LMFDB - Embedded newform 225.4.k.d.124.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.8
Character	$\chi$	$=$	225.124
Dual form			225.4.k.d.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.195072 + 0.112625i) q^{2} +(-4.76710 - 2.06755i) q^{3} +(-3.97463 - 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(27.0148 + 15.5970i) q^{7} -3.59257i q^{8} +(18.4505 + 19.7124i) q^{9} +O(q^{10})$	\(q+(0.195072 + 0.112625i) q^{2} +(-4.76710 - 2.06755i) q^{3} +(-3.97463 - 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(27.0148 + 15.5970i) q^{7} -3.59257i q^{8} +(18.4505 + 19.7124i) q^{9} +(-9.06424 + 15.6997i) q^{11} +(4.71394 + 41.0357i) q^{12} +(43.4366 - 25.0781i) q^{13} +(3.51322 + 6.08508i) q^{14} +(-31.3924 + 54.3733i) q^{16} -131.631i q^{17} +(1.37907 + 5.92333i) q^{18} -23.2428 q^{19} +(-96.5348 - 130.207i) q^{21} +(-3.53636 + 2.04172i) q^{22} +(28.5664 - 16.4928i) q^{23} +(-7.42780 + 17.1261i) q^{24} +11.2977 q^{26} +(-47.1991 - 132.118i) q^{27} -247.969i q^{28} +(62.9087 - 108.961i) q^{29} +(-62.5563 - 108.351i) q^{31} +(-37.1376 + 21.4414i) q^{32} +(75.6700 - 56.1014i) q^{33} +(14.8249 - 25.6775i) q^{34} +(62.3714 - 205.368i) q^{36} +99.9894i q^{37} +(-4.53402 - 2.61772i) q^{38} +(-258.917 + 29.7428i) q^{39} +(-122.663 - 212.458i) q^{41} +(-4.16670 - 36.2720i) q^{42} +(120.530 + 69.5882i) q^{43} +144.108 q^{44} +7.43001 q^{46} +(409.596 + 236.480i) q^{47} +(262.070 - 194.298i) q^{48} +(315.033 + 545.654i) q^{49} +(-272.153 + 627.498i) q^{51} +(-345.289 - 199.352i) q^{52} -421.529i q^{53} +(5.67258 - 31.0884i) q^{54} +(56.0333 - 97.0526i) q^{56} +(110.801 + 48.0556i) q^{57} +(24.5435 - 14.1702i) q^{58} +(-371.207 - 642.949i) q^{59} +(-4.48868 + 7.77462i) q^{61} -28.1816i q^{62} +(190.982 + 820.300i) q^{63} +492.620 q^{64} +(21.0795 - 2.42149i) q^{66} +(510.008 - 294.453i) q^{67} +(-906.182 + 523.185i) q^{68} +(-170.279 + 19.5606i) q^{69} -48.5526 q^{71} +(70.8182 - 66.2847i) q^{72} -409.800i q^{73} +(-11.2613 + 19.5051i) q^{74} +(92.3816 + 160.010i) q^{76} +(-489.737 + 282.750i) q^{77} +(-53.8572 - 23.3585i) q^{78} +(265.263 - 459.449i) q^{79} +(-48.1577 + 727.408i) q^{81} -55.2595i q^{82} +(-255.122 - 147.295i) q^{83} +(-512.688 + 1182.10i) q^{84} +(15.6747 + 27.1494i) q^{86} +(-525.174 + 389.362i) q^{87} +(56.4023 + 32.5639i) q^{88} -852.817 q^{89} +1564.57 q^{91} +(-227.082 - 131.106i) q^{92} +(74.1922 + 645.857i) q^{93} +(53.2672 + 92.2615i) q^{94} +(221.370 - 25.4296i) q^{96} +(336.096 + 194.045i) q^{97} +141.922i q^{98} +(-476.719 + 110.990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * 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 $

$2$	0.195072	+	0.112625i	0.0689684	+	0.0398189i	0.534088	−	0.845429i	$-0.320655\pi$
$2$	0.195072	+	0.112625i	0.0689684	+	0.0398189i	−0.465119	+	0.885248i	$0.653989\pi$
$3$	−4.76710	−	2.06755i	−0.917429	−	0.397899i
$3$	−4.76710	−	2.06755i	−0.917429	−	0.397899i
$4$	−3.97463	−	6.88426i	−0.496829	−	0.860533i
$5$		0			0
$5$		0			0
$6$	−0.697071	−	0.940215i	−0.0474297	−	0.0639735i
$7$	27.0148	+	15.5970i	1.45866	+	0.842159i	0.998946	−	0.0459062i	$-0.0146175\pi$
$7$	27.0148	+	15.5970i	1.45866	+	0.842159i	0.459717	+	0.888066i	$0.347951\pi$
$8$		−	3.59257i		−	0.158771i
$9$	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	$0.246588\pi$
$12$	4.71394	+	41.0357i	0.113400	+	0.987166i
$13$	43.4366	−	25.0781i	0.926702	−	0.535032i	0.0409353	−	0.999162i	$-0.486966\pi$
$13$	43.4366	−	25.0781i	0.926702	−	0.535032i	0.885767	+	0.464130i	$0.153633\pi$
$14$	3.51322	+	6.08508i	0.0670678	+	0.116165i
$15$		0			0
$16$	−31.3924	+	54.3733i	−0.490507	+	0.849583i
$17$		−	131.631i		−	1.87795i	−0.343981	−	0.938977i	$-0.611776\pi$
$17$		−	131.631i		−	1.87795i	0.343981	−	0.938977i	$-0.388224\pi$
$18$	1.37907	+	5.92333i	0.0180583	+	0.0775634i
$19$	−23.2428			−0.280646			−0.140323	−	0.990106i	$-0.544814\pi$
$19$	−23.2428			−0.280646			−0.140323	+	0.990106i	$0.544814\pi$
$20$		0			0
$21$	−96.5348	−	130.207i	−1.00312	−	1.35302i
$22$	−3.53636	+	2.04172i	−0.0342707	+	0.0197862i
$23$	28.5664	−	16.4928i	0.258978	−	0.149521i	−0.364890	−	0.931051i	$-0.618893\pi$
$23$	28.5664	−	16.4928i	0.258978	−	0.149521i	0.623868	+	0.781529i	$0.285560\pi$
$24$	−7.42780	+	17.1261i	−0.0631747	+	0.145661i
$25$		0			0
$26$	11.2977			0.0852176
$27$	−47.1991	−	132.118i	−0.336425	−	0.941710i
$28$		−	247.969i		−	1.67364i
$29$	62.9087	−	108.961i	0.402823	−	0.697709i	−0.591243	−	0.806494i	$-0.701363\pi$
$29$	62.9087	−	108.961i	0.402823	−	0.697709i	0.994065	+	0.108784i	$0.0346958\pi$
$30$		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	$0.951387\pi$
$32$	−37.1376	+	21.4414i	−0.205158	+	0.118448i
$33$	75.6700	−	56.1014i	0.399166	−	0.295940i
$34$	14.8249	−	25.6775i	0.0747781	−	0.129519i
$35$		0			0
$36$	62.3714	−	205.368i	0.288757	−	0.950776i
$37$			99.9894i			0.444274i	0.975015	+	0.222137i	$0.0713033\pi$
$37$			99.9894i			0.444274i	−0.975015	+	0.222137i	$0.928697\pi$
$38$	−4.53402	−	2.61772i	−0.0193557	−	0.0111750i
$39$	−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	$0.988084\pi$
$42$	−4.16670	−	36.2720i	−0.0153080	−	0.133259i
$43$	120.530	+	69.5882i	0.427458	+	0.246793i	0.698263	−	0.715841i	$-0.253957\pi$
$43$	120.530	+	69.5882i	0.427458	+	0.246793i	−0.270805	+	0.962634i	$0.587290\pi$
$44$	144.108			0.493752
$45$		0			0
$46$	7.43001			0.0238151
$47$	409.596	+	236.480i	1.27119	+	0.733919i	0.975211	−	0.221276i	$-0.0710223\pi$
$47$	409.596	+	236.480i	1.27119	+	0.733919i	0.295975	+	0.955196i	$0.404356\pi$
$48$	262.070	−	194.298i	0.788054	−	0.584259i
$49$	315.033	+	545.654i	0.918465	+	1.59083i
$50$		0			0
$51$	−272.153	+	627.498i	−0.747237	+	1.72289i
$52$	−345.289	−	199.352i	−0.920825	−	0.531639i
$53$		−	421.529i		−	1.09248i	−0.837628	−	0.546240i	$-0.816059\pi$
$53$		−	421.529i		−	1.09248i	0.837628	−	0.546240i	$-0.183941\pi$
$54$	5.67258	−	31.0884i	0.0142952	−	0.0783443i
$55$		0			0
$56$	56.0333	−	97.0526i	0.133710	−	0.231593i
$57$	110.801	+	48.0556i	0.257472	+	0.111669i
$58$	24.5435	−	14.1702i	0.0555641	−	0.0320799i
$59$	−371.207	−	642.949i	−0.819101	−	1.41873i	−0.906345	−	0.422538i	$-0.861139\pi$
$59$	−371.207	−	642.949i	−0.819101	−	1.41873i	0.0872437	−	0.996187i	$-0.472194\pi$
$60$		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	$0.169666\pi$
$62$		−	28.1816i		−	0.0577269i
$63$	190.982	+	820.300i	0.381929	+	1.64044i
$64$	492.620			0.962148
$65$		0			0
$66$	21.0795	−	2.42149i	0.0393138	−	0.00451613i
$67$	510.008	−	294.453i	0.929960	−	0.536913i	0.0431613	−	0.999068i	$-0.486257\pi$
$67$	510.008	−	294.453i	0.929960	−	0.536913i	0.886799	+	0.462155i	$0.152924\pi$
$68$	−906.182	+	523.185i	−1.61604	+	0.933021i
$69$	−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	$0.512920\pi$
$72$	70.8182	−	66.2847i	0.115917	−	0.108496i
$73$		−	409.800i		−	0.657034i	−0.944498	−	0.328517i	$-0.893451\pi$
$73$		−	409.800i		−	0.657034i	0.944498	−	0.328517i	$-0.106549\pi$
$74$	−11.2613	+	19.5051i	−0.0176905	+	0.0306409i
$75$		0			0
$76$	92.3816	+	160.010i	0.139433	+	0.241505i
$77$	−489.737	+	282.750i	−0.724815	+	0.418472i
$78$	−53.8572	−	23.3585i	−0.0781811	−	0.0339080i
$79$	265.263	−	459.449i	0.377778	−	0.654330i	−0.612961	−	0.790113i	$-0.710022\pi$
$79$	265.263	−	459.449i	0.377778	−	0.654330i	0.990739	+	0.135783i	$0.0433550\pi$
