483i
$397$	3744.62			0.473393			0.236696	−	0.971584i	$-0.423935\pi$
$397$	3744.62			0.473393			0.236696	+	0.971584i	$0.423935\pi$
$398$	237.625	−	411.579i	0.0299273	−	0.0518356i
$399$	−2243.74	−	3026.37i	−0.281523	−	0.379720i
$400$		0			0
$401$	900.435	+	1559.60i	0.112134	+	0.194221i	0.916630	−	0.399736i	$-0.130898\pi$
$401$	900.435	+	1559.60i	0.112134	+	0.194221i	−0.804497	+	0.593957i	$0.797565\pi$
$402$	274.262	−	632.361i	0.0340272	−	0.0784559i
$403$	−3137.59	+	5434.46i	−0.387827	+	0.671737i
$404$	8585.16			1.05725
$405$		0			0
$406$	884.049			0.108066
$407$	906.328	−	1569.81i	0.110381	−	0.191185i
$408$	977.729	−	2254.33i	0.118639	−	0.273544i
$409$	−7965.99	−	13797.5i	−0.963064	−	1.66808i	−0.714730	−	0.699401i	$-0.753450\pi$
$409$	−7965.99	−	13797.5i	−0.963064	−	1.66808i	−0.248334	−	0.968675i	$-0.579883\pi$
$410$		0			0
$411$	−3248.40	−	4381.46i	−0.389858	−	0.525843i
$412$	2364.89	−	4096.12i	0.282791	−	0.489809i
$413$	−23158.8			−2.75926
$414$	−137.087	−	146.463i	−0.0162741	−	0.0173871i
$415$		0			0
$416$	−1075.42	+	1862.68i	−0.126747	+	0.219532i
$417$	7406.84	−	850.854i	0.869820	−	0.0999196i
$418$	−47.4553	−	82.1949i	−0.00555290	−	0.00961791i
$419$	1723.87	+	2985.84i	0.200995	+	0.348133i	0.948849	−	0.315730i	$-0.102249\pi$
$419$	1723.87	+	2985.84i	0.200995	+	0.348133i	−0.747854	+	0.663863i	$0.768916\pi$
$420$		0			0
$421$	−2807.99	+	4863.58i	−0.325066	+	0.563032i	−0.981526	−	0.191330i	$-0.938720\pi$
$421$	−2807.99	+	4863.58i	−0.325066	+	0.563032i	0.656459	+	0.754361i	$0.272053\pi$
$422$	148.359			0.0171137
$423$	12437.3	−	2895.66i	1.42960	−	0.332841i
$424$	1514.37			0.173454
$425$		0			0
$426$	33.8446	+	45.6499i	0.00384924	+	0.00519189i
$427$	−140.020	−	242.522i	−0.0158689	−	0.0274858i
$428$	1982.12	+	3433.13i	0.223854	+	0.387726i
$429$	−1879.93	+	4334.51i	−0.211571	+	0.487814i
$430$		0			0
$431$	−3534.04			−0.394962			−0.197481	−	0.980307i	$-0.563276\pi$
$431$	−3534.04			−0.394962			−0.197481	+	0.980307i	$0.563276\pi$
$432$	−1581.14	+	8665.40i	−0.176094	+	0.965080i
$433$	−6674.80			−0.740809			−0.370405	−	0.928871i	$-0.620781\pi$
$433$	−6674.80			−0.740809			−0.370405	+	0.928871i	$0.620781\pi$
$434$	−439.549	+	761.321i	−0.0486153	+	0.0842041i
$435$		0			0
$436$	−3812.87	−	6604.08i	−0.418815	−	0.725408i
$437$	−383.339	−	663.963i	−0.0419625	−	0.0726812i
$438$	285.660	+	385.301i	0.0311629	+	0.0420328i
$439$	3271.76	−	5666.85i	0.355700	−	0.616091i	−0.631537	−	0.775346i	$-0.717576\pi$
$439$	3271.76	−	5666.85i	0.355700	−	0.616091i	0.987238	+	0.159254i	$0.0509090\pi$
$440$		0			0
$441$	−4943.62	+	16277.7i	−0.533811	+	1.75766i
$442$	1487.12			0.160035
$443$	7154.86	−	12392.6i	0.767353	−	1.32909i	−0.171640	−	0.985160i	$-0.554907\pi$
$443$	7154.86	−	12392.6i	0.767353	−	1.32909i	0.938993	−	0.343935i	$-0.111760\pi$
$444$	4103.14	−	471.344i	0.438573	−	0.0503806i
$445$		0			0
$446$	137.267	+	237.753i	0.0145734	+	0.0252420i
$447$	6289.95	−	722.552i	0.665558	−	0.0764553i
$448$	7683.39	−	13308.0i	0.810282	−	1.40345i
$449$	−14587.4			−1.53324			−0.766618	−	0.642104i	$-0.778062\pi$
$449$	−14587.4			−1.53324			−0.766618	+	0.642104i	$0.778062\pi$
$450$		0			0
$451$	4447.38			0.464343
$452$	−6871.31	+	11901.5i	−0.715043	+	1.23849i
$453$	−4980.86	−	6718.22i	−0.516603	−	0.696798i
$454$	−171.817	−	297.596i	−0.0177616	−	0.0307640i
$455$		0			0
$456$	172.643	−	398.060i	0.0177297	−	0.0408791i
$457$	1012.89	−	1754.37i	0.103678	−	0.179576i	−0.809519	−	0.587093i	$-0.800272\pi$
$457$	1012.89	−	1754.37i	0.103678	−	0.179576i	0.913197	+	0.407518i	$0.133606\pi$
$458$	−1392.64			−0.142083
$459$	17390.9	−	6212.87i	1.76849	−	0.631790i
$460$		0			0
$461$	1778.09	−	3079.75i	0.179640	−	0.311146i	−0.762117	−	0.647439i	$-0.775840\pi$
$461$	1778.09	−	3079.75i	0.179640	−	0.311146i	0.941757	+	0.336293i	$0.109173\pi$
$462$	−263.362	+	607.228i	−0.0265210	+	0.0611489i
$463$	−5141.34	−	8905.07i	−0.516066	−	0.893852i	−0.999826	−	0.0186517i	$-0.994063\pi$
$463$	−5141.34	−	8905.07i	−0.516066	−	0.893852i	0.483760	−	0.875201i	$-0.339271\pi$
$464$	−3949.72	−	6841.11i	−0.395174	−	0.684462i
$465$		0			0
$466$	−226.806	+	392.840i	−0.0225464	+	0.0390514i
$467$	−8217.44			−0.814256			−0.407128	−	0.913371i	$-0.633470\pi$
$467$	−8217.44			−0.814256			−0.407128	+	0.913371i	$0.633470\pi$
$468$	−10484.6	+	2441.03i	−1.03558	+	0.241104i
$469$	−18370.3			−1.80866
$470$		0			0
$471$	−6640.33	+	762.801i	−0.649618	+	0.0746242i
$472$	−1333.59	−	2309.84i	−0.130049	−	0.225252i
$473$	1261.53	+	2185.03i	0.122632	+	0.212406i
$474$	616.889	−	70.8645i	0.0597777	−	0.00686690i
$475$		0			0
$476$	−32640.5			−3.14301
$477$	7777.43	+	8309.35i	0.746549	+	0.797608i
$478$	1145.69			0.109629
