LMFDB - Embedded newform 2100.2.q.l.1201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1201,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("2100.1201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.q (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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.17819046144.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 10x^{6} + 8x^{5} + 38x^{4} - 4x^{3} + 16x^{2} + 4x + 4 $ x^8 - 2x^7 + 10x^6 + 8x^5 + 38x^4 - 4x^3 + 16x^2 + 4*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.2
Root			$-0.234240 + 0.405716i$ of defining polynomial
Character	$\chi$	$=$	2100.1201
Dual form			2100.2.q.l.1801.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.687541 - 2.55486i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.687541 - 2.55486i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.90032 + 3.29145i) q^{11} +2.31204 q^{13} +(-0.187541 + 0.324831i) q^{17} +(-0.453301 - 0.785140i) q^{19} +(2.55634 + 0.681999i) q^{21} +(0.656022 + 1.13626i) q^{23} +1.00000 q^{27} -6.15561 q^{29} +(-2.81204 + 4.87060i) q^{31} +(-1.90032 - 3.29145i) q^{33} +(-2.86880 - 4.96891i) q^{37} +(-1.15602 + 2.00229i) q^{39} +0.199364 q^{41} +12.4019 q^{43} +(5.40368 + 9.35944i) q^{47} +(-6.05457 + 3.51314i) q^{49} +(-0.187541 - 0.324831i) q^{51} +(-1.53152 + 2.65267i) q^{53} +0.906602 q^{57} +(-7.14756 + 12.3799i) q^{59} +(-1.08963 - 1.88729i) q^{61} +(-1.86880 + 1.87286i) q^{63} +(-2.78094 + 4.81673i) q^{67} -1.31204 q^{69} -9.88296 q^{71} +(-3.20095 + 5.54422i) q^{73} +(9.71572 + 2.59203i) q^{77} +(7.61645 + 13.1921i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.99917 q^{83} +(3.07780 - 5.33091i) q^{87} +(2.50512 + 4.33900i) q^{89} +(-1.58963 - 5.90694i) q^{91} +(-2.81204 - 4.87060i) q^{93} -6.36252 q^{97} +3.80064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.687541	−	2.55486i	−0.259866	−	0.965645i
$7$	−0.687541	−	2.55486i	−0.259866	−	0.965645i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.90032	+	3.29145i	−0.572967	+	0.992409i	0.423292	+	0.905993i	$0.360875\pi$
$11$	−1.90032	+	3.29145i	−0.572967	+	0.992409i	−0.996259	+	0.0864153i	$0.972459\pi$
$12$		0			0
$13$	2.31204			0.641246			0.320623	−	0.947207i	$-0.396108\pi$
$13$	2.31204			0.641246			0.320623	+	0.947207i	$0.396108\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.187541	+	0.324831i	−0.0454855	+	0.0787832i	−0.887872	−	0.460091i	$-0.847817\pi$
$17$	−0.187541	+	0.324831i	−0.0454855	+	0.0787832i	0.842386	+	0.538874i	$0.181150\pi$
$18$		0			0
$19$	−0.453301	−	0.785140i	−0.103994	−	0.180124i	0.809333	−	0.587351i	$-0.199829\pi$
$19$	−0.453301	−	0.785140i	−0.103994	−	0.180124i	−0.913327	+	0.407227i	$0.866496\pi$
$20$		0			0
$21$	2.55634	+	0.681999i	0.557839	+	0.148824i
$22$		0			0
$23$	0.656022	+	1.13626i	0.136790	+	0.236927i	0.926280	−	0.376836i	$-0.122988\pi$
$23$	0.656022	+	1.13626i	0.136790	+	0.236927i	−0.789490	+	0.613764i	$0.789655\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−6.15561			−1.14307			−0.571534	−	0.820578i	$-0.693651\pi$
$29$	−6.15561			−1.14307			−0.571534	+	0.820578i	$0.693651\pi$