$80$		0			0
$81$	−48.1577	+	727.408i	−0.0660600	+	0.997816i
$82$		−	55.2595i		−	0.0744195i
$83$	−255.122	−	147.295i	−0.337389	−	0.194792i	0.321728	−	0.946832i	$-0.395736\pi$
$83$	−255.122	−	147.295i	−0.337389	−	0.194792i	−0.659117	+	0.752040i	$0.729070\pi$
$84$	−512.688	+	1182.10i	−0.665939	+	1.53544i
$85$		0			0
$86$	15.6747	+	27.1494i	0.0196541	+	0.0340418i
$87$	−525.174	+	389.362i	−0.647179	+	0.479816i
$88$	56.4023	+	32.5639i	0.0683240	+	0.0394469i
$89$	−852.817			−1.01571			−0.507856	−	0.861442i	$-0.669562\pi$
$89$	−852.817			−1.01571			−0.507856	+	0.861442i	$0.669562\pi$
$90$		0			0
$91$	1564.57			1.80233
$92$	−227.082	−	131.106i	−0.257336	−	0.148573i
$93$	74.1922	+	645.857i	0.0827244	+	0.720132i
$94$	53.2672	+	92.2615i	0.0584478	+	0.101234i
$95$		0			0
$96$	221.370	−	25.4296i	0.235349	−	0.0270354i
$97$	336.096	+	194.045i	0.351808	+	0.203117i	0.665481	−	0.746414i	$-0.268226\pi$
$97$	336.096	+	194.045i	0.351808	+	0.203117i	−0.313673	+	0.949531i	$0.601560\pi$
$98$			141.922i			0.146289i
$99$	−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	$-0.0118916\pi$
$102$	−123.761	+	91.7562i	−0.120139	+	0.0890707i
$103$	515.282	−	297.498i	0.492935	−	0.284596i	−0.232856	−	0.972511i	$-0.574807\pi$
$103$	515.282	−	297.498i	0.492935	−	0.284596i	0.725791	+	0.687915i	$0.241474\pi$
$104$	−90.0948	−	156.049i	−0.0849473	−	0.147133i
$105$		0			0
$106$	47.4747	−	82.2286i	0.0435014	−	0.0753467i
$107$		−	498.693i		−	0.450565i	−0.974293	−	0.225282i	$-0.927670\pi$
$107$		−	498.693i		−	0.450565i	0.974293	−	0.225282i	$-0.0723305\pi$
$108$	−721.938	+	850.053i	−0.643227	+	0.757374i
$109$	959.301			0.842976			0.421488	−	0.906834i	$-0.361508\pi$
$109$	959.301			0.842976			0.421488	+	0.906834i	$0.361508\pi$
$110$		0			0
$111$	206.733	−	476.660i	0.176777	−	0.407590i
$112$	−1696.12	+	979.256i	−1.43097	+	0.826170i
$113$	−1497.18	+	864.396i	−1.24640	+	0.719607i	−0.970389	−	0.241549i	$-0.922345\pi$
$113$	−1497.18	+	864.396i	−1.24640	+	0.719607i	−0.276007	+	0.961156i	$0.589011\pi$
$114$	16.2019	+	21.8532i	0.0133109	+	0.0179539i
$115$		0			0
$116$	−1000.16			−0.800536
$117$	1295.78	+	393.535i	1.02388	+	0.310960i
$118$		−	167.228i		−	0.130463i
$119$	2053.05	−	3555.99i	1.58154	−	2.73930i
$120$		0			0
$121$	501.179	+	868.068i	0.376543	+	0.652192i
$122$	−1.75123	+	1.01107i	−0.00129958	+	0.000750315i
$123$	145.479	+	1266.42i	0.106645	+	0.928368i
$124$	−497.277	+	861.309i	−0.360135	+	0.623773i
$125$		0			0
$126$	−55.1308	+	181.527i	−0.0389797	+	0.128347i
$127$			1019.95i			0.712647i	0.934363	+	0.356324i	$0.115970\pi$
$127$			1019.95i			0.712647i	−0.934363	+	0.356324i	$0.884030\pi$
$128$	393.197	+	227.013i	0.271516	+	0.156760i
$129$	−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	$0.641165\pi$
$132$	−686.977	−	297.950i	−0.452983	−	0.196464i
$133$	−627.900	−	362.518i	−0.409367	−	0.236348i
$134$	132.651			0.0855172
$135$		0			0
$136$	−472.893			−0.298164
$137$	909.049	+	524.839i	0.566900	+	0.327300i	0.755910	−	0.654675i	$-0.227195\pi$
$137$	909.049	+	524.839i	0.566900	+	0.327300i	−0.189010	+	0.981975i	$0.560528\pi$
$138$	−35.4196	−	15.3619i	−0.0218487	−	0.00947602i
$139$	717.411	+	1242.59i	0.437770	+	0.758240i	0.997517	−	0.0704236i	$-0.0224351\pi$
$139$	717.411	+	1242.59i	0.437770	+	0.758240i	−0.559747	+	0.828663i	$0.689102\pi$
$140$		0			0
$141$	−1463.65	−	1974.18i	−0.874197	−	1.17912i
$142$	−9.47126	−	5.46823i	−0.00559726	−	0.00323158i
$143$			909.256i			0.531719i
$144$	−1651.03	+	384.394i	−0.955460	+	0.222450i
$145$		0			0
$146$	46.1537	−	79.9406i	0.0261624	−	0.0453146i
$147$	−373.631	−	3252.53i	−0.209637	−	1.82493i
$148$	688.353	−	397.421i	0.382313	−	0.220728i
$149$	609.231	+	1055.22i	0.334968	+	0.580181i	0.983479	−	0.181024i	$-0.0579413\pi$
$149$	609.231	+	1055.22i	0.334968	+	0.580181i	−0.648511	+	0.761205i	$0.724608\pi$
$150$		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	$0.309461\pi$
$152$			83.5014i			0.0445583i
$153$	2594.76	−	2428.66i	1.37107	−	1.28330i
$154$	−127.379			−0.0666524
$155$		0			0
$156$	1233.86	+	1664.23i	0.633253	+	0.854137i
$157$	1114.00	−	643.168i	0.566286	−	0.326945i	−0.189379	−	0.981904i	$-0.560647\pi$
$157$	1114.00	−	643.168i	0.566286	−	0.326945i	0.755664	+	0.654959i	$0.227314\pi$
$158$	103.491	−	59.7505i	0.0521095	−	0.0300854i
$159$	−871.531	+	2009.47i	−0.434698	+	1.00227i
$160$		0			0
$161$	1028.95			0.503683
$162$	−91.3185	+	136.473i	−0.0442880	+	0.0661873i
$163$		−	1416.84i		−	0.680830i	−0.940275	−	0.340415i	$-0.889432\pi$
$163$		−	1416.84i		−	0.680830i	0.940275	−	0.340415i	$-0.110568\pi$
$164$	−975.079	+	1688.89i	−0.464273	+	0.804145i
$165$		0			0
$166$	−33.1782	−	57.4663i	−0.0155128	−	0.0268690i
$167$	775.071	−	447.487i	0.359142	−	0.207351i	−0.309562	−	0.950879i	$-0.600182\pi$
$167$	775.071	−	447.487i	0.359142	−	0.207351i	0.668704	+	0.743528i	$0.266849\pi$
$168$	−467.777	+	346.808i	−0.214820	+	0.159267i
$169$	159.323	−	275.955i	0.0725183	−	0.125605i
$170$		0			0
$171$	−428.842	−	458.172i	−0.191780	−	0.204896i
$172$		−	1106.35i		−	0.490456i
$173$	−1502.64	−	867.548i	−0.660367	−	0.381263i	0.132050	−	0.991243i	$-0.457844\pi$
$173$	−1502.64	−	867.548i	−0.660367	−	0.381263i	−0.792417	+	0.609980i	$0.791177\pi$
$174$	−146.299	+	16.8059i	−0.0637407	+	0.00732214i
$175$		0			0
$176$	−569.097	−	985.705i	−0.243735	−	0.422161i
$177$	440.253	+	3832.49i	0.186957	+	1.62750i
$178$	−166.361	−	96.0485i	−0.0700521	−	0.0404446i
$179$	−2133.37			−0.890815			−0.445408	−	0.895328i	$-0.646941\pi$
$179$	−2133.37			−0.890815			−0.445408	+	0.895328i	$0.646941\pi$
$180$		0			0
$181$	−3611.98			−1.48330			−0.741648	−	0.670789i	$-0.765955\pi$
$181$	−3611.98			−1.48330			−0.741648	+	0.670789i	$0.765955\pi$
$182$	305.205	+	176.210i	0.124304	+	0.0717668i
$183$	37.4724	−	27.7819i	0.0151368	−	0.0112224i
$184$	−59.2516	−	102.627i	−0.0237396	−	0.0411182i
$185$		0			0
$186$	−58.2668	+	134.345i	−0.0229695	+	0.0529603i
$187$	2066.57	+	1193.13i	0.808142	+	0.466581i
$188$		−	3759.69i		−	1.45853i
$189$	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	$0.130595\pi$
$192$	−2348.37	−	1018.51i	−0.882702	−	0.382838i
$193$	1045.94	−	603.872i	0.390094	−	0.225221i	−0.292107	−	0.956386i	$-0.594356\pi$
$193$	1045.94	−	603.872i	0.390094	−	0.225221i	0.682201	+	0.731165i	$0.261023\pi$
$194$	43.7087	+	75.7056i	0.0161758	+	0.0280173i
$195$		0			0
$196$	2504.28	−	4337.54i	0.912639	−	1.58074i
$197$		−	3268.56i		−	1.18211i	−0.806632	−	0.591054i	$-0.798712\pi$
$197$		−	3268.56i		−	1.18211i	0.806632	−	0.591054i	$-0.201288\pi$
$198$	−105.495	−	32.0394i	−0.0378646	−	0.0114997i
$199$	2109.88			0.751585			0.375793	−	0.926704i	$-0.377371\pi$
$199$	2109.88			0.751585			0.375793	+	0.926704i	$0.377371\pi$
$200$		0			0
$201$	−3040.05	+	349.223i	−1.06681	+	0.122549i
$202$	210.677	−	121.634i	0.0733820	−	0.0423671i
$203$	3398.93	−	1962.38i	1.17516	−	0.678482i
$204$	5401.57	−	620.500i	1.85385	−	0.212959i
$205$		0			0
$206$	134.023			0.0453292
$207$	852.177	+	258.811i	0.286137	+	0.0869017i
$208$			3149.05i			1.04975i
$209$	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	$0.867601\pi$
$212$	−2901.92	+	1675.42i	−0.940116	+	0.542776i
$213$	231.455	+	100.385i	0.0744556	+	0.0322923i
$214$	56.1652	−	97.2810i	0.0179410	−	0.0310747i
$215$		0			0