$479$	−6842.59	+	11851.7i	−0.652705	+	1.13052i	0.329759	+	0.944065i	$0.393033\pi$
$479$	−6842.59	+	11851.7i	−0.652705	+	1.13052i	−0.982464	+	0.186453i	$0.940301\pi$
$480$		0			0
$481$	2507.54	+	4343.19i	0.237701	+	0.411710i
$482$	−370.178	−	641.168i	−0.0349817	−	0.0605900i
$483$	−2127.41	+	4905.13i	−0.200415	+	0.462093i
$484$	−3984.00	+	6900.50i	−0.374155	+	0.648056i
$485$		0			0
$486$	717.489	−	461.776i	0.0669670	−	0.0431000i
$487$	3239.59			0.301437			0.150718	−	0.988577i	$-0.451841\pi$
$487$	3239.59			0.301437			0.150718	+	0.988577i	$0.451841\pi$
$488$	16.1259	−	27.9309i	0.00149587	−	0.00259092i
$489$	2929.38	−	6754.21i	0.270902	−	0.624613i
$490$		0			0
$491$	−5564.04	−	9637.20i	−0.511409	−	0.885786i	−0.999913	−	0.0132239i	$-0.995791\pi$
$491$	−5564.04	−	9637.20i	−0.511409	−	0.885786i	0.488504	−	0.872562i	$-0.337543\pi$
$492$	6035.07	+	8140.15i	0.553012	+	0.745907i
$493$	−8280.74	+	14342.7i	−0.756482	+	1.31027i
$494$	262.590			0.0239159
$495$		0			0
$496$	7855.18			0.711105
$497$	757.276	−	1311.64i	0.0683470	−	0.118380i
$498$	342.545	−	39.3495i	0.0308229	−	0.00354075i
$499$	2713.61	+	4700.11i	0.243443	+	0.421655i	0.961693	−	0.274130i	$-0.0883899\pi$
$499$	2713.61	+	4700.11i	0.243443	+	0.421655i	−0.718250	+	0.695785i	$0.755057\pi$
$500$		0			0
$501$	−4620.04	+	530.723i	−0.411992	+	0.0473272i
$502$	−391.997	+	678.958i	−0.0348519	+	0.0603653i
$503$	9600.22			0.850999			0.425500	−	0.904959i	$-0.360098\pi$
$503$	9600.22			0.850999			0.425500	+	0.904959i	$0.360098\pi$
$504$	−2946.98	+	686.117i	−0.260454	+	0.0606391i
$505$		0			0
$506$	−67.3474	+	116.649i	−0.00591691	+	0.0102484i
$507$	−986.098	−	1330.06i	−0.0863790	−	0.116509i
$508$	−4053.94	−	7021.62i	−0.354064	−	0.613256i
$509$	9469.94	+	16402.4i	0.824652	+	1.42834i	0.902185	+	0.431349i	$0.141962\pi$
$509$	9469.94	+	16402.4i	0.824652	+	1.42834i	−0.0775333	+	0.996990i	$0.524704\pi$
$510$		0			0
$511$	6391.66	−	11070.7i	0.553328	−	0.958392i
$512$	4496.87			0.388155
$513$	3070.80	−	1097.04i	0.264287	−	0.0944162i
$514$	1530.57			0.131343
$515$		0			0
$516$	−2287.43	+	5274.08i	−0.195152	+	0.449958i
$517$	−4287.03	−	7425.35i	−0.364687	−	0.631657i
$518$	351.285	+	608.444i	0.0297965	+	0.0516090i
$519$	−5369.53	−	7242.46i	−0.454135	−	0.612541i
$520$		0			0
$521$	19292.6			1.62231			0.811155	−	0.584831i	$-0.198839\pi$
$521$	19292.6			1.62231			0.811155	+	0.584831i	$0.198839\pi$
$522$	−222.364	+	732.168i	−0.0186448	+	0.0613910i
$523$	−17967.5			−1.50223			−0.751114	−	0.660172i	$-0.770483\pi$
$523$	−17967.5			−1.50223			−0.751114	+	0.660172i	$0.770483\pi$
$524$	−6766.38	+	11719.7i	−0.564104	+	0.977057i
$525$		0			0
$526$	604.147	+	1046.41i	0.0500799	+	0.0867410i
$527$	−8234.35	−	14262.3i	−0.680634	−	1.17889i
$528$	5875.59	−	674.952i	0.484285	−	0.0556317i
$529$	5539.47	−	9594.65i	0.455287	−	0.788580i
$530$		0			0
$531$	5825.11	−	19180.1i	0.476061	−	1.56751i
$532$	−5763.51			−0.469699
$533$	−6152.30	+	10656.1i	−0.499973	+	0.865979i
$534$	−594.474	−	801.832i	−0.0481749	−	0.0649787i
$535$		0			0
$536$	−1057.84	−	1832.24i	−0.0852460	−	0.147650i
$537$	−4410.85	+	10170.0i	−0.354455	+	0.817260i
$538$	−5.46214	+	9.46070i	−0.000437713	+	0.000758141i
$539$	11422.1			0.912777
$540$		0			0
$541$	−8299.36			−0.659552			−0.329776	−	0.944059i	$-0.606973\pi$
$541$	−8299.36			−0.659552			−0.329776	+	0.944059i	$0.606973\pi$
$542$	−860.811	+	1490.97i	−0.0682195	+	0.118160i
$543$	7467.94	−	17218.7i	0.590203	−	1.36082i
$544$	−2822.35	−	4888.46i	−0.222440	−	0.385278i
$545$		0			0
$546$	−1090.62	−	1471.04i	−0.0854839	−	0.115301i
$547$	42.3605	−	73.3706i	0.00331116	−	0.00573510i	−0.864365	−	0.502865i	$-0.832279\pi$
$547$	42.3605	−	73.3706i	0.00331116	−	0.00573510i	0.867676	+	0.497130i	$0.165613\pi$
$548$	−8344.17			−0.650448
$549$	236.075	−	54.9630i	0.0183523	−	0.00427280i
$550$		0			0
$551$	−1462.18	+	2532.56i	−0.113050	+	0.195809i
$552$	−611.737	+	70.2727i	−0.0471690	+	0.00541849i
$553$	−8274.63	−	14332.1i	−0.636298	−	1.10210i
$554$	579.571	+	1003.85i	0.0444469	+	0.0769843i
$555$		0			0
$556$	5702.89	−	9877.69i	0.434994	−	0.753431i
$557$	20914.0			1.59094			0.795469	−	0.605994i	$-0.207224\pi$
$557$	20914.0			1.59094			0.795469	+	0.605994i	$0.207224\pi$
$558$	−519.965	−	555.527i	−0.0394478	−	0.0421458i
$559$	−6980.56			−0.528169
$560$		0			0
$561$	−7384.69	−	9960.52i	−0.555761	−	0.749614i
$562$	−659.389	−	1142.10i	−0.0494923	−	0.0857231i
$563$	5520.48	+	9561.76i	0.413252	+	0.715773i	0.995243	−	0.0974220i	$-0.0310596\pi$
$563$	5520.48	+	9561.76i	0.413252	+	0.715773i	−0.581991	+	0.813195i	$0.697726\pi$
$564$	7773.33	−	17922.8i	0.580348	−	1.33810i
$565$		0			0
$566$	−2115.96			−0.157139
$567$	−18899.7	−	12646.4i	−1.39984	−	0.936679i