$30$		0			0
$31$	−2.81204	+	4.87060i	−0.505058	+	0.874786i	0.494925	+	0.868936i	$0.335196\pi$
$31$	−2.81204	+	4.87060i	−0.505058	+	0.874786i	−0.999983	+	0.00585051i	$0.998138\pi$
$32$		0			0
$33$	−1.90032	−	3.29145i	−0.330803	−	0.572967i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.86880	−	4.96891i	−0.471628	−	0.816883i	0.527845	−	0.849340i	$-0.323000\pi$
$37$	−2.86880	−	4.96891i	−0.471628	−	0.816883i	−0.999473	+	0.0324574i	$0.989667\pi$
$38$		0			0
$39$	−1.15602	+	2.00229i	−0.185112	+	0.320623i
$40$		0			0
$41$	0.199364			0.0311354			0.0155677	−	0.999879i	$-0.495044\pi$
$41$	0.199364			0.0311354			0.0155677	+	0.999879i	$0.495044\pi$
$42$		0			0
$43$	12.4019			1.89127			0.945637	−	0.325225i	$-0.105440\pi$
$43$	12.4019			1.89127			0.945637	+	0.325225i	$0.105440\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.40368	+	9.35944i	0.788207	+	1.36521i	0.927064	+	0.374902i	$0.122324\pi$
$47$	5.40368	+	9.35944i	0.788207	+	1.36521i	−0.138857	+	0.990312i	$0.544343\pi$
$48$		0			0
$49$	−6.05457	+	3.51314i	−0.864939	+	0.501877i
$50$		0			0
$51$	−0.187541	−	0.324831i	−0.0262611	−	0.0454855i
$52$		0			0
$53$	−1.53152	+	2.65267i	−0.210370	+	0.364372i	−0.951830	−	0.306625i	$-0.900800\pi$
$53$	−1.53152	+	2.65267i	−0.210370	+	0.364372i	0.741460	+	0.670997i	$0.234134\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.906602			0.120082
$58$		0			0
$59$	−7.14756	+	12.3799i	−0.930533	+	1.61173i	−0.148120	+	0.988969i	$0.547322\pi$
$59$	−7.14756	+	12.3799i	−0.930533	+	1.61173i	−0.782412	+	0.622761i	$0.786011\pi$
$60$		0			0
$61$	−1.08963	−	1.88729i	−0.139512	−	0.241643i	0.787800	−	0.615931i	$-0.211220\pi$
$61$	−1.08963	−	1.88729i	−0.139512	−	0.241643i	−0.927312	+	0.374289i	$0.877887\pi$
$62$		0			0
$63$	−1.86880	+	1.87286i	−0.235447	+	0.235958i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.78094	+	4.81673i	−0.339746	+	0.588457i	−0.984385	−	0.176030i	$-0.943674\pi$
$67$	−2.78094	+	4.81673i	−0.339746	+	0.588457i	0.644639	+	0.764487i	$0.277008\pi$
$68$		0			0
$69$	−1.31204			−0.157952
$70$		0			0
$71$	−9.88296			−1.17289			−0.586446	−	0.809989i	$-0.699473\pi$
$71$	−9.88296			−1.17289			−0.586446	+	0.809989i	$0.699473\pi$
$72$		0			0
$73$	−3.20095	+	5.54422i	−0.374643	+	0.648901i	−0.990274	−	0.139134i	$-0.955568\pi$
$73$	−3.20095	+	5.54422i	−0.374643	+	0.648901i	0.615630	+	0.788035i	$0.288902\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.71572	+	2.59203i	1.10721	+	0.295389i
$78$		0			0
$79$	7.61645	+	13.1921i	0.856918	+	1.48423i	0.874854	+	0.484386i	$0.160957\pi$
$79$	7.61645	+	13.1921i	0.856918	+	1.48423i	−0.0179364	+	0.999839i	$0.505710\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−8.99917			−0.987787			−0.493894	−	0.869522i	$-0.664427\pi$
$83$	−8.99917			−0.987787			−0.493894	+	0.869522i	$0.664427\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.07780	−	5.33091i	0.329975	−	0.571534i
$88$		0			0
$89$	2.50512	+	4.33900i	0.265543	+	0.459933i	0.967706	−	0.252083i	$-0.0811155\pi$
$89$	2.50512	+	4.33900i	0.265543	+	0.459933i	−0.702163	+	0.712016i	$0.747782\pi$