$216$	−474.644	+	169.566i	−0.149516	+	0.0534144i
$217$		−	3902.77i		−	1.22091i
$218$	187.133	+	108.041i	0.0581387	+	0.0335664i
$219$	−847.281	+	1953.56i	−0.261434	+	0.602783i
$220$		0			0
$221$	−3301.06	−	5717.60i	−1.00476	−	1.74030i
$222$	94.0115	−	69.6997i	0.0284218	−	0.0210718i
$223$	1055.51	+	609.397i	0.316959	+	0.182997i	0.650036	−	0.759903i	$-0.274754\pi$
$223$	1055.51	+	609.397i	0.316959	+	0.182997i	−0.333077	+	0.942900i	$0.608087\pi$
$224$	−1337.69			−0.399009
$225$		0			0
$226$	−389.410			−0.114616
$227$	1321.18	+	762.785i	0.386299	+	0.223030i	0.680555	−	0.732697i	$-0.261739\pi$
$227$	1321.18	+	762.785i	0.386299	+	0.223030i	−0.294256	+	0.955727i	$0.595072\pi$
$228$	−109.565	−	953.785i	−0.0318251	−	0.277044i
$229$	−3091.33	−	5354.33i	−0.892055	−	1.54508i	−0.837408	−	0.546578i	$-0.815930\pi$
$229$	−3091.33	−	5354.33i	−0.892055	−	1.54508i	−0.0546469	−	0.998506i	$-0.517403\pi$
$230$		0			0
$231$	2919.23	−	335.343i	0.831476	−	0.0955150i
$232$	−391.450	−	226.004i	−0.110776	−	0.0639564i
$233$			2013.82i			0.566222i	0.959087	+	0.283111i	$0.0913665\pi$
$233$			2013.82i			0.566222i	−0.959087	+	0.283111i	$0.908633\pi$
$234$	208.448	+	222.704i	0.0582336	+	0.0622164i
$235$		0			0
$236$	−2950.82	+	5110.97i	−0.813906	+	1.40973i
$237$	−2214.47	+	1641.80i	−0.606942	+	0.449984i
$238$	800.985	−	462.449i	0.218152	−	0.125950i
$239$	2543.15	+	4404.87i	0.688297	+	1.19216i	0.972389	+	0.233368i	$0.0749746\pi$
$239$	2543.15	+	4404.87i	0.688297	+	1.19216i	−0.284092	+	0.958797i	$0.591692\pi$
$240$		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	$0.311426\pi$
$242$			225.781i			0.0599742i
$243$	1733.52	−	3368.06i	0.457636	−	0.889140i
$244$	71.3634			0.0187237
$245$		0			0
$246$	−114.252	+	263.428i	−0.0296115	+	0.0682746i
$247$	−1009.59	+	582.886i	−0.260075	+	0.150154i
$248$	−389.258	+	224.738i	−0.0996689	+	0.0575439i
$249$	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	$0.355818\pi$
$252$	4888.07	−	4575.16i	1.22190	−	1.14368i
$253$			597.979i			0.148595i
$254$	−114.872	+	198.964i	−0.0283768	+	0.0491501i
$255$		0			0
$256$	−1919.34	−	3324.40i	−0.468590	−	0.811621i
$257$	−5884.62	+	3397.49i	−1.42830	+	0.824628i	−0.996987	−	0.0775746i	$-0.975282\pi$
$257$	−5884.62	+	3397.49i	−1.42830	+	0.824628i	−0.431312	+	0.902203i	$0.641949\pi$
$258$	−18.5903	−	161.832i	−0.00448598	−	0.0390513i
$259$	−1559.54	+	2701.19i	−0.374150	+	0.648047i
$260$		0			0
$261$	3308.58	−	770.305i	0.784659	−	0.182685i
$262$			383.464i			0.0904216i
$263$	4645.56	+	2682.12i	1.08919	+	0.628846i	0.933362	−	0.358938i	$-0.116861\pi$
$263$	4645.56	+	2682.12i	1.08919	+	0.628846i	0.155832	+	0.987784i	$0.450194\pi$
$264$	−201.548	−	271.850i	−0.0469865	−	0.0633758i
$265$		0			0
$266$	−81.6572	−	141.434i	−0.0188223	−	0.0326011i
$267$	4065.47	+	1763.24i	0.931845	+	0.404152i
$268$	−4054.18	−	2340.68i	−0.924062	−	0.533508i
$269$	−48.4985			−0.0109926			−0.00549629	−	0.999985i	$-0.501750\pi$
$269$	−48.4985			−0.0109926			−0.00549629	+	0.999985i	$0.501750\pi$
$270$		0			0
$271$	7643.16			1.71324			0.856622	−	0.515945i	$-0.172559\pi$
$271$	7643.16			1.71324			0.856622	+	0.515945i	$0.172559\pi$
$272$	7157.21	+	4132.22i	1.59548	+	0.921149i
$273$	−7458.48	−	3234.83i	−1.65351	−	0.717145i
$274$	118.220	+	204.763i	0.0260654	+	0.0451467i
$275$		0			0
$276$	811.454	+	1094.50i	0.176970	+	0.238699i
$277$	−4456.59	−	2573.01i	−0.966680	−	0.558113i	−0.0684576	−	0.997654i	$-0.521808\pi$
$277$	−4456.59	−	2573.01i	−0.966680	−	0.558113i	−0.898223	+	0.439541i	$0.855141\pi$
$278$			323.193i			0.0697261i
$279$	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	$0.953204\pi$
$282$	−63.1752	−	549.952i	−0.0133405	−	0.116132i
$283$	−8135.31	+	4696.92i	−1.70881	+	0.986583i	−0.772776	+	0.634679i	$0.781132\pi$
$283$	−8135.31	+	4696.92i	−1.70881	+	0.986583i	−0.936036	+	0.351904i	$0.885534\pi$
$284$	192.979	+	334.249i	0.0403211	+	0.0698381i
$285$		0			0
$286$	−102.405	+	177.370i	−0.0211725	+	0.0366718i
$287$		−	7652.69i		−	1.57395i
$288$	−1107.87	−	336.467i	−0.226673	−	0.0688420i
$289$	−12413.7			−2.52671
$290$		0			0
$291$	−1201.01	−	1619.93i	−0.241939	−	0.326329i
$292$	−2821.17	+	1628.81i	−0.565400	+	0.326434i
$293$	1542.03	−	890.291i	0.307462	−	0.177513i	−0.338328	−	0.941028i	$-0.609861\pi$
$293$	1542.03	−	890.291i	0.307462	−	0.177513i	0.645790	+	0.763515i	$0.276528\pi$
$294$	293.431	−	676.559i	0.0582083	−	0.134210i
$295$		0			0
$296$	359.219			0.0705377
$297$	2502.04	+	456.539i	0.488833	+	0.0891955i
$298$			274.458i			0.0533522i
$299$	827.217	−	1432.78i	0.159997	−	0.277123i
$300$		0			0
$301$	2170.74	+	3759.82i	0.415678	+	0.719976i
$302$	−313.969	+	181.270i	−0.0598241	+	0.0345395i
$303$	−4508.00	+	3342.21i	−0.854713	+	0.633680i
$304$	729.649	−	1263.79i	0.137659	−	0.238432i
$305$		0			0
$306$	779.693	−	181.528i	0.145660	−	0.0339127i
$307$			8480.18i			1.57651i	0.615347	+	0.788256i	$0.289016\pi$
$307$			8480.18i			1.57651i	−0.615347	+	0.788256i	$0.710984\pi$
$308$	3893.05	+	2247.65i	0.720218	+	0.415818i
$309$	−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	$0.620097\pi$
$312$	106.853	+	930.176i	0.0193890	+	0.168785i
$313$	6968.74	+	4023.41i	1.25846	+	0.726570i	0.972774	−	0.231755i	$-0.0744467\pi$
$313$	6968.74	+	4023.41i	1.25846	+	0.726570i	0.285682	+	0.958325i	$0.407780\pi$
$314$	289.747			0.0520744
$315$		0			0
$316$	−4217.30			−0.750764
$317$	−1356.39	−	783.112i	−0.240323	−	0.138751i	0.375002	−	0.927024i	$-0.377642\pi$
$317$	−1356.39	−	783.112i	−0.240323	−	0.138751i	−0.615325	+	0.788273i	$0.710975\pi$
$318$	−396.328	+	293.836i	−0.0698898	+	0.0518160i
$319$	1140.44	+	1975.30i	0.200164	+	0.346694i
$320$		0			0
$321$	−1031.07	+	2377.32i	−0.179280	+	0.413361i
$322$	200.720	+	115.886i	0.0347382	+	0.0200561i
$323$			3059.47i			0.527039i
$324$	5199.07	−	2559.65i	0.891474	−	0.438897i
$325$		0			0
$326$	159.571	−	276.385i	0.0271099	−	0.0469557i
$327$	−4573.08	−	1983.40i	−0.773371	−	0.335420i
$328$	−763.271	+	440.674i	−0.128490	+	0.0741835i
$329$	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	$0.231672\pi$
$332$			2341.77i			0.387113i
$333$	−1971.03	+	1844.85i	−0.324360	+	0.303596i
$334$	201.593			0.0330260
$335$		0			0
$336$	10110.2	−	1161.40i	1.64154	−	0.188571i
$337$	8203.84	−	4736.49i	1.32609	−	0.765617i	0.341396	−	0.939920i	$-0.389100\pi$
$337$	8203.84	−	4736.49i	1.32609	−	0.765617i	0.984692	+	0.174302i	$0.0557670\pi$
$338$	62.1588	−	35.8874i	0.0100029	−	0.00577520i
$339$	8924.38	−	1025.18i	1.42981	−	0.164248i
$340$		0			0
$341$	2268.10			0.360190
$342$	−32.0535	−	137.675i	−0.00506799	−	0.0217678i
$343$			8954.76i			1.40966i
$344$	250.000	−	433.013i	0.0391835	−	0.0678678i
$345$		0			0
$346$	−195.415	−	338.469i	−0.0303630	−	0.0525902i
$347$	−2868.68	+	1656.23i	−0.443801	+	0.256229i	−0.705209	−	0.709000i	$-0.749147\pi$
$347$	−2868.68	+	1656.23i	−0.443801	+	0.256229i	0.261408	+	0.965229i	$0.415813\pi$
$348$	4767.84	+	2067.87i	0.734435	+	0.318533i
$349$	2834.48	−	4909.46i	0.434745	−	0.753001i	−0.562530	−	0.826777i	$-0.690172\pi$
$349$	2834.48	−	4909.46i	0.434745	−	0.753001i	0.997275	+	0.0737765i	$0.0235052\pi$
$350$		0			0
$351$	−5363.44	−	4555.10i	−0.815611	−	0.692687i
$352$		−	777.400i		−	0.117715i
$353$	−1506.09	−	869.541i	−0.227085	−	0.131108i	0.382142	−	0.924104i	$-0.375187\pi$