$568$	174.429			0.0128853
$569$	3007.31	−	5208.81i	0.221569	−	0.383770i	−0.733715	−	0.679457i	$-0.762215\pi$
$569$	3007.31	−	5208.81i	0.221569	−	0.383770i	0.955285	+	0.295688i	$0.0955487\pi$
$570$		0			0
$571$	10968.7	+	18998.3i	0.803896	+	1.39239i	0.917034	+	0.398810i	$0.130577\pi$
$571$	10968.7	+	18998.3i	0.803896	+	1.39239i	−0.113137	+	0.993579i	$0.536090\pi$
$572$	3613.96	+	6259.56i	0.264173	+	0.457561i
$573$	1847.48	+	2491.89i	0.134694	+	0.181676i
$574$	−861.884	+	1492.83i	−0.0626730	+	0.108553i
$575$		0			0
$576$	9089.08	+	9710.72i	0.657486	+	0.702454i
$577$	−473.507			−0.0341635			−0.0170818	−	0.999854i	$-0.505438\pi$
$577$	−473.507			−0.0341635			−0.0170818	+	0.999854i	$0.505438\pi$
$578$	−1398.09	+	2421.57i	−0.100611	+	0.174263i
$579$	6234.62	−	716.196i	0.447499	−	0.0514060i
$580$		0			0
$581$	−4594.72	−	7958.29i	−0.328092	−	0.568271i
$582$	451.266	−	51.8387i	0.0321402	−	0.00369207i
$583$	3820.84	−	6617.89i	0.271429	−	0.470129i
$584$	1472.24			0.104318
$585$		0			0
$586$	401.076			0.0282735
$587$	6510.17	−	11275.9i	0.457757	−	0.792859i	−0.541085	−	0.840968i	$-0.681986\pi$
$587$	6510.17	−	11275.9i	0.457757	−	0.792859i	0.998842	+	0.0481093i	$0.0153196\pi$
$588$	15499.8	+	20906.2i	1.08708	+	1.46626i
$589$	−1453.99	−	2518.38i	−0.101715	−	0.176176i
$590$		0			0
$591$	−6757.90	+	15581.6i	−0.470360	+	1.08450i
$592$	3138.91	−	5436.75i	0.217920	−	0.377448i
$593$	12887.3			0.892441			0.446220	−	0.894923i	$-0.352770\pi$
$593$	12887.3			0.892441			0.446220	+	0.894923i	$0.352770\pi$
$594$	−436.661	−	370.851i	−0.0301623	−	0.0256165i
$595$		0			0
$596$	4842.94	−	8388.22i	0.332843	−	0.576501i
$597$	4362.28	−	10058.0i	0.299055	−	0.689526i
$598$	−186.330	−	322.734i	−0.0127418	−	0.0220695i
$599$	4337.24	+	7512.32i	0.295851	+	0.512429i	0.975182	−	0.221403i	$-0.0710635\pi$
$599$	4337.24	+	7512.32i	0.295851	+	0.512429i	−0.679332	+	0.733832i	$0.737730\pi$
$600$		0			0
$601$	−5467.86	+	9470.61i	−0.371112	+	0.642786i	−0.989737	−	0.142901i	$-0.954357\pi$
$601$	−5467.86	+	9470.61i	−0.371112	+	0.642786i	0.618625	+	0.785687i	$0.287690\pi$
$602$	−977.916			−0.0662074
$603$	4620.67	−	15214.3i	0.312053	−	1.02748i
$604$	−12794.4			−0.861913
$605$		0			0
$606$	−1255.80	+	144.259i	−0.0841806	+	0.00967016i
$607$	10835.2	+	18767.1i	0.724527	+	1.25492i	0.959168	+	0.282836i	$0.0912751\pi$
$607$	10835.2	+	18767.1i	0.724527	+	1.25492i	−0.234641	+	0.972082i	$0.575392\pi$
$608$	−498.359	−	863.183i	−0.0332420	−	0.0575768i
$609$	20260.4	−	2327.39i	1.34810	−	0.154861i
$610$		0			0
$611$	23721.9			1.57068
$612$	8210.01	−	27032.7i	0.542271	−	1.78551i
$613$	15571.2			1.02596			0.512982	−	0.858399i	$-0.328541\pi$
$613$	15571.2			1.02596			0.512982	+	0.858399i	$0.328541\pi$
$614$	955.079	−	1654.25i	0.0627750	−	0.108730i
$615$		0			0
$616$	1015.80	+	1759.42i	0.0664411	+	0.115079i
$617$	4863.27	+	8423.43i	0.317322	+	0.549618i	0.979928	−	0.199350i	$-0.0638829\pi$
$617$	4863.27	+	8423.43i	0.317322	+	0.549618i	−0.662606	+	0.748968i	$0.730550\pi$
$618$	−277.099	+	638.901i	−0.0180365	+	0.0415864i
$619$	−3148.79	+	5453.87i	−0.204460	+	0.354135i	−0.949961	−	0.312370i	$-0.898877\pi$
$619$	−3148.79	+	5453.87i	−0.204460	+	0.354135i	0.745501	+	0.666505i	$0.232210\pi$
$620$		0			0
$621$	−3527.31	−	2995.70i	−0.227933	−	0.193580i
$622$	−1534.13			−0.0988955
$623$	−13301.4	+	23038.7i	−0.855392	+	1.48158i
$624$	−6510.81	+	15011.8i	−0.417694	+	0.963069i
$625$		0			0
$626$	906.272	+	1569.71i	0.0578625	+	0.100221i
$627$	−1303.95	−	1758.78i	−0.0830541	−	0.112024i
$628$	−5112.71	+	8855.47i	−0.324872	+	0.562694i
$629$	−13161.7			−0.834327
$630$		0			0
$631$	−5670.98			−0.357778			−0.178889	−	0.983869i	$-0.557250\pi$
$631$	−5670.98			−0.357778			−0.178889	+	0.983869i	$0.557250\pi$
$632$	952.977	−	1650.60i	0.0599800	−	0.103888i
$633$	3400.04	−	390.576i	0.213491	−	0.0245245i
$634$	176.396	+	305.527i	0.0110498	+	0.0191388i
$635$		0			0
$636$	17297.7	−	1987.06i	1.07846	−	0.123887i
$637$	−15800.9	+	27367.9i	−0.982816	+	1.70229i
$638$	513.767			0.0318813
$639$	895.820	+	957.089i	0.0554587	+	0.0592517i
$640$		0			0
$641$	−10832.3	+	18762.0i	−0.667470	+	1.15609i	0.311140	+	0.950364i	$0.399289\pi$
$641$	−10832.3	+	18762.0i	−0.667470	+	1.15609i	−0.978609	+	0.205727i	$0.934044\pi$
$642$	−347.624	−	468.878i	−0.0213701	−	0.0288242i
$643$	3111.86	+	5389.90i	0.190855	+	0.330570i	0.945534	−	0.325524i	$-0.105541\pi$
$643$	3111.86	+	5389.90i	0.190855	+	0.330570i	−0.754679	+	0.656094i	$0.772207\pi$
$644$	4089.71	+	7083.59i	0.250244	+	0.433436i
$645$		0			0
$646$	−344.573	+	596.818i	−0.0209861	+	0.0363491i
$647$	−20451.9			−1.24273			−0.621365	−	0.783521i	$-0.713422\pi$
$647$	−20451.9			−1.24273			−0.621365	+	0.783521i	$0.713422\pi$