$90$		0			0
$91$	−1.58963	−	5.90694i	−0.166638	−	0.619216i
$92$		0			0
$93$	−2.81204	−	4.87060i	−0.291595	−	0.505058i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.36252			−0.646016			−0.323008	−	0.946396i	$-0.604694\pi$
$97$	−6.36252			−0.646016			−0.323008	+	0.946396i	$0.604694\pi$
$98$		0			0
$99$	3.80064			0.381978
$100$		0			0
$101$	2.94148	−	5.09479i	0.292688	−	0.506951i	−0.681756	−	0.731579i	$-0.738784\pi$
$101$	2.94148	−	5.09479i	0.292688	−	0.506951i	0.974444	+	0.224629i	$0.0721169\pi$
$102$		0			0
$103$	−6.33728	−	10.9765i	−0.624431	−	1.08155i	−0.988651	−	0.150233i	$-0.951998\pi$
$103$	−6.33728	−	10.9765i	−0.624431	−	1.08155i	0.364220	−	0.931313i	$-0.381336\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.25906	+	2.18076i	0.121718	+	0.210822i	0.920445	−	0.390871i	$-0.127826\pi$
$107$	1.25906	+	2.18076i	0.121718	+	0.210822i	−0.798727	+	0.601693i	$0.794493\pi$
$108$		0			0
$109$	−5.65938	+	9.80233i	−0.542070	+	0.938893i	0.456715	+	0.889613i	$0.349026\pi$
$109$	−5.65938	+	9.80233i	−0.542070	+	0.938893i	−0.998785	+	0.0492801i	$0.984307\pi$
$110$		0			0
$111$	5.73760			0.544589
$112$		0			0
$113$	15.4752			1.45578			0.727892	−	0.685692i	$-0.240500\pi$
$113$	15.4752			1.45578			0.727892	+	0.685692i	$0.240500\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.15602	−	2.00229i	−0.106874	−	0.185112i
$118$		0			0
$119$	0.958839	+	0.255806i	0.0878967	+	0.0234497i
$120$		0			0
$121$	−1.72242	−	2.98332i	−0.156583	−	0.271211i
$122$		0			0
$123$	−0.0996818	+	0.172654i	−0.00898801	+	0.0155677i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−15.1159			−1.34132			−0.670658	−	0.741767i	$-0.733988\pi$
$127$	−15.1159			−1.34132			−0.670658	+	0.741767i	$0.733988\pi$
$128$		0			0
$129$	−6.20095	+	10.7404i	−0.545964	+	0.945637i
$130$		0			0
$131$	1.93519	+	3.35186i	0.169079	+	0.292853i	0.938096	−	0.346375i	$-0.112587\pi$
$131$	1.93519	+	3.35186i	0.169079	+	0.292853i	−0.769017	+	0.639228i	$0.779254\pi$
$132$		0			0
$133$	−1.69426	+	1.69793i	−0.146911	+	0.147230i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.49782	+	14.7187i	−0.726018	+	1.25750i	0.232536	+	0.972588i	$0.425298\pi$
$137$	−8.49782	+	14.7187i	−0.726018	+	1.25750i	−0.958554	+	0.284912i	$0.908036\pi$
$138$		0			0
$139$	−8.19500			−0.695091			−0.347546	−	0.937663i	$-0.612985\pi$
$139$	−8.19500			−0.695091			−0.347546	+	0.937663i	$0.612985\pi$
$140$		0			0
$141$	−10.8074			−0.910143
$142$		0			0
$143$	−4.39362	+	7.60997i	−0.367413	+	0.636378i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.0151800	−	6.99998i	−0.00125202	−	0.577349i
$148$		0			0
$149$	−5.97812	−	10.3544i	−0.489747	−	0.848266i	0.510184	−	0.860066i	$-0.329577\pi$
$149$	−5.97812	−	10.3544i	−0.489747	−	0.848266i	−0.999930	+	0.0117991i	$0.996244\pi$
$150$		0			0
$151$	−9.02305	+	15.6284i	−0.734286	+	1.27182i	0.220750	+	0.975330i	$0.429149\pi$
$151$	−9.02305	+	15.6284i	−0.734286	+	1.27182i	−0.955036	+	0.296490i	$0.904184\pi$
$152$		0			0
$153$	0.375083			0.0303237
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.2455	−	19.4777i	0.897486	−	1.55449i	0.0667896	−	0.997767i	$-0.478724\pi$