$353$	−1506.09	−	869.541i	−0.227085	−	0.131108i	−0.609227	+	0.792996i	$0.708520\pi$
$354$	−345.753	+	797.195i	−0.0519111	+	0.119690i
$355$		0			0
$356$	3389.63	+	5871.02i	0.504636	+	0.874054i
$357$	−17139.3	+	12707.0i	−2.54091	+	1.88382i
$358$	−416.162	−	240.271i	−0.0614381	−	0.0354713i
$359$	−8624.58			−1.26793			−0.633966	−	0.773361i	$-0.718574\pi$
$359$	−8624.58			−1.26793			−0.633966	+	0.773361i	$0.718574\pi$
$360$		0			0
$361$	−6318.77			−0.921238
$362$	−704.597	−	406.799i	−0.102301	−	0.0590632i
$363$	−594.401	−	5174.38i	−0.0859449	−	0.748166i
$364$	−6218.60	−	10770.9i	−0.895449	−	1.55096i
$365$		0			0
$366$	10.4387	−	1.19914i	0.00149083	−	0.000171257i
$367$	5290.70	+	3054.59i	0.752513	+	0.434463i	0.826601	−	0.562788i	$-0.190271\pi$
$367$	5290.70	+	3054.59i	0.752513	+	0.434463i	−0.0740883	+	0.997252i	$0.523605\pi$
$368$			2071.00i			0.293365i
$369$	1924.87	−	6337.94i	0.271558	−	0.894146i
$370$		0			0
$371$	6574.59	−	11387.5i	0.920043	−	1.59356i
$372$	4151.36	−	3077.80i	0.578597	−	0.428969i
$373$	−5677.08	+	3277.67i	−0.788065	+	0.454990i	−0.839281	−	0.543698i	$-0.817024\pi$
$373$	−5677.08	+	3277.67i	−0.788065	+	0.454990i	0.0512159	+	0.998688i	$0.483690\pi$
$374$	268.753	+	465.494i	0.0371575	+	0.0643587i
$375$		0			0
$376$	849.572	−	1471.50i	0.116525	−	0.201827i
$377$		−	6310.52i		−	0.862092i
$378$	638.130	−	751.372i	0.0868303	−	0.102239i
$379$	−5032.40			−0.682050			−0.341025	−	0.940054i	$-0.610774\pi$
$379$	−5032.40			−0.682050			−0.341025	+	0.940054i	$0.610774\pi$
$380$		0			0
$381$	2108.80	−	4862.22i	0.283562	−	0.653803i
$382$	116.456	−	67.2359i	0.0155979	−	0.00900547i
$383$	−3172.24	+	1831.49i	−0.423222	+	0.244347i	−0.696455	−	0.717601i	$-0.745240\pi$
$383$	−3172.24	+	1831.49i	−0.423222	+	0.244347i	0.273233	+	0.961948i	$0.411907\pi$
$384$	−1405.05	−	1895.15i	−0.186722	−	0.251852i
$385$		0			0
$386$	272.044			0.0358722
$387$	852.094	+	3659.88i	0.111923	+	0.480729i
$388$		−	3085.03i		−	0.403657i
$389$	−2435.48	+	4218.37i	−0.317439	+	0.549820i	−0.979953	−	0.199229i	$-0.936156\pi$
$389$	−2435.48	+	4218.37i	−0.317439	+	0.549820i	0.662514	+	0.749049i	$0.269489\pi$
$390$		0			0
$391$	−2170.97	−	3760.22i	−0.280794	−	0.486349i
$392$	1960.30	−	1131.78i	0.252577	−	0.145825i
$393$	−1009.52	−	8788.09i	−0.129577	−	1.12799i
$394$	368.121	−	637.605i	0.0470703	−	0.0815281i
$395$		0			0
$396$	2658.87	+	2840.72i	0.337407	+	0.360483i
$397$		−	3744.62i		−	0.473393i	−0.971584	−	0.236696i	$-0.923935\pi$
$397$		−	3744.62i		−	0.473393i	0.971584	−	0.236696i	$-0.0760647\pi$
$398$	411.579	+	237.625i	0.0518356	+	0.0299273i
$399$	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	$0.797565\pi$
$402$	−632.361	−	274.262i	−0.0784559	−	0.0340272i
$403$	−5434.46	−	3137.59i	−0.671737	−	0.387827i
$404$	−8585.16			−1.05725
$405$		0			0
$406$	884.049			0.108066
$407$	−1569.81	−	906.328i	−0.191185	−	0.110381i
$408$	2254.33	+	977.729i	0.273544	+	0.118639i
$409$	7965.99	+	13797.5i	0.963064	+	1.66808i	0.714730	+	0.699401i	$0.246550\pi$
$409$	7965.99	+	13797.5i	0.963064	+	1.66808i	0.248334	+	0.968675i	$0.420117\pi$
$410$		0			0
$411$	−3248.40	−	4381.46i	−0.389858	−	0.525843i
$412$	−4096.12	−	2364.89i	−0.489809	−	0.282791i
$413$		−	23158.8i		−	2.75926i
$414$	137.087	+	146.463i	0.0162741	+	0.0173871i
$415$		0			0
$416$	−1075.42	+	1862.68i	−0.126747	+	0.219532i
$417$	−850.854	−	7406.84i	−0.0999196	−	0.869820i
$418$	82.1949	−	47.4553i	0.00961791	−	0.00555290i
$419$	−1723.87	−	2985.84i	−0.200995	−	0.348133i	0.747854	−	0.663863i	$-0.231084\pi$
$419$	−1723.87	−	2985.84i	−0.200995	−	0.348133i	−0.948849	+	0.315730i	$0.897751\pi$
$420$		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	$0.272053\pi$
$422$		−	148.359i		−	0.0171137i
$423$	2895.66	+	12437.3i	0.332841	+	1.42960i
$424$	−1514.37			−0.173454
$425$		0			0
$426$	33.8446	+	45.6499i	0.00384924	+	0.00519189i
$427$	−242.522	+	140.020i	−0.0274858	+	0.0158689i
$428$	−3433.13	+	1982.12i	−0.387726	+	0.223854i
$429$	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	$0.563276\pi$
$432$	8665.40	+	1581.14i	0.965080	+	0.176094i
$433$		−	6674.80i		−	0.740809i	−0.928871	−	0.370405i	$-0.879219\pi$
$433$		−	6674.80i		−	0.740809i	0.928871	−	0.370405i	$-0.120781\pi$
$434$	439.549	−	761.321i	0.0486153	−	0.0842041i
$435$		0			0
$436$	−3812.87	−	6604.08i	−0.418815	−	0.725408i
$437$	−663.963	+	383.339i	−0.0726812	+	0.0419625i
$438$	−385.301	+	285.660i	−0.0420328	+	0.0311629i
$439$	−3271.76	+	5666.85i	−0.355700	+	0.616091i	−0.987238	−	0.159254i	$-0.949091\pi$
$439$	−3271.76	+	5666.85i	−0.355700	+	0.616091i	0.631537	+	0.775346i	$0.282424\pi$
$440$		0			0
$441$	−4943.62	+	16277.7i	−0.533811	+	1.75766i
$442$		−	1487.12i		−	0.160035i
$443$	12392.6	+	7154.86i	1.32909	+	0.767353i	0.985160	−	0.171640i	$-0.0549066\pi$
$443$	12392.6	+	7154.86i	1.32909	+	0.767353i	0.343935	+	0.938993i	$0.388240\pi$
$444$	−4103.14	+	471.344i	−0.438573	+	0.0503806i
$445$		0			0
$446$	137.267	+	237.753i	0.0145734	+	0.0252420i
$447$	−722.552	−	6289.95i	−0.0764553	−	0.665558i
$448$	13308.0	+	7683.39i	1.40345	+	0.810282i
$449$	14587.4			1.53324			0.766618	−	0.642104i	$-0.221938\pi$
$449$	14587.4			1.53324			0.766618	+	0.642104i	$0.221938\pi$
$450$		0			0
$451$	4447.38			0.464343
$452$	11901.5	+	6871.31i	1.23849	+	0.715043i
$453$	6718.22	−	4980.86i	0.696798	−	0.516603i
$454$	171.817	+	297.596i	0.0177616	+	0.0307640i
$455$		0			0
$456$	172.643	−	398.060i	0.0177297	−	0.0408791i
$457$	−1754.37	−	1012.89i	−0.179576	−	0.103678i	0.407518	−	0.913197i	$-0.366394\pi$
$457$	−1754.37	−	1012.89i	−0.179576	−	0.103678i	−0.587093	+	0.809519i	$0.699728\pi$
$458$		−	1392.64i		−	0.142083i
$459$	−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	$0.109173\pi$
$462$	607.228	+	263.362i	0.0611489	+	0.0265210i
$463$	8905.07	−	5141.34i	0.893852	−	0.516066i	0.0186517	−	0.999826i	$-0.494063\pi$
$463$	8905.07	−	5141.34i	0.893852	−	0.516066i	0.875201	+	0.483760i	$0.160729\pi$
$464$	3949.72	+	6841.11i	0.395174	+	0.684462i
$465$		0			0
$466$	−226.806	+	392.840i	−0.0225464	+	0.0390514i
$467$			8217.44i			0.814256i	0.913371	+	0.407128i	$0.133470\pi$
$467$			8217.44i			0.814256i	−0.913371	+	0.407128i	$0.866530\pi$
$468$	−2441.03	−	10484.6i	−0.241104	−	1.03558i
$469$	18370.3			1.80866
$470$		0			0
$471$	−6640.33	+	762.801i	−0.649618	+	0.0746242i
$472$	−2309.84	+	1333.59i	−0.225252	+	0.130049i
$473$	−2185.03	+	1261.53i	−0.212406	+	0.122632i
$474$	−616.889	+	70.8645i	−0.0597777	+	0.00686690i
$475$		0			0
$476$	−32640.5			−3.14301
$477$	8309.35	−	7777.43i	0.797608	−	0.746549i
$478$			1145.69i			0.109629i
$479$	6842.59	−	11851.7i	0.652705	−	1.13052i	−0.329759	−	0.944065i	$-0.606967\pi$
$479$	6842.59	−	11851.7i	0.652705	−	1.13052i	0.982464	−	0.186453i	$-0.0596993\pi$
$480$		0			0
$481$	2507.54	+	4343.19i	0.237701	+	0.411710i
$482$	−641.168	+	370.178i	−0.0605900	+	0.0349817i
$483$	−4905.13	−	2127.41i	−0.462093	−	0.200415i
$484$	3984.00	−	6900.50i	0.374155	−	0.648056i
$485$		0			0
$486$	717.489	−	461.776i	0.0669670	−	0.0431000i
$487$		−	3239.59i		−	0.301437i	−0.988577	−	0.150718i	$-0.951841\pi$
$487$		−	3239.59i		−	0.301437i	0.988577	−	0.150718i	$-0.0481587\pi$
$488$	27.9309	+	16.1259i	0.00259092	+	0.00149587i
$489$	−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	$-0.337543\pi$
$492$	8140.15	−	6035.07i	0.745907	−	0.553012i