$648$	173.010	−	2613.26i	0.0104884	−	0.158424i
$649$	−13458.8			−0.814029
$650$		0			0
$651$	−8069.15	+	18604.9i	−0.485799	+	1.12010i
$652$	−5631.41	−	9753.88i	−0.338256	−	0.585876i
$653$	3724.22	+	6450.54i	0.223185	+	0.386568i	0.955773	−	0.294104i	$-0.0950211\pi$
$653$	3724.22	+	6450.54i	0.223185	+	0.386568i	−0.732588	+	0.680672i	$0.761688\pi$
$654$	668.701	+	901.949i	0.0399821	+	0.0539281i
$655$		0			0
$656$	15402.7			0.916731
$657$	7561.03	+	8078.15i	0.448986	+	0.479694i
$658$	3323.23			0.196889
$659$	−413.185	+	715.658i	−0.0244240	+	0.0423036i	−0.877979	−	0.478699i	$-0.841109\pi$
$659$	−413.185	+	715.658i	−0.0244240	+	0.0423036i	0.853555	+	0.521003i	$0.174442\pi$
$660$		0			0
$661$	3129.11	+	5419.77i	0.184127	+	0.318918i	0.943282	−	0.331992i	$-0.107721\pi$
$661$	3129.11	+	5419.77i	0.184127	+	0.318918i	−0.759155	+	0.650910i	$0.774387\pi$
$662$	−275.093	−	476.475i	−0.0161507	−	0.0279739i
$663$	34081.4	−	3915.07i	1.99640	−	0.229334i
$664$	529.167	−	916.545i	0.0309272	−	0.0535675i
$665$		0			0
$666$	−592.270	+	137.892i	−0.0344594	+	0.00802286i
$667$	4150.17			0.240922
$668$	−3557.19	+	6161.24i	−0.206036	+	0.356865i
$669$	3771.75	+	5087.36i	0.217973	+	0.294004i
$670$		0			0
$671$	−81.3729	−	140.942i	−0.00468162	−	0.00810880i
$672$	−2765.73	+	6376.89i	−0.158765	+	0.366062i
$673$	−5039.90	+	8729.36i	−0.288668	+	0.499988i	−0.973492	−	0.228720i	$-0.926546\pi$
$673$	−5039.90	+	8729.36i	−0.288668	+	0.499988i	0.684824	+	0.728709i	$0.259879\pi$
$674$	−2133.79			−0.121944
$675$		0			0
$676$	−2532.99			−0.144117
$677$	−12855.2	+	22265.9i	−0.729788	+	1.26403i	0.227185	+	0.973852i	$0.427048\pi$
$677$	−12855.2	+	22265.9i	−0.729788	+	1.26403i	−0.956973	+	0.290178i	$0.906285\pi$
$678$	805.124	−	1856.36i	0.0456056	−	0.105152i
$679$	−6053.05	−	10484.2i	−0.342113	−	0.592557i
$680$		0			0
$681$	−4721.11	−	6367.88i	−0.265659	−	0.358322i
$682$	−255.445	+	442.443i	−0.0143424	+	0.0248417i
$683$	32091.0			1.79784			0.898922	−	0.438109i	$-0.144352\pi$
$683$	32091.0			1.79784			0.898922	+	0.438109i	$0.144352\pi$
$684$	1449.69	−	4773.32i	0.0810383	−	0.266831i
$685$		0			0
$686$	−1008.53	+	1746.82i	−0.0561310	+	0.0972217i
$687$	−31916.1	+	3666.33i	−1.77245	+	0.203609i
$688$	4369.09	+	7567.48i	0.242107	+	0.419342i
$689$	10571.2	+	18309.8i	0.584512	+	1.01240i
$690$		0			0
$691$	−5282.87	+	9150.20i	−0.290839	+	0.503748i	−0.974008	−	0.226512i	$-0.927268\pi$
$691$	−5282.87	+	9150.20i	−0.290839	+	0.503748i	0.683169	+	0.730260i	$0.260601\pi$
$692$	−13792.7			−0.757690
$693$	−4437.02	+	14609.6i	−0.243216	+	0.800826i
$694$	746.133			0.0408110
$695$		0			0
$696$	1398.81	+	1886.72i	0.0761806	+	0.102753i
$697$	−16146.2	−	27966.1i	−0.877449	−	1.51979i
$698$	−638.465	−	1105.85i	−0.0346222	−	0.0599673i
$699$	−4163.67	+	9600.09i	−0.225300	+	0.519469i
$700$		0			0
$701$	13081.8			0.704837			0.352419	−	0.935842i	$-0.385359\pi$
$701$	13081.8			0.704837			0.352419	+	0.935842i	$0.385359\pi$
$702$	1492.63	−	533.240i	0.0802503	−	0.0286693i
$703$	−2324.04			−0.124684
$704$	4465.22	−	7733.99i	0.239047	−	0.414042i
$705$		0			0
$706$	−195.864	−	339.246i	−0.0104411	−	0.0180846i
$707$	16844.7	+	29175.8i	0.896053	+	1.55201i
$708$	−18263.5	−	24634.0i	−0.969472	−	1.30763i
$709$	14110.6	−	24440.3i	0.747440	−	1.29460i	−0.201606	−	0.979467i	$-0.564616\pi$
$709$	14110.6	−	24440.3i	0.747440	−	1.29460i	0.949046	−	0.315137i	$-0.102051\pi$
$710$		0			0
$711$	13951.1	−	3248.10i	0.735875	−	0.171327i
$712$	−3063.80			−0.161265
$713$	−2063.46	+	3574.02i	−0.108383	+	0.187725i
$714$	4774.51	−	548.467i	0.250254	−	0.0287477i
$715$		0			0
$716$	8479.38	+	14686.7i	0.442583	+	0.766576i
$717$	26256.5	−	3016.19i	1.36760	−	0.157102i
$718$	−971.342	+	1682.41i	−0.0504877	+	0.0874473i
$719$	−11471.4			−0.595010			−0.297505	−	0.954720i	$-0.596154\pi$
$719$	−11471.4			−0.595010			−0.297505	+	0.954720i	$0.596154\pi$
$720$		0			0
$721$	18560.3			0.958701
$722$	711.651	−	1232.62i	0.0366827	−	0.0635363i
$723$	−10171.6	−	13719.5i	−0.523217	−	0.705719i
$724$	−14356.3	−	24865.8i	−0.736944	−	1.27642i
$725$		0			0
$726$	466.813	−	1076.32i	0.0238637	−	0.0550221i
$727$	10829.6	−	18757.5i	0.552475	−	0.956914i	−0.445621	−	0.895222i	$-0.647017\pi$
$727$	10829.6	−	18757.5i	0.552475	−	0.956914i	0.998095	−	0.0616922i	$-0.0196497\pi$
$728$	−5620.84			−0.286157
$729$	15227.5	−	12471.7i	0.773636	−	0.633630i
$730$		0			0
$731$	9159.96	−	15865.5i	0.463466	−	0.802746i
$732$	147.547	−	340.197i	0.00745013	−	0.0171776i
$733$	2840.86	+	4920.51i	0.143151	+	0.247944i	0.928682	−	0.370878i	$-0.120943\pi$
$733$	2840.86	+	4920.51i	0.143151	+	0.247944i	−0.785531	+	0.618823i	$0.787610\pi$
$734$	−688.045	−	1191.73i	−0.0345997	−	0.0599285i