$157$	11.2455	−	19.4777i	0.897486	−	1.55449i	0.830697	−	0.556725i	$-0.187942\pi$
$158$		0			0
$159$	−1.53152	−	2.65267i	−0.121457	−	0.210370i
$160$		0			0
$161$	2.45195	−	2.45727i	0.193241	−	0.193660i
$162$		0			0
$163$	−5.17572	−	8.96461i	−0.405394	−	0.702162i	0.588974	−	0.808152i	$-0.299532\pi$
$163$	−5.17572	−	8.96461i	−0.405394	−	0.702162i	−0.994367	+	0.105990i	$0.966199\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.08083			0.161020			0.0805098	−	0.996754i	$-0.474345\pi$
$167$	2.08083			0.161020			0.0805098	+	0.996754i	$0.474345\pi$
$168$		0			0
$169$	−7.65445			−0.588804
$170$		0			0
$171$	−0.453301	+	0.785140i	−0.0346648	+	0.0600412i
$172$		0			0
$173$	−11.9352	−	20.6724i	−0.907416	−	1.57169i	−0.817641	−	0.575729i	$-0.804718\pi$
$173$	−11.9352	−	20.6724i	−0.907416	−	1.57169i	−0.0897753	−	0.995962i	$-0.528615\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.14756	−	12.3799i	−0.537243	−	0.930533i
$178$		0			0
$179$	−6.40544	+	11.0946i	−0.478765	+	0.829246i	−0.999704	−	0.0243486i	$-0.992249\pi$
$179$	−6.40544	+	11.0946i	−0.478765	+	0.829246i	0.520938	+	0.853594i	$0.325582\pi$
$180$		0			0
$181$	−3.04611			−0.226416			−0.113208	−	0.993571i	$-0.536113\pi$
$181$	−3.04611			−0.226416			−0.113208	+	0.993571i	$0.536113\pi$
$182$		0			0
$183$	2.17925			0.161095
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.712777	−	1.23457i	−0.0521234	−	0.0902804i
$188$		0			0
$189$	−0.687541	−	2.55486i	−0.0500113	−	0.185838i
$190$		0			0
$191$	8.58116	+	14.8630i	0.620911	+	1.07545i	0.989316	+	0.145784i	$0.0465705\pi$
$191$	8.58116	+	14.8630i	0.620911	+	1.07545i	−0.368405	+	0.929665i	$0.620096\pi$
$192$		0			0
$193$	−7.06816	+	12.2424i	−0.508777	+	0.881228i	0.491171	+	0.871063i	$0.336569\pi$
$193$	−7.06816	+	12.2424i	−0.508777	+	0.881228i	−0.999948	+	0.0101652i	$0.996764\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.80818			0.128827			0.0644137	−	0.997923i	$-0.479482\pi$
$197$	1.80818			0.128827			0.0644137	+	0.997923i	$0.479482\pi$
$198$		0			0
$199$	9.11645	−	15.7902i	0.646248	−	1.11933i	−0.337764	−	0.941231i	$-0.609670\pi$
$199$	9.11645	−	15.7902i	0.646248	−	1.11933i	0.984012	−	0.178104i	$-0.0569963\pi$
$200$		0			0
$201$	−2.78094	−	4.81673i	−0.196152	−	0.339746i
$202$		0			0
$203$	4.23224	+	15.7267i	0.297045	+	1.10380i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.656022	−	1.13626i	0.0455967	−	0.0789758i
$208$		0			0
$209$	3.44566			0.238342
$210$		0			0
$211$	16.1927			1.11475			0.557375	−	0.830261i	$-0.311809\pi$
$211$	16.1927			1.11475			0.557375	+	0.830261i	$0.311809\pi$
$212$		0			0
$213$	4.94148	−	8.55889i	0.338585	−	0.586446i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	14.3771	+	3.83563i	0.975980	+	0.260379i
$218$		0			0
$219$	−3.20095	−	5.54422i	−0.216300	−	0.374643i
$220$		0			0
$221$	−0.433604	+	0.751024i	−0.0291674	+	0.0505194i
$222$		0			0
$223$	−9.91415			−0.663900			−0.331950	−	0.943297i	$-0.607707\pi$
$223$	−9.91415			−0.663900			−0.331950	+	0.943297i	$0.607707\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.80986	+	11.7950i	−0.451987	+	0.782864i	−0.998509	−	0.0545806i	$-0.982618\pi$