$493$	−14342.7	−	8280.74i	−1.31027	−	0.756482i
$494$	−262.590			−0.0239159
$495$		0			0
$496$	7855.18			0.711105
$497$	−1311.64	−	757.276i	−0.118380	−	0.0683470i
$498$	39.3495	+	342.545i	0.00354075	+	0.0308229i
$499$	−2713.61	−	4700.11i	−0.243443	−	0.421655i	0.718250	−	0.695785i	$-0.244943\pi$
$499$	−2713.61	−	4700.11i	−0.243443	−	0.421655i	−0.961693	+	0.274130i	$0.911610\pi$
$500$		0			0
$501$	−4620.04	+	530.723i	−0.411992	+	0.0473272i
$502$	678.958	+	391.997i	0.0603653	+	0.0348519i
$503$			9600.22i			0.850999i	0.904959	+	0.425500i	$0.139902\pi$
$503$			9600.22i			0.850999i	−0.904959	+	0.425500i	$0.860098\pi$
$504$	2946.98	−	686.117i	0.260454	−	0.0606391i
$505$		0			0
$506$	−67.3474	+	116.649i	−0.00591691	+	0.0102484i
$507$	−1330.06	+	986.098i	−0.116509	+	0.0863790i
$508$	7021.62	−	4053.94i	0.613256	−	0.354064i
$509$	−9469.94	−	16402.4i	−0.824652	−	1.42834i	−0.902185	−	0.431349i	$-0.858038\pi$
$509$	−9469.94	−	16402.4i	−0.824652	−	1.42834i	0.0775333	−	0.996990i	$-0.475296\pi$
$510$		0			0
$511$	6391.66	−	11070.7i	0.553328	−	0.958392i
$512$		−	4496.87i		−	0.388155i
$513$	1097.04	+	3070.80i	0.0944162	+	0.264287i
$514$	−1530.57			−0.131343
$515$		0			0
$516$	−2287.43	+	5274.08i	−0.195152	+	0.449958i
$517$	−7425.35	+	4287.03i	−0.631657	+	0.364687i
$518$	−608.444	+	351.285i	−0.0516090	+	0.0297965i
$519$	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	$0.198839\pi$
$522$	732.168	+	222.364i	0.0613910	+	0.0186448i
$523$		−	17967.5i		−	1.50223i	−0.660172	−	0.751114i	$-0.729517\pi$
$523$		−	17967.5i		−	1.50223i	0.660172	−	0.751114i	$-0.270483\pi$
$524$	6766.38	−	11719.7i	0.564104	−	0.977057i
$525$		0			0
$526$	604.147	+	1046.41i	0.0500799	+	0.0867410i
$527$	−14262.3	+	8234.35i	−1.17889	+	0.680634i
$528$	674.952	+	5875.59i	0.0556317	+	0.484285i
$529$	−5539.47	+	9594.65i	−0.455287	+	0.788580i
$530$		0			0
$531$	5825.11	−	19180.1i	0.476061	−	1.56751i
$532$			5763.51i			0.469699i
$533$	−10656.1	−	6152.30i	−0.865979	−	0.499973i
$534$	594.474	+	801.832i	0.0481749	+	0.0649787i
$535$		0			0
$536$	−1057.84	−	1832.24i	−0.0852460	−	0.147650i
$537$	10170.0	+	4410.85i	0.817260	+	0.354455i
$538$	−9.46070	−	5.46214i	−0.000758141	−	0.000437713i
$539$	−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	$0.606973\pi$
$542$	1490.97	+	860.811i	0.118160	+	0.0682195i
$543$	17218.7	+	7467.94i	1.36082	+	0.590203i
$544$	2822.35	+	4888.46i	0.222440	+	0.385278i
$545$		0			0
$546$	−1090.62	−	1471.04i	−0.0854839	−	0.115301i
$547$	−73.3706	−	42.3605i	−0.00573510	−	0.00331116i	0.497130	−	0.867676i	$-0.334387\pi$
$547$	−73.3706	−	42.3605i	−0.00573510	−	0.00331116i	−0.502865	+	0.864365i	$0.667721\pi$
$548$		−	8344.17i		−	0.650448i
$549$	−236.075	+	54.9630i	−0.0183523	+	0.00427280i
$550$		0			0
$551$	−1462.18	+	2532.56i	−0.113050	+	0.195809i
$552$	70.2727	+	611.737i	0.00541849	+	0.0471690i
$553$	14332.1	−	8274.63i	1.10210	−	0.636298i
$554$	−579.571	−	1003.85i	−0.0444469	−	0.0769843i
$555$		0			0
$556$	5702.89	−	9877.69i	0.434994	−	0.753431i
$557$		−	20914.0i		−	1.59094i	−0.605994	−	0.795469i	$-0.707224\pi$
$557$		−	20914.0i		−	1.59094i	0.605994	−	0.795469i	$-0.292776\pi$
$558$	555.527	−	519.965i	0.0421458	−	0.0394478i
$559$	6980.56			0.528169
$560$		0			0
$561$	−7384.69	−	9960.52i	−0.555761	−	0.749614i
$562$	−1142.10	+	659.389i	−0.0857231	+	0.0494923i
$563$	−9561.76	+	5520.48i	−0.715773	+	0.413252i	−0.813195	−	0.581991i	$-0.802274\pi$
$563$	−9561.76	+	5520.48i	−0.715773	+	0.413252i	0.0974220	+	0.995243i	$0.468940\pi$
$564$	−7773.33	+	17922.8i	−0.580348	+	1.33810i
$565$		0			0
$566$	−2115.96			−0.157139
$567$	−12646.4	+	18899.7i	−0.936679	+	1.39984i
$568$			174.429i			0.0128853i
$569$	−3007.31	+	5208.81i	−0.221569	+	0.383770i	−0.955285	−	0.295688i	$-0.904451\pi$
$569$	−3007.31	+	5208.81i	−0.221569	+	0.383770i	0.733715	+	0.679457i	$0.237785\pi$
$570$		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	$0.536090\pi$
$572$	6259.56	−	3613.96i	0.457561	−	0.264173i
$573$	−2491.89	+	1847.48i	−0.181676	+	0.134694i
$574$	861.884	−	1492.83i	0.0626730	−	0.108553i
$575$		0			0
$576$	9089.08	+	9710.72i	0.657486	+	0.702454i
$577$			473.507i			0.0341635i	0.999854	+	0.0170818i	$0.00543756\pi$
$577$			473.507i			0.0341635i	−0.999854	+	0.0170818i	$0.994562\pi$
$578$	−2421.57	−	1398.09i	−0.174263	−	0.100611i
$579$	−6234.62	+	716.196i	−0.447499	+	0.0514060i
$580$		0			0
$581$	−4594.72	−	7958.29i	−0.328092	−	0.568271i
$582$	−51.8387	−	451.266i	−0.00369207	−	0.0321402i
$583$	6617.89	+	3820.84i	0.470129	+	0.271429i
$584$	−1472.24			−0.104318
$585$		0			0
$586$	401.076			0.0282735
$587$	−11275.9	−	6510.17i	−0.792859	−	0.457757i	0.0481093	−	0.998842i	$-0.484680\pi$
$587$	−11275.9	−	6510.17i	−0.792859	−	0.457757i	−0.840968	+	0.541085i	$0.818014\pi$
$588$	−20906.2	+	15499.8i	−1.46626	+	1.08708i
$589$	1453.99	+	2518.38i	0.101715	+	0.176176i
$590$		0			0
$591$	−6757.90	+	15581.6i	−0.470360	+	1.08450i
$592$	−5436.75	−	3138.91i	−0.377448	−	0.217920i
$593$			12887.3i			0.892441i	0.894923	+	0.446220i	$0.147230\pi$
$593$			12887.3i			0.892441i	−0.894923	+	0.446220i	$0.852770\pi$
$594$	436.661	+	370.851i	0.0301623	+	0.0256165i
$595$		0			0
$596$	4842.94	−	8388.22i	0.332843	−	0.576501i
$597$	−10058.0	−	4362.28i	−0.689526	−	0.299055i
$598$	322.734	−	186.330i	0.0220695	−	0.0127418i
$599$	−4337.24	−	7512.32i	−0.295851	−	0.512429i	0.679332	−	0.733832i	$-0.262270\pi$
$599$	−4337.24	−	7512.32i	−0.295851	−	0.512429i	−0.975182	+	0.221403i	$0.928937\pi$
$600$		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	$0.287690\pi$
$602$			977.916i			0.0662074i
$603$	15214.3	+	4620.67i	1.02748	+	0.312053i
$604$	12794.4			0.861913
$605$		0			0
$606$	−1255.80	+	144.259i	−0.0841806	+	0.00967016i
$607$	18767.1	−	10835.2i	1.25492	−	0.724527i	0.282836	−	0.959168i	$-0.408725\pi$
$607$	18767.1	−	10835.2i	1.25492	−	0.724527i	0.972082	+	0.234641i	$0.0753916\pi$
$608$	863.183	−	498.359i	0.0575768	−	0.0332420i
$609$	−20260.4	+	2327.39i	−1.34810	+	0.154861i
$610$		0			0
$611$	23721.9			1.57068
$612$	−27032.7	−	8210.01i	−1.78551	−	0.542271i
$613$			15571.2i			1.02596i	0.858399	+	0.512982i	$0.171459\pi$
$613$			15571.2i			1.02596i	−0.858399	+	0.512982i	$0.828541\pi$
$614$	−955.079	+	1654.25i	−0.0627750	+	0.108730i
$615$		0			0
$616$	1015.80	+	1759.42i	0.0664411	+	0.115079i
$617$	8423.43	−	4863.27i	0.549618	−	0.317322i	−0.199350	−	0.979928i	$-0.563883\pi$
$617$	8423.43	−	4863.27i	0.549618	−	0.317322i	0.748968	+	0.662606i	$0.230550\pi$
$618$	−638.901	−	277.099i	−0.0415864	−	0.0180365i
$619$	3148.79	−	5453.87i	0.204460	−	0.354135i	−0.745501	−	0.666505i	$-0.767790\pi$
$619$	3148.79	−	5453.87i	0.204460	−	0.354135i	0.949961	+	0.312370i	$0.101123\pi$
$620$		0			0
$621$	−3527.31	−	2995.70i	−0.227933	−	0.193580i
$622$			1534.13i			0.0988955i
$623$	−23038.7	−	13301.4i	−1.48158	−	0.855392i
$624$	6510.81	−	15011.8i	0.417694	−	0.963069i
$625$		0			0
$626$	906.272	+	1569.71i	0.0578625	+	0.100221i
$627$	−1758.78	+	1303.95i	−0.112024	+	0.0830541i
$628$	−8855.47	−	5112.71i	−0.562694	−	0.324872i
$629$	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	$0.557250\pi$
$632$	−1650.60	−	952.977i	−0.103888	−	0.0599800i
$633$	390.576	+	3400.04i	0.0245245	+	0.213491i
$634$	−176.396	−	305.527i	−0.0110498	−	0.0191388i