$735$		0			0
$736$	−707.259	+	1225.01i	−0.0354211	+	0.0613511i
$737$	−10676.0			−0.533588
$738$	−1019.57	−	1089.30i	−0.0508547	−	0.0543328i
$739$	261.324			0.0130080			0.00650402	−	0.999979i	$-0.497930\pi$
$739$	261.324			0.0130080			0.00650402	+	0.999979i	$0.497930\pi$
$740$		0			0
$741$	6017.95	−	691.306i	0.298347	−	0.0342723i
$742$	1480.93	+	2565.04i	0.0732702	+	0.126908i
$743$	−8202.97	−	14208.0i	−0.405031	−	0.701533i	0.589294	−	0.807918i	$-0.299406\pi$
$743$	−8202.97	−	14208.0i	−0.405031	−	0.701533i	−0.994325	+	0.106385i	$0.966072\pi$
$744$	−2320.29	+	266.541i	−0.114336	+	0.0131342i
$745$		0			0
$746$	−1476.59			−0.0724688
$747$	7746.74	−	1803.60i	0.379436	−	0.0883403i
$748$	−18969.1			−0.927244
$749$	−7778.11	+	13472.1i	−0.379447	+	0.657222i
$750$		0			0
$751$	−10737.3	−	18597.5i	−0.521716	−	0.903639i	−0.999681	−	0.0252601i	$-0.991959\pi$
$751$	−10737.3	−	18597.5i	−0.521716	−	0.903639i	0.477965	−	0.878379i	$-0.341375\pi$
$752$	−14847.4	−	25716.4i	−0.719985	−	1.24705i
$753$	−7196.20	+	16592.1i	−0.348266	+	0.802989i
$754$	−710.722	+	1231.01i	−0.0343276	+	0.0594571i
$755$		0			0
$756$	−32761.3	+	11703.9i	−1.57608	+	0.563053i
$757$	13643.2			0.655046			0.327523	−	0.944843i	$-0.393786\pi$
$757$	13643.2			0.655046			0.327523	+	0.944843i	$0.393786\pi$
$758$	−566.773	+	981.680i	−0.0271585	+	0.0470399i
$759$	−1236.35	+	2850.63i	−0.0591260	+	0.136326i
$760$		0			0
$761$	−13469.0	−	23328.9i	−0.641589	−	1.11127i	−0.985078	−	0.172109i	$-0.944942\pi$
$761$	−13469.0	−	23328.9i	−0.641589	−	1.11127i	0.343489	−	0.939157i	$-0.388391\pi$
$762$	710.980	+	958.975i	0.0338006	+	0.0455905i
$763$	14962.2	−	25915.3i	0.709920	−	1.22962i
$764$	4745.63			0.224726
$765$		0			0
$766$	−825.088			−0.0389186
$767$	18618.3	−	32247.9i	0.876491	−	1.51813i
$768$	19816.1	−	2276.35i	0.931057	−	0.106954i
$769$	14442.7	+	25015.5i	0.677265	+	1.17306i	0.975801	+	0.218659i	$0.0701683\pi$
$769$	14442.7	+	25015.5i	0.677265	+	1.17306i	−0.298536	+	0.954398i	$0.596498\pi$
$770$		0			0
$771$	35077.1	−	4029.44i	1.63848	−	0.188219i
$772$	4800.34	−	8314.43i	0.223793	−	0.387620i
$773$	−3031.34			−0.141048			−0.0705238	−	0.997510i	$-0.522467\pi$
$773$	−3031.34			−0.141048			−0.0705238	+	0.997510i	$0.522467\pi$
$774$	245.974	−	809.907i	0.0114229	−	0.0376118i
$775$		0			0
$776$	697.121	−	1207.45i	0.0322490	−	0.0558568i
$777$	9652.46	+	13019.3i	0.445663	+	0.601113i
$778$	548.591	+	950.188i	0.0252801	+	0.0437865i
$779$	−2851.03	−	4938.13i	−0.131128	−	0.227120i
$780$		0			0
$781$	440.092	−	762.262i	0.0201636	−	0.0349243i
$782$	978.019			0.0447236
$783$	−3168.52	+	17365.0i	−0.144615	+	0.792559i
$784$	39558.7			1.80205
$785$		0			0
$786$	792.829	−	1828.01i	0.0359787	−	0.0829554i
$787$	7577.38	+	13124.4i	0.343208	+	0.594453i	0.985026	−	0.172403i	$-0.0551532\pi$
$787$	7577.38	+	13124.4i	0.343208	+	0.594453i	−0.641819	+	0.766856i	$0.721820\pi$
$788$	12991.3	+	22501.6i	0.587306	+	1.01724i
$789$	16600.5	+	22390.8i	0.749040	+	1.01031i
$790$		0			0
$791$	−53928.0			−2.42409
$792$	−1712.65	+	398.739i	−0.0768387	+	0.0178896i
$793$	450.270			0.0201634
$794$	−421.737	+	730.470i	−0.0188500	+	0.0326491i
$795$		0			0
$796$	−8386.00	−	14525.0i	−0.373409	−	0.646764i
$797$	14190.3	+	24578.3i	0.630673	+	1.09236i	0.987414	+	0.158155i	$0.0505546\pi$
$797$	14190.3	+	24578.3i	0.630673	+	1.09236i	−0.356741	+	0.934203i	$0.616112\pi$
$798$	843.062	−	96.8459i	0.0373986	−	0.00429613i
$799$	−31128.1	+	53915.5i	−1.37827	+	2.38723i
$800$		0			0
$801$	−15734.9	−	16811.1i	−0.694089	−	0.741561i
$802$	−405.646			−0.0178602
$803$	3714.53	−	6433.75i	0.163241	−	0.282742i
$804$	−14487.2	−	19540.5i	−0.635479	−	0.857139i
$805$		0			0
$806$	−706.741	−	1224.11i	−0.0308857	−	0.0534957i
$807$	−100.273	+	231.197i	−0.00437394	+	0.0100849i
$808$	−1939.98	+	3360.14i	−0.0844655	+	0.146299i
$809$	−14569.6			−0.633175			−0.316588	−	0.948563i	$-0.602537\pi$
$809$	−14569.6			−0.633175			−0.316588	+	0.948563i	$0.602537\pi$
$810$		0			0
$811$	27927.7			1.20921			0.604607	−	0.796524i	$-0.293330\pi$
$811$	27927.7			1.20921			0.604607	+	0.796524i	$0.293330\pi$
$812$	15599.4	−	27019.0i	0.674178	−	1.16771i
$813$	−15802.6	+	36435.7i	−0.681699	+	1.57178i
$814$	204.150	+	353.598i	0.00879049	+	0.0152256i
$815$		0			0
$816$	−25575.6	−	34496.6i	−1.09721	−	1.47993i
$817$	1617.43	−	2801.46i	0.0692614	−	0.119964i
$818$	3588.68			0.153393
$819$	−28867.2	−	30841.5i	−1.23162	−	1.31586i
$820$		0			0
$821$	−9022.03	+	15626.6i	−0.383521	+	0.664279i	−0.991563	−	0.129627i	$-0.958622\pi$
$821$	−9022.03	+	15626.6i	−0.383521	+	0.664279i	0.608041	+	0.793905i	$0.291955\pi$
$822$	1220.55	−	140.210i	0.0517903	−	0.00594936i