$227$	−6.80986	+	11.7950i	−0.451987	+	0.782864i	0.546523	+	0.837444i	$0.315951\pi$
$228$		0			0
$229$	−11.5268	−	19.9650i	−0.761714	−	1.31933i	−0.941966	−	0.335707i	$-0.891025\pi$
$229$	−11.5268	−	19.9650i	−0.761714	−	1.31933i	0.180252	−	0.983620i	$-0.442309\pi$
$230$		0			0
$231$	−7.10263	+	7.11804i	−0.467318	+	0.468333i
$232$		0			0
$233$	15.1606	+	26.2589i	0.993201	+	1.72027i	0.597416	+	0.801932i	$0.296194\pi$
$233$	15.1606	+	26.2589i	0.993201	+	1.72027i	0.395786	+	0.918343i	$0.370472\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−15.2329			−0.989484
$238$		0			0
$239$	11.0327			0.713647			0.356823	−	0.934172i	$-0.383860\pi$
$239$	11.0327			0.713647			0.356823	+	0.934172i	$0.383860\pi$
$240$		0			0
$241$	−3.16021	+	5.47364i	−0.203567	+	0.352588i	−0.949675	−	0.313236i	$-0.898587\pi$
$241$	−3.16021	+	5.47364i	−0.203567	+	0.352588i	0.746108	+	0.665825i	$0.231920\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.04805	−	1.81528i	−0.0666860	−	0.115503i
$248$		0			0
$249$	4.49959	−	7.79351i	0.285150	−	0.493894i
$250$		0			0
$251$	19.3161			1.21922			0.609609	−	0.792702i	$-0.291326\pi$
$251$	19.3161			1.21922			0.609609	+	0.792702i	$0.291326\pi$
$252$		0			0
$253$	−4.98660			−0.313505
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.17238	+	12.4229i	0.447401	+	0.774921i	0.998216	−	0.0597064i	$-0.0190165\pi$
$257$	7.17238	+	12.4229i	0.447401	+	0.774921i	−0.550815	+	0.834627i	$0.685683\pi$
$258$		0			0
$259$	−10.7224	+	10.7457i	−0.666259	+	0.667705i
$260$		0			0
$261$	3.07780	+	5.33091i	0.190511	+	0.329975i
$262$		0			0
$263$	−4.53329	+	7.85188i	−0.279534	+	0.484168i	−0.971269	−	0.237984i	$-0.923513\pi$
$263$	−4.53329	+	7.85188i	−0.279534	+	0.484168i	0.691735	+	0.722152i	$0.256847\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.01025			−0.306622
$268$		0			0
$269$	5.33309	−	9.23719i	0.325165	−	0.563201i	−0.656381	−	0.754429i	$-0.727914\pi$
$269$	5.33309	−	9.23719i	0.325165	−	0.563201i	0.981546	+	0.191228i	$0.0612470\pi$
$270$		0			0
$271$	10.2721	+	17.7917i	0.623983	+	1.08077i	0.988737	+	0.149667i	$0.0478200\pi$
$271$	10.2721	+	17.7917i	0.623983	+	1.08077i	−0.364753	+	0.931104i	$0.618847\pi$
$272$		0			0
$273$	5.91037	+	1.57681i	0.357712	+	0.0954331i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.55593	−	11.3552i	0.393907	−	0.682268i	−0.599054	−	0.800709i	$-0.704456\pi$
$277$	6.55593	−	11.3552i	0.393907	−	0.682268i	0.992961	+	0.118441i	$0.0377897\pi$
$278$		0			0
$279$	5.62409			0.336705
$280$		0			0
$281$	−12.3701			−0.737936			−0.368968	−	0.929442i	$-0.620289\pi$
$281$	−12.3701			−0.737936			−0.368968	+	0.929442i	$0.620289\pi$
$282$		0			0
$283$	9.64932	−	16.7131i	0.573593	−	0.993492i	−0.422600	−	0.906316i	$-0.638883\pi$
$283$	9.64932	−	16.7131i	0.573593	−	0.993492i	0.996193	−	0.0871757i	$-0.0277841\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.137071	−	0.509345i	−0.00809103	−	0.0300657i
$288$		0			0
$289$	8.42966	+	14.6006i	0.495862	+	0.858858i
$290$		0			0
$291$	3.18126	−	5.51010i	0.186489	−	0.323008i