$635$		0			0
$636$	17297.7	−	1987.06i	1.07846	−	0.123887i
$637$	27367.9	+	15800.9i	1.70229	+	0.982816i
$638$			513.767i			0.0318813i
$639$	−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	$0.934044\pi$
$642$	−468.878	+	347.624i	−0.0288242	+	0.0213701i
$643$	−5389.90	+	3111.86i	−0.330570	+	0.190855i	−0.656094	−	0.754679i	$-0.727793\pi$
$643$	−5389.90	+	3111.86i	−0.330570	+	0.190855i	0.325524	+	0.945534i	$0.394459\pi$
$644$	−4089.71	−	7083.59i	−0.250244	−	0.433436i
$645$		0			0
$646$	−344.573	+	596.818i	−0.0209861	+	0.0363491i
$647$			20451.9i			1.24273i	0.783521	+	0.621365i	$0.213422\pi$
$647$			20451.9i			1.24273i	−0.783521	+	0.621365i	$0.786578\pi$
$648$	2613.26	+	173.010i	0.158424	+	0.0104884i
$649$	13458.8			0.814029
$650$		0			0
$651$	−8069.15	+	18604.9i	−0.485799	+	1.12010i
$652$	−9753.88	+	5631.41i	−0.585876	+	0.338256i
$653$	−6450.54	+	3724.22i	−0.386568	+	0.223185i	−0.680672	−	0.732588i	$-0.738312\pi$
$653$	−6450.54	+	3724.22i	−0.386568	+	0.223185i	0.294104	+	0.955773i	$0.404979\pi$
$654$	−668.701	−	901.949i	−0.0399821	−	0.0539281i
$655$		0			0
$656$	15402.7			0.916731
$657$	8078.15	−	7561.03i	0.479694	−	0.448986i
$658$			3323.23i			0.196889i
$659$	413.185	−	715.658i	0.0244240	−	0.0423036i	−0.853555	−	0.521003i	$-0.825558\pi$
$659$	413.185	−	715.658i	0.0244240	−	0.0423036i	0.877979	+	0.478699i	$0.158891\pi$
$660$		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	$0.774387\pi$
$662$	−476.475	+	275.093i	−0.0279739	+	0.0161507i
$663$	3915.07	+	34081.4i	0.229334	+	1.99640i
$664$	−529.167	+	916.545i	−0.0309272	+	0.0535675i
$665$		0			0
$666$	−592.270	+	137.892i	−0.0344594	+	0.00802286i
$667$		−	4150.17i		−	0.240922i
$668$	−6161.24	−	3557.19i	−0.356865	−	0.206036i
$669$	−3771.75	−	5087.36i	−0.217973	−	0.294004i
$670$		0			0
$671$	−81.3729	−	140.942i	−0.00468162	−	0.00810880i
$672$	6376.89	+	2765.73i	0.366062	+	0.158765i
$673$	−8729.36	−	5039.90i	−0.499988	−	0.288668i	0.228720	−	0.973492i	$-0.426546\pi$
$673$	−8729.36	−	5039.90i	−0.499988	−	0.288668i	−0.728709	+	0.684824i	$0.759879\pi$
$674$	2133.79			0.121944
$675$		0			0
$676$	−2532.99			−0.144117
$677$	22265.9	+	12855.2i	1.26403	+	0.729788i	0.973852	−	0.227185i	$-0.0729522\pi$
$677$	22265.9	+	12855.2i	1.26403	+	0.729788i	0.290178	+	0.956973i	$0.406285\pi$
$678$	1856.36	+	805.124i	0.105152	+	0.0456056i
$679$	6053.05	+	10484.2i	0.342113	+	0.592557i
$680$		0			0
$681$	−4721.11	−	6367.88i	−0.265659	−	0.358322i
$682$	442.443	+	255.445i	0.0248417	+	0.0143424i
$683$			32091.0i			1.79784i	0.438109	+	0.898922i	$0.355648\pi$
$683$			32091.0i			1.79784i	−0.438109	+	0.898922i	$0.644352\pi$
$684$	−1449.69	+	4773.32i	−0.0810383	+	0.266831i
$685$		0			0
$686$	−1008.53	+	1746.82i	−0.0561310	+	0.0972217i
$687$	3666.33	+	31916.1i	0.203609	+	1.77245i
$688$	−7567.48	+	4369.09i	−0.419342	+	0.242107i
$689$	−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	$0.260601\pi$
$692$			13792.7i			0.757690i
$693$	−14609.6	−	4437.02i	−0.800826	−	0.243216i
$694$	−746.133			−0.0408110
$695$		0			0
$696$	1398.81	+	1886.72i	0.0761806	+	0.102753i
$697$	−27966.1	+	16146.2i	−1.51979	+	0.877449i
$698$	1105.85	−	638.465i	0.0599673	−	0.0346222i
$699$	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	$0.385359\pi$
$702$	−533.240	−	1492.63i	−0.0286693	−	0.0802503i
$703$		−	2324.04i		−	0.124684i
$704$	−4465.22	+	7733.99i	−0.239047	+	0.414042i
$705$		0			0
$706$	−195.864	−	339.246i	−0.0104411	−	0.0180846i
$707$	29175.8	−	16844.7i	1.55201	−	0.896053i
$708$	24634.0	−	18263.5i	1.30763	−	0.969472i
$709$	−14110.6	+	24440.3i	−0.747440	+	1.29460i	0.201606	+	0.979467i	$0.435384\pi$
$709$	−14110.6	+	24440.3i	−0.747440	+	1.29460i	−0.949046	+	0.315137i	$0.897949\pi$
$710$		0			0
$711$	13951.1	−	3248.10i	0.735875	−	0.171327i
$712$			3063.80i			0.161265i
$713$	−3574.02	−	2063.46i	−0.187725	−	0.108383i
$714$	−4774.51	+	548.467i	−0.250254	+	0.0287477i
$715$		0			0
$716$	8479.38	+	14686.7i	0.442583	+	0.766576i
$717$	−3016.19	−	26256.5i	−0.157102	−	1.36760i
$718$	−1682.41	−	971.342i	−0.0874473	−	0.0504877i
$719$	11471.4			0.595010			0.297505	−	0.954720i	$-0.403846\pi$
$719$	11471.4			0.595010			0.297505	+	0.954720i	$0.403846\pi$
$720$		0			0
$721$	18560.3			0.958701
$722$	−1232.62	−	711.651i	−0.0635363	−	0.0366827i
$723$	13719.5	−	10171.6i	0.705719	−	0.523217i
$724$	14356.3	+	24865.8i	0.736944	+	1.27642i
$725$		0			0
$726$	466.813	−	1076.32i	0.0238637	−	0.0550221i
$727$	−18757.5	−	10829.6i	−0.956914	−	0.552475i	−0.0616922	−	0.998095i	$-0.519650\pi$
$727$	−18757.5	−	10829.6i	−0.956914	−	0.552475i	−0.895222	+	0.445621i	$0.852983\pi$
$728$		−	5620.84i		−	0.286157i
$729$	−15227.5	+	12471.7i	−0.773636	+	0.633630i
$730$		0			0
$731$	9159.96	−	15865.5i	0.463466	−	0.802746i
$732$	−340.197	−	147.547i	−0.0171776	−	0.00745013i
$733$	−4920.51	+	2840.86i	−0.247944	+	0.143151i	−0.618823	−	0.785531i	$-0.712390\pi$
$733$	−4920.51	+	2840.86i	−0.247944	+	0.143151i	0.370878	+	0.928682i	$0.379057\pi$
$734$	688.045	+	1191.73i	0.0345997	+	0.0599285i
$735$		0			0
$736$	−707.259	+	1225.01i	−0.0354211	+	0.0613511i
$737$			10676.0i			0.533588i
$738$	1089.30	−	1019.57i	0.0543328	−	0.0508547i
$739$	−261.324			−0.0130080			−0.00650402	−	0.999979i	$-0.502070\pi$
$739$	−261.324			−0.0130080			−0.00650402	+	0.999979i	$0.502070\pi$
$740$		0			0
$741$	6017.95	−	691.306i	0.298347	−	0.0342723i
$742$	2565.04	−	1480.93i	0.126908	−	0.0732702i
$743$	14208.0	−	8202.97i	0.701533	−	0.405031i	−0.106385	−	0.994325i	$-0.533928\pi$
$743$	14208.0	−	8202.97i	0.701533	−	0.405031i	0.807918	+	0.589294i	$0.200594\pi$
$744$	2320.29	−	266.541i	0.114336	−	0.0131342i
$745$		0			0
$746$	−1476.59			−0.0724688
$747$	−1803.60	−	7746.74i	−0.0883403	−	0.379436i
$748$		−	18969.1i		−	0.927244i
$749$	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	$-0.341375\pi$
$752$	−25716.4	+	14847.4i	−1.24705	+	0.719985i
$753$	−16592.1	−	7196.20i	−0.802989	−	0.348266i
$754$	710.722	−	1231.01i	0.0343276	−	0.0594571i
$755$		0			0
$756$	−32761.3	+	11703.9i	−1.57608	+	0.563053i
$757$		−	13643.2i		−	0.655046i	−0.944843	−	0.327523i	$-0.893786\pi$
$757$		−	13643.2i		−	0.655046i	0.944843	−	0.327523i	$-0.106214\pi$
$758$	−981.680	−	566.773i	−0.0470399	−	0.0271585i
$759$	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	$-0.388391\pi$
$762$	958.975	−	710.980i	0.0455905	−	0.0338006i
$763$	25915.3	+	14962.2i	1.22962	+	0.709920i
$764$	−4745.63			−0.224726
$765$		0			0
$766$	−825.088			−0.0389186
$767$	−32247.9	−	18618.3i	−1.51813	−	0.876491i
$768$	2276.35	+	19816.1i	0.106954	+	0.931057i
$769$	−14442.7	−	25015.5i	−0.677265	−	1.17306i	−0.975801	−	0.218659i	$-0.929832\pi$
$769$	−14442.7	−	25015.5i	−0.677265	−	1.17306i	0.298536	−	0.954398i	$-0.403502\pi$
$770$		0			0
$771$	35077.1	−	4029.44i	1.63848	−	0.188219i
$772$	−8314.43	−	4800.34i	−0.387620	−	0.223793i
$773$		−	3031.34i		−	0.141048i	−0.997510	−	0.0705238i	$-0.977533\pi$
$773$		−	3031.34i		−	0.141048i	0.997510	−	0.0705238i	$-0.0224671\pi$
$774$	−245.974	+	809.907i	−0.0114229	+	0.0376118i
$775$		0			0
$776$	697.121	−	1207.45i	0.0322490	−	0.0558568i
$777$	13019.3	−	9652.46i	0.601113	−	0.445663i
$778$	−950.188	+	548.591i	−0.0437865	+	0.0252801i
$779$	2851.03	+	4938.13i	0.131128	+	0.227120i
$780$		0			0
$781$	440.092	−	762.262i	0.0201636	−	0.0349243i