$823$	−16126.4	−	27931.8i	−0.683028	−	1.18304i	−0.974052	−	0.226323i	$-0.927330\pi$
$823$	−16126.4	−	27931.8i	−0.683028	−	1.18304i	0.291025	−	0.956716i	$-0.406004\pi$
$824$	1068.78	+	1851.19i	0.0451855	+	0.0782636i
$825$		0			0
$826$	2608.26	−	4517.64i	0.109871	−	0.190301i
$827$	−13569.5			−0.570566			−0.285283	−	0.958443i	$-0.592088\pi$
$827$	−13569.5			−0.570566			−0.285283	+	0.958443i	$0.592088\pi$
$828$	−6895.29	+	1605.36i	−0.289406	+	0.0673795i
$829$	742.559			0.0311099			0.0155550	−	0.999879i	$-0.495049\pi$
$829$	742.559			0.0311099			0.0155550	+	0.999879i	$0.495049\pi$
$830$		0			0
$831$	15925.2	+	21480.0i	0.664788	+	0.896671i
$832$	12354.0	+	21397.7i	0.514780	+	0.891625i
$833$	−41468.1	−	71824.9i	−1.72483	−	2.98750i
$834$	−668.217	+	1540.70i	−0.0277440	+	0.0639688i
$835$		0			0
$836$	−3349.48			−0.138569
$837$	−13378.9	−	11362.5i	−0.552500	−	0.469231i
$838$	−776.605			−0.0320136
$839$	17752.3	−	30747.9i	0.730487	−	1.26524i	−0.226189	−	0.974083i	$-0.572627\pi$
$839$	17752.3	−	30747.9i	0.730487	−	1.26524i	0.956675	−	0.291157i	$-0.0940401\pi$
$840$		0			0
$841$	4279.49	+	7412.29i	0.175468	+	0.303919i
$842$	−632.499	−	1095.52i	−0.0258876	−	0.0448386i
$843$	−18118.4	−	24438.2i	−0.740250	−	0.998455i
$844$	2617.86	−	4534.26i	0.106766	−	0.184924i
$845$		0			0
$846$	−835.889	+	2752.29i	−0.0339698	+	0.111851i
$847$	−31267.6			−1.26844
$848$	13232.8	−	22919.9i	0.535869	−	0.928153i
$849$	−48492.9	+	5570.58i	−1.96027	+	0.225185i
$850$		0			0
$851$	1649.11	+	2856.34i	0.0664285	+	0.115058i
$852$	1992.39	−	228.874i	0.0801153	−	0.00920316i
$853$	187.524	−	324.801i	0.00752719	−	0.0130375i	−0.862237	−	0.506505i	$-0.830937\pi$
$853$	187.524	−	324.801i	0.00752719	−	0.0130375i	0.869764	+	0.493467i	$0.164271\pi$
$854$	63.0790			0.00252754
$855$		0			0
$856$	−1791.59			−0.0715365
$857$	16097.4	−	27881.5i	0.641629	−	1.11133i	−0.343440	−	0.939174i	$-0.611592\pi$
$857$	16097.4	−	27881.5i	0.641629	−	1.11133i	0.985069	−	0.172159i	$-0.0550743\pi$
$858$	−633.816	−	854.896i	−0.0252192	−	0.0340159i
$859$	14068.8	+	24367.8i	0.558813	+	0.967893i	0.997596	+	0.0692994i	$0.0220764\pi$
$859$	14068.8	+	24367.8i	0.558813	+	0.967893i	−0.438783	+	0.898593i	$0.644590\pi$
$860$		0			0
$861$	−15822.3	+	36481.1i	−0.626274	+	1.44399i
$862$	398.021	−	689.392i	0.0157270	−	0.0272399i
$863$	−15724.6			−0.620244			−0.310122	−	0.950697i	$-0.600370\pi$
$863$	−15724.6			−0.620244			−0.310122	+	0.950697i	$0.600370\pi$
$864$	−4585.67	−	3894.54i	−0.180564	−	0.153351i
$865$		0			0
$866$	751.749	−	1302.07i	0.0294982	−	0.0510924i
$867$	−25665.9	+	59177.4i	−1.00538	+	2.31807i
$868$	15512.1	+	26867.7i	0.606583	+	1.05063i
$869$	−4808.82	−	8329.12i	−0.187719	−	0.325139i
$870$		0			0
$871$	14768.6	−	25580.0i	0.574531	−	0.995117i
$872$	3446.35			0.133840
$873$	10205.5	−	2376.05i	0.395652	−	0.0921157i
$874$	172.694			0.00668361
$875$		0			0
$876$	16816.5	−	1931.77i	0.648602	−	0.0745075i
$877$	7640.23	+	13233.3i	0.294176	+	0.509528i	0.974793	−	0.223112i	$-0.0716215\pi$
$877$	7640.23	+	13233.3i	0.294176	+	0.509528i	−0.680617	+	0.732639i	$0.738288\pi$
$878$	736.963	+	1276.46i	0.0283272	+	0.0490642i
$879$	9191.72	−	1055.89i	0.352707	−	0.0405168i
$880$		0			0
$881$	−24687.6			−0.944092			−0.472046	−	0.881574i	$-0.656484\pi$
$881$	−24687.6			−0.944092			−0.472046	+	0.881574i	$0.656484\pi$
$882$	−2618.54	−	2797.63i	−0.0999669	−	0.106804i
$883$	−6562.59			−0.250112			−0.125056	−	0.992150i	$-0.539911\pi$
$883$	−6562.59			−0.250112			−0.125056	+	0.992150i	$0.539911\pi$
$884$	26241.0	−	45450.7i	0.998392	−	1.72927i
$885$		0			0
$886$	1611.63	+	2791.43i	0.0611104	+	0.105846i
$887$	25255.5	+	43743.9i	0.956030	+	1.65589i	0.731994	+	0.681311i	$0.238590\pi$
$887$	25255.5	+	43743.9i	0.956030	+	1.65589i	0.224035	+	0.974581i	$0.428077\pi$
$888$	−742.702	+	1712.43i	−0.0280669	+	0.0647134i
$889$	15908.2	−	27553.8i	0.600162	−	1.03951i
$890$		0			0
$891$	−10983.6	−	7349.46i	−0.412979	−	0.276337i
$892$	9688.51			0.363672
$893$	−5496.47	+	9520.17i	−0.205971	+	0.356753i
$894$	−567.456	+	1308.37i	−0.0212288	+	0.0489468i
$895$		0			0
$896$	7081.43	+	12265.4i	0.264034	+	0.457320i
$897$	−5119.91	−	6905.77i	−0.190578	−	0.257053i
$898$	1642.91	−	2845.60i	0.0610518	−	0.105745i
$899$	15741.4			0.583986
$900$		0			0
$901$	−55486.3			−2.05163
$902$	−500.886	+	867.559i	−0.0184897	+	0.0320250i
$903$	−22411.6	+	2574.51i	−0.825925	+	0.0948773i
$904$	−3105.40	−	5378.72i	−0.114252	−	0.197891i
$905$		0			0
$906$	1871.51	−	214.987i	0.0686276	−	0.00788353i
$907$	−3508.72	+	6077.28i	−0.128451	+	0.222484i	−0.923077	−	0.384616i	$-0.874334\pi$
$907$	−3508.72	+	6077.28i	−0.128451	+	0.222484i	0.794626	+	0.607100i	$0.207667\pi$
$908$	−12127.2			−0.443231