$782$		−	978.019i		−	0.0447236i
$783$	−17365.0	−	3168.52i	−0.792559	−	0.144615i
$784$	−39558.7			−1.80205
$785$		0			0
$786$	792.829	−	1828.01i	0.0359787	−	0.0829554i
$787$	13124.4	−	7577.38i	0.594453	−	0.343208i	−0.172403	−	0.985026i	$-0.555153\pi$
$787$	13124.4	−	7577.38i	0.594453	−	0.343208i	0.766856	+	0.641819i	$0.221820\pi$
$788$	−22501.6	+	12991.3i	−1.01724	+	0.587306i
$789$	−16600.5	−	22390.8i	−0.749040	−	1.01031i
$790$		0			0
$791$	−53928.0			−2.42409
$792$	398.739	+	1712.65i	0.0178896	+	0.0768387i
$793$			450.270i			0.0201634i
$794$	421.737	−	730.470i	0.0188500	−	0.0326491i
$795$		0			0
$796$	−8386.00	−	14525.0i	−0.373409	−	0.646764i
$797$	24578.3	−	14190.3i	1.09236	−	0.630673i	0.158155	−	0.987414i	$-0.449445\pi$
$797$	24578.3	−	14190.3i	1.09236	−	0.630673i	0.934203	+	0.356741i	$0.116112\pi$
$798$	96.8459	+	843.062i	0.00429613	+	0.0373986i
$799$	31128.1	−	53915.5i	1.37827	−	2.38723i
$800$		0			0
$801$	−15734.9	−	16811.1i	−0.694089	−	0.741561i
$802$			405.646i			0.0178602i
$803$	6433.75	+	3714.53i	0.282742	+	0.163241i
$804$	14487.2	+	19540.5i	0.635479	+	0.857139i
$805$		0			0
$806$	−706.741	−	1224.11i	−0.0308857	−	0.0534957i
$807$	231.197	+	100.273i	0.0100849	+	0.00437394i
$808$	−3360.14	−	1939.98i	−0.146299	−	0.0844655i
$809$	14569.6			0.633175			0.316588	−	0.948563i	$-0.397463\pi$
$809$	14569.6			0.633175			0.316588	+	0.948563i	$0.397463\pi$
$810$		0			0
$811$	27927.7			1.20921			0.604607	−	0.796524i	$-0.293330\pi$
$811$	27927.7			1.20921			0.604607	+	0.796524i	$0.293330\pi$
$812$	−27019.0	−	15599.4i	−1.16771	−	0.674178i
$813$	−36435.7	−	15802.6i	−1.57178	−	0.681699i
$814$	−204.150	−	353.598i	−0.00879049	−	0.0152256i
$815$		0			0
$816$	−25575.6	−	34496.6i	−1.09721	−	1.47993i
$817$	−2801.46	−	1617.43i	−0.119964	−	0.0692614i
$818$			3588.68i			0.153393i
$819$	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	$0.291955\pi$
$822$	−140.210	−	1220.55i	−0.00594936	−	0.0517903i
$823$	27931.8	−	16126.4i	1.18304	−	0.683028i	0.226323	−	0.974052i	$-0.427330\pi$
$823$	27931.8	−	16126.4i	1.18304	−	0.683028i	0.956716	+	0.291025i	$0.0939962\pi$
$824$	−1068.78	−	1851.19i	−0.0451855	−	0.0782636i
$825$		0			0
$826$	2608.26	−	4517.64i	0.109871	−	0.190301i
$827$			13569.5i			0.570566i	0.958443	+	0.285283i	$0.0920876\pi$
$827$			13569.5i			0.570566i	−0.958443	+	0.285283i	$0.907912\pi$
$828$	−1605.36	−	6895.29i	−0.0673795	−	0.289406i
$829$	−742.559			−0.0311099			−0.0155550	−	0.999879i	$-0.504951\pi$
$829$	−742.559			−0.0311099			−0.0155550	+	0.999879i	$0.504951\pi$
$830$		0			0
$831$	15925.2	+	21480.0i	0.664788	+	0.896671i
$832$	21397.7	−	12354.0i	0.891625	−	0.514780i
$833$	71824.9	−	41468.1i	2.98750	−	1.72483i
$834$	668.217	−	1540.70i	0.0277440	−	0.0639688i
$835$		0			0
$836$	−3349.48			−0.138569
$837$	−11362.5	+	13378.9i	−0.469231	+	0.552500i
$838$		−	776.605i		−	0.0320136i
$839$	−17752.3	+	30747.9i	−0.730487	+	1.26524i	0.226189	+	0.974083i	$0.427373\pi$
$839$	−17752.3	+	30747.9i	−0.730487	+	1.26524i	−0.956675	+	0.291157i	$0.905960\pi$
$840$		0			0
$841$	4279.49	+	7412.29i	0.175468	+	0.303919i
$842$	−1095.52	+	632.499i	−0.0448386	+	0.0258876i
$843$	24438.2	−	18118.4i	0.998455	−	0.740250i
$844$	−2617.86	+	4534.26i	−0.106766	+	0.184924i
$845$		0			0
$846$	−835.889	+	2752.29i	−0.0339698	+	0.111851i
$847$			31267.6i			1.26844i
$848$	22919.9	+	13232.8i	0.928153	+	0.535869i
$849$	48492.9	−	5570.58i	1.96027	−	0.225185i
$850$		0			0
$851$	1649.11	+	2856.34i	0.0664285	+	0.115058i
$852$	−228.874	−	1992.39i	−0.00920316	−	0.0801153i
$853$	324.801	+	187.524i	0.0130375	+	0.00752719i	0.506505	−	0.862237i	$-0.330937\pi$
$853$	324.801	+	187.524i	0.0130375	+	0.00752719i	−0.493467	+	0.869764i	$0.664271\pi$
$854$	−63.0790			−0.00252754
$855$		0			0
$856$	−1791.59			−0.0715365
$857$	−27881.5	−	16097.4i	−1.11133	−	0.641629i	−0.172159	−	0.985069i	$-0.555074\pi$
$857$	−27881.5	−	16097.4i	−1.11133	−	0.641629i	−0.939174	+	0.343440i	$0.888408\pi$
$858$	854.896	−	633.816i	0.0340159	−	0.0252192i
$859$	−14068.8	−	24367.8i	−0.558813	−	0.967893i	−0.997596	−	0.0692994i	$-0.977924\pi$
$859$	−14068.8	−	24367.8i	−0.558813	−	0.967893i	0.438783	−	0.898593i	$-0.355410\pi$
$860$		0			0
$861$	−15822.3	+	36481.1i	−0.626274	+	1.44399i
$862$	−689.392	−	398.021i	−0.0272399	−	0.0157270i
$863$		−	15724.6i		−	0.620244i	−0.950697	−	0.310122i	$-0.899630\pi$
$863$		−	15724.6i		−	0.620244i	0.950697	−	0.310122i	$-0.100370\pi$
$864$	4585.67	+	3894.54i	0.180564	+	0.153351i
$865$		0			0
$866$	751.749	−	1302.07i	0.0294982	−	0.0510924i
$867$	59177.4	+	25665.9i	2.31807	+	1.00538i
$868$	−26867.7	+	15512.1i	−1.05063	+	0.606583i
$869$	4808.82	+	8329.12i	0.187719	+	0.325139i
$870$		0			0
$871$	14768.6	−	25580.0i	0.574531	−	0.995117i
$872$		−	3446.35i		−	0.133840i
$873$	2376.05	+	10205.5i	0.0921157	+	0.395652i
$874$	−172.694			−0.00668361
$875$		0			0
$876$	16816.5	−	1931.77i	0.648602	−	0.0745075i
$877$	13233.3	−	7640.23i	0.509528	−	0.294176i	−0.223112	−	0.974793i	$-0.571622\pi$
$877$	13233.3	−	7640.23i	0.509528	−	0.294176i	0.732639	+	0.680617i	$0.238288\pi$
$878$	−1276.46	+	736.963i	−0.0490642	+	0.0283272i
$879$	−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	$0.656484\pi$
$882$	−2797.63	+	2618.54i	−0.106804	+	0.0999669i
$883$		−	6562.59i		−	0.250112i	−0.992150	−	0.125056i	$-0.960089\pi$
$883$		−	6562.59i		−	0.250112i	0.992150	−	0.125056i	$-0.0399110\pi$
$884$	−26241.0	+	45450.7i	−0.998392	+	1.72927i
$885$		0			0
$886$	1611.63	+	2791.43i	0.0611104	+	0.105846i
$887$	43743.9	−	25255.5i	1.65589	−	0.956030i	0.681311	−	0.731994i	$-0.261410\pi$
$887$	43743.9	−	25255.5i	1.65589	−	0.956030i	0.974581	−	0.224035i	$-0.0719231\pi$
$888$	−1712.43	−	742.702i	−0.0647134	−	0.0280669i
$889$	−15908.2	+	27553.8i	−0.600162	+	1.03951i
$890$		0			0
$891$	−10983.6	−	7349.46i	−0.412979	−	0.276337i
$892$		−	9688.51i		−	0.363672i
$893$	−9520.17	−	5496.47i	−0.356753	−	0.205971i
$894$	567.456	−	1308.37i	0.0212288	−	0.0489468i
$895$		0			0
$896$	7081.43	+	12265.4i	0.264034	+	0.457320i
$897$	−6905.77	+	5119.91i	−0.257053	+	0.190578i
$898$	2845.60	+	1642.91i	0.105745	+	0.0610518i
$899$	−15741.4			−0.583986
$900$		0			0
$901$	−55486.3			−2.05163
$902$	867.559	+	500.886i	0.0320250	+	0.0184897i
$903$	−2574.51	−	22411.6i	−0.0948773	−	0.825925i
$904$	3105.40	+	5378.72i	0.114252	+	0.197891i
$905$		0			0
$906$	1871.51	−	214.987i	0.0686276	−	0.00788353i
$907$	6077.28	+	3508.72i	0.222484	+	0.128451i	0.607100	−	0.794626i	$-0.292333\pi$
$907$	6077.28	+	3508.72i	0.222484	+	0.128451i	−0.384616	+	0.923077i	$0.625666\pi$
$908$		−	12127.2i		−	0.443231i
$909$	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	$0.131143\pi$
$912$	−6091.25	+	4516.02i	−0.221164	+	0.163970i
$913$	4624.98	−	2670.23i	0.167650	−	0.0967928i
$914$	−228.153	−	395.172i	−0.00825669	−	0.0143010i
$915$		0			0
$916$	−24573.8	+	42563.0i	−0.886397	+	1.53528i
$917$			53104.4i			1.91239i
$918$	−4092.19	−	746.688i	−0.147127	−	0.0268457i
$919$	−23780.7			−0.853594			−0.426797	−	0.904347i	$-0.640358\pi$
$919$	−23780.7			−0.853594			−0.426797	+	0.904347i	$0.640358\pi$
$920$		0			0
$921$	17533.2	−	40425.9i	0.627293	−	1.44634i
$922$	693.713	−	400.515i	0.0247790	−	0.0143062i
$923$	−2108.96	+	1217.61i	−0.0752082	+	0.0434215i