$909$	−28400.3	+	6612.16i	−1.03628	+	0.241267i
$910$		0			0
$911$	3062.30	−	5304.05i	0.111370	−	0.192899i	−0.804953	−	0.593339i	$-0.797809\pi$
$911$	3062.30	−	5304.05i	0.111370	−	0.192899i	0.916323	+	0.400440i	$0.131143\pi$
$912$	−4516.02	−	6091.25i	−0.163970	−	0.221164i
$913$	−2670.23	−	4624.98i	−0.0967928	−	0.167650i
$914$	228.153	+	395.172i	0.00825669	+	0.0143010i
$915$		0			0
$916$	−24573.8	+	42563.0i	−0.886397	+	1.53528i
$917$	−53104.4			−1.91239
$918$	−746.688	+	4092.19i	−0.0268457	+	0.147127i
$919$	23780.7			0.853594			0.426797	−	0.904347i	$-0.359642\pi$
$919$	23780.7			0.853594			0.426797	+	0.904347i	$0.359642\pi$
$920$		0			0
$921$	17533.2	−	40425.9i	0.627293	−	1.44634i
$922$	400.515	+	693.713i	0.0143062	+	0.0247790i
$923$	1217.61	+	2108.96i	0.0434215	+	0.0752082i
$924$	13911.4	+	18763.9i	0.495295	+	0.668058i
$925$		0			0
$926$	2316.17			0.0821967
$927$	−4668.46	+	15371.6i	−0.165407	+	0.544628i
$928$	5395.41			0.190854
$929$	−5094.54	+	8824.01i	−0.179921	+	0.311632i	−0.941853	−	0.336024i	$-0.890918\pi$
$929$	−5094.54	+	8824.01i	−0.179921	+	0.311632i	0.761932	+	0.647657i	$0.224251\pi$
$930$		0			0
$931$	−7322.26	−	12682.5i	−0.257763	−	0.446459i
$932$	8004.19	+	13863.7i	0.281316	+	0.487253i
$933$	−35158.7	+	4038.82i	−1.23370	+	0.141720i
$934$	925.488	−	1602.99i	0.0324228	−	0.0561579i
$935$		0			0
$936$	1413.80	−	4655.16i	0.0493713	−	0.162563i
$937$	3880.22			0.135284			0.0676421	−	0.997710i	$-0.478452\pi$
$937$	3880.22			0.135284			0.0676421	+	0.997710i	$0.478452\pi$
$938$	2068.96	−	3583.54i	0.0720191	−	0.124741i
$939$	24902.1	+	33588.2i	0.865442	+	1.16732i
$940$		0			0
$941$	19336.9	+	33492.6i	0.669890	+	1.16028i	0.977935	+	0.208911i	$0.0669919\pi$
$941$	19336.9	+	33492.6i	0.669890	+	1.16028i	−0.308045	+	0.951372i	$0.599675\pi$
$942$	599.065	−	1381.25i	0.0207204	−	0.0477746i
$943$	−4046.11	+	7008.07i	−0.139724	+	0.242008i
$944$	−46612.3			−1.60710
$945$		0			0
$946$	−568.318			−0.0195324
$947$	−3877.44	+	6715.92i	−0.133052	+	0.230452i	−0.924851	−	0.380328i	$-0.875811\pi$
$947$	−3877.44	+	6715.92i	−0.133052	+	0.230452i	0.791800	+	0.610781i	$0.209144\pi$
$948$	8719.45	−	20104.3i	0.298729	−	0.688773i
$949$	10277.0	+	17800.3i	0.351534	+	0.608875i
$950$		0			0
$951$	4846.93	+	6537.58i	0.165271	+	0.222918i
$952$	7375.72	−	12775.1i	0.251101	−	0.434920i
$953$	22527.9			0.765739			0.382870	−	0.923802i	$-0.374936\pi$
$953$	22527.9			0.765739			0.382870	+	0.923802i	$0.374936\pi$
$954$	−2496.85	+	581.318i	−0.0847365	+	0.0197284i
$955$		0			0
$956$	20216.2	−	35015.5i	0.683931	−	1.18460i
$957$	11774.4	−	1352.57i	0.397713	−	0.0456868i
$958$	−1541.29	−	2669.60i	−0.0519800	−	0.0900321i
$959$	−16371.9	−	28356.9i	−0.551277	−	0.954840i
$960$		0			0
$961$	7068.91	−	12243.7i	0.237283	−	0.410987i
$962$	−1129.65			−0.0378600
$963$	−9201.13	−	9830.43i	−0.307894	−	0.328952i
$964$	−26127.8			−0.872947
$965$		0			0
$966$	−717.254	−	967.438i	−0.0238895	−	0.0322224i
$967$	−2826.20	−	4895.13i	−0.0939861	−	0.162789i	0.815199	−	0.579181i	$-0.196628\pi$
$967$	−2826.20	−	4895.13i	−0.0939861	−	0.162789i	−0.909185	+	0.416392i	$0.863294\pi$
$968$	−1800.52	−	3118.59i	−0.0597840	−	0.103549i
$969$	−6325.60	+	14584.8i	−0.209709	+	0.483521i
$970$		0			0
$971$	19612.4			0.648188			0.324094	−	0.946025i	$-0.394941\pi$
$971$	19612.4			0.648188			0.324094	+	0.946025i	$0.394941\pi$
$972$	−1452.77	−	30076.7i	−0.0479398	−	0.992501i
$973$	44757.9			1.47469
$974$	−364.858	+	631.953i	−0.0120029	+	0.0207896i
$975$		0			0
$976$	−281.821	−	488.129i	−0.00924270	−	0.0160088i
$977$	−13841.8	−	23974.7i	−0.453264	−	0.785076i	0.545323	−	0.838226i	$-0.316407\pi$
$977$	−13841.8	−	23974.7i	−0.453264	−	0.785076i	−0.998587	+	0.0531500i	$0.983074\pi$
$978$	987.636	+	1332.13i	0.0322915	+	0.0435551i
$979$	−7730.14	+	13389.0i	−0.252356	+	0.437093i
$980$		0			0
$981$	17699.6	+	18910.1i	0.576049	+	0.615447i
$982$	2506.60			0.0814549
$983$	−15308.2	+	26514.6i	−0.496700	+	0.860310i	−0.999993	−	0.00380619i	$-0.998788\pi$
$983$	−15308.2	+	26514.6i	−0.496700	+	0.860310i	0.503293	+	0.864116i	$0.332122\pi$
$984$	−4549.70	+	522.643i	−0.147398	+	0.0169321i
$985$		0			0
$986$	−1865.23	−	3230.68i	−0.0602446	−	0.104347i
$987$	76160.8	−	8748.90i	2.45616	−	0.282148i
$988$	4633.51	−	8025.48i	0.149202	−	0.258426i
$989$	−4590.82			−0.147603
$990$		0			0
$991$	−14462.4			−0.463587			−0.231793	−	0.972765i	$-0.574459\pi$
$991$	−14462.4			−0.463587			−0.231793	+	0.972765i	$0.574459\pi$
$992$	−2682.59	+	4646.39i	−0.0858593	+	0.148713i
$993$	−7558.88	−	10195.5i	−0.241565	−	0.325824i
$994$	170.576	+	295.447i	0.00544301	+	0.00942756i
$995$		0			0
$996$	4841.72	−	11163.5i	0.154032	−	0.355149i
$997$	−3448.63	+	5973.20i	−0.109548	+	0.189743i	−0.915587	−	0.402120i	$-0.868274\pi$
$997$	−3448.63	+	5973.20i	−0.109548	+	0.189743i	0.806039	+	0.591862i	$0.201607\pi$
$998$	−1222.48			−0.0387745
$999$	−13210.4	+	4719.41i	−0.418378	+	0.149465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.d.151.4		14
5.2	odd	4		225.4.k.d.124.7		28
5.3	odd	4		225.4.k.d.124.8		28
5.4	even	2		45.4.e.c.16.4	✓	14
9.2	odd	6		2025.4.a.ba.1.4		7
9.4	even	3	inner	225.4.e.d.76.4		14
9.7	even	3		2025.4.a.bb.1.4		7
15.14	odd	2		135.4.e.c.46.4		14
45.4	even	6		45.4.e.c.31.4	yes	14
45.13	odd	12		225.4.k.d.49.7		28
45.14	odd	6		135.4.e.c.91.4		14
45.22	odd	12		225.4.k.d.49.8		28
45.29	odd	6		405.4.a.n.1.4		7
45.34	even	6		405.4.a.m.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.4	✓	14	5.4	even	2
45.4.e.c.31.4	yes	14	45.4	even	6
135.4.e.c.46.4		14	15.14	odd	2
135.4.e.c.91.4		14	45.14	odd	6
225.4.e.d.76.4		14	9.4	even	3	inner
225.4.e.d.151.4		14	1.1	even	1	trivial
225.4.k.d.49.7		28	45.13	odd	12
225.4.k.d.49.8		28	45.22	odd	12
225.4.k.d.124.7		28	5.2	odd	4
225.4.k.d.124.8		28	5.3	odd	4
405.4.a.m.1.4		7	45.34	even	6
405.4.a.n.1.4		7	45.29	odd	6
2025.4.a.ba.1.4		7	9.2	odd	6
2025.4.a.bb.1.4		7	9.7	even	3

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.112625 + 0.195072i) q^{2} +(-2.06755 + 4.76710i) q^{3} +(3.97463 + 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(-15.5970 + 27.0148i) q^{7} -3.59257 q^{8} +(-18.4505 - 19.7124i) q^{9} +O(q^{10})\)	\(q+(-0.112625 + 0.195072i) q^{2} +(-2.06755 + 4.76710i) q^{3} +(3.97463 + 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(-15.5970 + 27.0148i) q^{7} -3.59257 q^{8} +(-18.4505 - 19.7124i) q^{9} +(-9.06424 + 15.6997i) q^{11} +(-41.0357 + 4.71394i) q^{12} +(-25.0781 - 43.4366i) q^{13} +(-3.51322 - 6.08508i) q^{14} +(-31.3924 + 54.3733i) q^{16} +131.631 q^{17} +(5.92333 - 1.37907i) q^{18} +23.2428 q^{19} +(-96.5348 - 130.207i) q^{21} +(-2.04172 - 3.53636i) q^{22} +(-16.4928 - 28.5664i) q^{23} +(7.42780 - 17.1261i) q^{24} +11.2977 q^{26} +(132.118 - 47.1991i) q^{27} -247.969 q^{28} +(-62.9087 + 108.961i) q^{29} +(-62.5563 - 108.351i) q^{31} +(-21.4414 - 37.1376i) q^{32} +(-56.1014 - 75.6700i) q^{33} +(-14.8249 + 25.6775i) q^{34} +(62.3714 - 205.368i) q^{36} -99.9894 q^{37} +(-2.61772 + 4.53402i) q^{38} +(258.917 - 29.7428i) q^{39} +(-122.663 - 212.458i) q^{41} +(36.2720 - 4.16670i) q^{42} +(69.5882 - 120.530i) q^{43} -144.108 q^{44} +7.43001 q^{46} +(-236.480 + 409.596i) q^{47} +(-194.298 - 262.070i) q^{48} +(-315.033 - 545.654i) q^{49} +(-272.153 + 627.498i) q^{51} +(199.352 - 345.289i) q^{52} -421.529 q^{53} +(-5.67258 + 31.0884i) q^{54} +(56.0333 - 97.0526i) q^{56} +(-48.0556 + 110.801i) q^{57} +(-14.1702 - 24.5435i) q^{58} +(371.207 + 642.949i) q^{59} +(-4.48868 + 7.77462i) q^{61} +28.1816 q^{62} +(820.300 - 190.982i) q^{63} -492.620 q^{64} +(21.0795 - 2.42149i) q^{66} +(294.453 + 510.008i) q^{67} +(523.185 + 906.182i) q^{68} +(170.279 - 19.5606i) q^{69} -48.5526 q^{71} +(66.2847 + 70.8182i) q^{72} -409.800 q^{73} +(11.2613 - 19.5051i) q^{74} +(92.3816 + 160.010i) q^{76} +(-282.750 - 489.737i) q^{77} +(-23.3585 + 53.8572i) q^{78} +(-265.263 + 459.449i) q^{79} +(-48.1577 + 727.408i) q^{81} +55.2595 q^{82} +(-147.295 + 255.122i) q^{83} +(512.688 - 1182.10i) q^{84} +(15.6747 + 27.1494i) q^{86} +(-389.362 - 525.174i) q^{87} +(32.5639 - 56.4023i) q^{88} +852.817 q^{89} +1564.57 q^{91} +(131.106 - 227.082i) q^{92} +(645.857 - 74.1922i) q^{93} +(-53.2672 - 92.2615i) q^{94} +(221.370 - 25.4296i) q^{96} +(-194.045 + 336.096i) q^{97} +141.922 q^{98} +(476.719 - 110.990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9 + 23 * q^11 - 287 * q^12 + 96 * q^13 - 21 * q^14 - 324 * q^16 + 322 * q^17 + 89 * q^18 + 558 * q^19 + 180 * q^21 + 311 * q^22 - 96 * q^23 + 48 * q^24 + 716 * q^26 + 470 * q^27 - 674 * q^28 - 296 * q^29 - 244 * q^31 + 314 * q^32 + 211 * q^33 - 125 * q^34 - 2399 * q^36 - 808 * q^37 - 305 * q^38 + 634 * q^39 - 47 * q^41 - 1941 * q^42 + 525 * q^43 - 110 * q^44 + 1434 * q^46 - 164 * q^47 - 2051 * q^48 - 1225 * q^49 + 1517 * q^51 + 1682 * q^52 + 1012 * q^53 - 4066 * q^54 - 981 * q^56 - 337 * q^57 + 1183 * q^58 - 85 * q^59 - 828 * q^61 - 1572 * q^62 + 828 * q^63 + 4472 * q^64 + 4930 * q^66 + 1093 * q^67 - 2473 * q^68 - 822 * q^69 - 656 * q^71 + 4626 * q^72 - 4170 * q^73 - 1316 * q^74 - 2789 * q^76 - 24 * q^77 + 5314 * q^78 - 2110 * q^79 - 2167 * q^81 + 124 * q^82 - 1290 * q^83 + 5775 * q^84 - 2569 * q^86 - 3604 * q^87 + 2271 * q^88 + 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 696 * q^93 + 517 * q^94 - 593 * q^96 + 1787 * q^97 + 2558 * q^98 + 2320 * q^99

Introduction

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