$924$	−13911.4	−	18763.9i	−0.495295	−	0.668058i
$925$		0			0
$926$	2316.17			0.0821967
$927$	15371.6	+	4668.46i	0.544628	+	0.165407i
$928$			5395.41i			0.190854i
$929$	5094.54	−	8824.01i	0.179921	−	0.311632i	−0.761932	−	0.647657i	$-0.775749\pi$
$929$	5094.54	−	8824.01i	0.179921	−	0.311632i	0.941853	+	0.336024i	$0.109082\pi$
$930$		0			0
$931$	−7322.26	−	12682.5i	−0.257763	−	0.446459i
$932$	13863.7	−	8004.19i	0.487253	−	0.281316i
$933$	−4038.82	−	35158.7i	−0.141720	−	1.23370i
$934$	−925.488	+	1602.99i	−0.0324228	+	0.0561579i
$935$		0			0
$936$	1413.80	−	4655.16i	0.0493713	−	0.162563i
$937$		−	3880.22i		−	0.135284i	−0.997710	−	0.0676421i	$-0.978452\pi$
$937$		−	3880.22i		−	0.135284i	0.997710	−	0.0676421i	$-0.0215476\pi$
$938$	3583.54	+	2068.96i	0.124741	+	0.0720191i
$939$	−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	$0.599675\pi$
$942$	−1381.25	−	599.065i	−0.0477746	−	0.0207204i
$943$	−7008.07	−	4046.11i	−0.242008	−	0.139724i
$944$	46612.3			1.60710
$945$		0			0
$946$	−568.318			−0.0195324
$947$	6715.92	+	3877.44i	0.230452	+	0.133052i	0.610781	−	0.791800i	$-0.290856\pi$
$947$	6715.92	+	3877.44i	0.230452	+	0.133052i	−0.380328	+	0.924851i	$0.624189\pi$
$948$	20104.3	+	8719.45i	0.688773	+	0.298729i
$949$	−10277.0	−	17800.3i	−0.351534	−	0.608875i
$950$		0			0
$951$	4846.93	+	6537.58i	0.165271	+	0.222918i
$952$	−12775.1	−	7375.72i	−0.434920	−	0.251101i
$953$			22527.9i			0.765739i	0.923802	+	0.382870i	$0.125064\pi$
$953$			22527.9i			0.765739i	−0.923802	+	0.382870i	$0.874936\pi$
$954$	2496.85	−	581.318i	0.0847365	−	0.0197284i
$955$		0			0
$956$	20216.2	−	35015.5i	0.683931	−	1.18460i
$957$	−1352.57	−	11774.4i	−0.0456868	−	0.397713i
$958$	2669.60	−	1541.29i	0.0900321	−	0.0519800i
$959$	16371.9	+	28356.9i	0.551277	+	0.954840i
$960$		0			0
$961$	7068.91	−	12243.7i	0.237283	−	0.410987i
$962$			1129.65i			0.0378600i
$963$	9830.43	−	9201.13i	0.328952	−	0.307894i
$964$	26127.8			0.872947
$965$		0			0
$966$	−717.254	−	967.438i	−0.0238895	−	0.0322224i
$967$	−4895.13	+	2826.20i	−0.162789	+	0.0939861i	−0.579181	−	0.815199i	$-0.696628\pi$
$967$	−4895.13	+	2826.20i	−0.162789	+	0.0939861i	0.416392	+	0.909185i	$0.363294\pi$
$968$	3118.59	−	1800.52i	0.103549	−	0.0597840i
$969$	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	$0.394941\pi$
$972$	−30076.7	+	1452.77i	−0.992501	+	0.0479398i
$973$			44757.9i			1.47469i
$974$	364.858	−	631.953i	0.0120029	−	0.0207896i
$975$		0			0
$976$	−281.821	−	488.129i	−0.00924270	−	0.0160088i
$977$	−23974.7	+	13841.8i	−0.785076	+	0.453264i	−0.838226	−	0.545323i	$-0.816407\pi$
$977$	−23974.7	+	13841.8i	−0.785076	+	0.453264i	0.0531500	+	0.998587i	$0.483074\pi$
$978$	−1332.13	+	987.636i	−0.0435551	+	0.0322915i
$979$	7730.14	−	13389.0i	0.252356	−	0.437093i
$980$		0			0
$981$	17699.6	+	18910.1i	0.576049	+	0.615447i
$982$		−	2506.60i		−	0.0814549i
$983$	−26514.6	−	15308.2i	−0.860310	−	0.496700i	0.00380619	−	0.999993i	$-0.498788\pi$
$983$	−26514.6	−	15308.2i	−0.860310	−	0.496700i	−0.864116	+	0.503293i	$0.832122\pi$
$984$	4549.70	−	522.643i	0.147398	−	0.0169321i
$985$		0			0
$986$	−1865.23	−	3230.68i	−0.0602446	−	0.104347i
$987$	−8748.90	−	76160.8i	−0.282148	−	2.45616i
$988$	8025.48	+	4633.51i	0.258426	+	0.149202i
$989$	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	$0.574459\pi$
$992$	4646.39	+	2682.59i	0.148713	+	0.0858593i
$993$	10195.5	−	7558.88i	0.325824	−	0.241565i
$994$	−170.576	−	295.447i	−0.00544301	−	0.00942756i
$995$		0			0
$996$	4841.72	−	11163.5i	0.154032	−	0.355149i
$997$	5973.20	+	3448.63i	0.189743	+	0.109548i	0.591862	−	0.806039i	$-0.298393\pi$
$997$	5973.20	+	3448.63i	0.189743	+	0.109548i	−0.402120	+	0.915587i	$0.631726\pi$
$998$		−	1222.48i		−	0.0387745i
$999$	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.k.d.124.8		28
5.2	odd	4		225.4.e.d.151.4		14
5.3	odd	4		45.4.e.c.16.4	✓	14
5.4	even	2	inner	225.4.k.d.124.7		28
9.4	even	3	inner	225.4.k.d.49.7		28
15.8	even	4		135.4.e.c.46.4		14
45.2	even	12		2025.4.a.ba.1.4		7
45.4	even	6	inner	225.4.k.d.49.8		28
45.7	odd	12		2025.4.a.bb.1.4		7
45.13	odd	12		45.4.e.c.31.4	yes	14
45.22	odd	12		225.4.e.d.76.4		14
45.23	even	12		135.4.e.c.91.4		14
45.38	even	12		405.4.a.n.1.4		7
45.43	odd	12		405.4.a.m.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.4	✓	14	5.3	odd	4
45.4.e.c.31.4	yes	14	45.13	odd	12
135.4.e.c.46.4		14	15.8	even	4
135.4.e.c.91.4		14	45.23	even	12
225.4.e.d.76.4		14	45.22	odd	12
225.4.e.d.151.4		14	5.2	odd	4
225.4.k.d.49.7		28	9.4	even	3	inner
225.4.k.d.49.8		28	45.4	even	6	inner
225.4.k.d.124.7		28	5.4	even	2	inner
225.4.k.d.124.8		28	1.1	even	1	trivial
405.4.a.m.1.4		7	45.43	odd	12
405.4.a.n.1.4		7	45.38	even	12
2025.4.a.ba.1.4		7	45.2	even	12
2025.4.a.bb.1.4		7	45.7	odd	12

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.195072 + 0.112625i) q^{2} +(-4.76710 - 2.06755i) q^{3} +(-3.97463 - 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(27.0148 + 15.5970i) q^{7} -3.59257i q^{8} +(18.4505 + 19.7124i) q^{9} +O(q^{10})\)	\(q+(0.195072 + 0.112625i) q^{2} +(-4.76710 - 2.06755i) q^{3} +(-3.97463 - 6.88426i) q^{4} +(-0.697071 - 0.940215i) q^{6} +(27.0148 + 15.5970i) q^{7} -3.59257i q^{8} +(18.4505 + 19.7124i) q^{9} +(-9.06424 + 15.6997i) q^{11} +(4.71394 + 41.0357i) q^{12} +(43.4366 - 25.0781i) q^{13} +(3.51322 + 6.08508i) q^{14} +(-31.3924 + 54.3733i) q^{16} -131.631i q^{17} +(1.37907 + 5.92333i) q^{18} -23.2428 q^{19} +(-96.5348 - 130.207i) q^{21} +(-3.53636 + 2.04172i) q^{22} +(28.5664 - 16.4928i) q^{23} +(-7.42780 + 17.1261i) q^{24} +11.2977 q^{26} +(-47.1991 - 132.118i) q^{27} -247.969i q^{28} +(62.9087 - 108.961i) q^{29} +(-62.5563 - 108.351i) q^{31} +(-37.1376 + 21.4414i) q^{32} +(75.6700 - 56.1014i) q^{33} +(14.8249 - 25.6775i) q^{34} +(62.3714 - 205.368i) q^{36} +99.9894i q^{37} +(-4.53402 - 2.61772i) q^{38} +(-258.917 + 29.7428i) q^{39} +(-122.663 - 212.458i) q^{41} +(-4.16670 - 36.2720i) q^{42} +(120.530 + 69.5882i) q^{43} +144.108 q^{44} +7.43001 q^{46} +(409.596 + 236.480i) q^{47} +(262.070 - 194.298i) q^{48} +(315.033 + 545.654i) q^{49} +(-272.153 + 627.498i) q^{51} +(-345.289 - 199.352i) q^{52} -421.529i q^{53} +(5.67258 - 31.0884i) q^{54} +(56.0333 - 97.0526i) q^{56} +(110.801 + 48.0556i) q^{57} +(24.5435 - 14.1702i) q^{58} +(-371.207 - 642.949i) q^{59} +(-4.48868 + 7.77462i) q^{61} -28.1816i q^{62} +(190.982 + 820.300i) q^{63} +492.620 q^{64} +(21.0795 - 2.42149i) q^{66} +(510.008 - 294.453i) q^{67} +(-906.182 + 523.185i) q^{68} +(-170.279 + 19.5606i) q^{69} -48.5526 q^{71} +(70.8182 - 66.2847i) q^{72} -409.800i q^{73} +(-11.2613 + 19.5051i) q^{74} +(92.3816 + 160.010i) q^{76} +(-489.737 + 282.750i) q^{77} +(-53.8572 - 23.3585i) q^{78} +(265.263 - 459.449i) q^{79} +(-48.1577 + 727.408i) q^{81} -55.2595i q^{82} +(-255.122 - 147.295i) q^{83} +(-512.688 + 1182.10i) q^{84} +(15.6747 + 27.1494i) q^{86} +(-525.174 + 389.362i) q^{87} +(56.4023 + 32.5639i) q^{88} -852.817 q^{89} +1564.57 q^{91} +(-227.082 - 131.106i) q^{92} +(74.1922 + 645.857i) q^{93} +(53.2672 + 92.2615i) q^{94} +(221.370 - 25.4296i) q^{96} +(336.096 + 194.045i) q^{97} +141.922i q^{98} +(-476.719 + 110.990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Introduction

L-functions

Modular forms

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