$292$		0			0
$293$	18.6340			1.08861			0.544305	−	0.838888i	$-0.316794\pi$
$293$	18.6340			1.08861			0.544305	+	0.838888i	$0.316794\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.90032	+	3.29145i	−0.110268	+	0.190989i
$298$		0			0
$299$	1.51675	+	2.62709i	0.0877161	+	0.151929i
$300$		0			0
$301$	−8.52683	−	31.6851i	−0.491478	−	1.82630i
$302$		0			0
$303$	2.94148	+	5.09479i	0.168984	+	0.292688i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	17.3278			0.988949			0.494475	−	0.869192i	$-0.335360\pi$
$307$	17.3278			0.988949			0.494475	+	0.869192i	$0.335360\pi$
$308$		0			0
$309$	12.6746			0.721031
$310$		0			0
$311$	0.484075	−	0.838442i	0.0274494	−	0.0475437i	−0.851974	−	0.523583i	$-0.824595\pi$
$311$	0.484075	−	0.838442i	0.0274494	−	0.0475437i	0.879424	+	0.476040i	$0.157928\pi$
$312$		0			0
$313$	−13.3373	−	23.1008i	−0.753868	−	1.30574i	−0.945935	−	0.324355i	$-0.894853\pi$
$313$	−13.3373	−	23.1008i	−0.753868	−	1.30574i	0.192068	−	0.981382i	$-0.438481\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.0177	+	27.7435i	0.899644	+	1.55823i	0.827949	+	0.560803i	$0.189507\pi$
$317$	16.0177	+	27.7435i	0.899644	+	1.55823i	0.0716949	+	0.997427i	$0.477159\pi$
$318$		0			0
$319$	11.6976	−	20.2609i	0.654941	−	1.13439i
$320$		0			0
$321$	−2.51812			−0.140548
$322$		0			0
$323$	0.340051			0.0189209
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−5.65938	−	9.80233i	−0.312964	−	0.542070i
$328$		0			0
$329$	20.1968	−	20.2406i	1.11348	−	1.11590i
$330$		0			0
$331$	0.343564	+	0.595070i	0.0188840	+	0.0327080i	0.875313	−	0.483557i	$-0.160655\pi$
$331$	0.343564	+	0.595070i	0.0188840	+	0.0327080i	−0.856429	+	0.516265i	$0.827322\pi$
$332$		0			0
$333$	−2.86880	+	4.96891i	−0.157209	+	0.272294i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	15.0220			0.818300			0.409150	−	0.912467i	$-0.365825\pi$
$337$	15.0220			0.818300			0.409150	+	0.912467i	$0.365825\pi$
$338$		0			0
$339$	−7.73760	+	13.4019i	−0.420249	+	0.727892i
$340$		0			0
$341$	−10.6876	−	18.5114i	−0.578764	−	1.00245i
$342$		0			0
$343$	13.1383	+	13.0531i	0.709403	+	0.704803i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.4247	+	21.5203i	−0.666994	+	1.15527i	0.311746	+	0.950165i	$0.399086\pi$
$347$	−12.4247	+	21.5203i	−0.666994	+	1.15527i	−0.978740	+	0.205102i	$0.934247\pi$
$348$		0			0
$349$	25.4530			1.36247			0.681235	−	0.732065i	$-0.261443\pi$
$349$	25.4530			1.36247			0.681235	+	0.732065i	$0.261443\pi$
$350$		0			0
$351$	2.31204			0.123408
$352$		0			0
$353$	7.32964	−	12.6953i	0.390118	−	0.675703i	−0.602347	−	0.798234i	$-0.705768\pi$
$353$	7.32964	−	12.6953i	0.390118	−	0.675703i	0.992465	+	0.122531i	$0.0391010\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.700954	+	0.702476i	−0.0370984	+	0.0371790i
$358$		0			0
$359$	2.96430	+	5.13431i	0.156450	+	0.270979i	0.933586	−	0.358354i	$-0.116662\pi$
$359$	2.96430	+	5.13431i	0.156450	+	0.270979i	−0.777136	+	0.629332i	$0.783328\pi$
$360$		0			0
$361$	9.08904	−	15.7427i	0.478370	−	0.828562i
$362$		0			0
$363$	3.44484			0.180807
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.55122	−	4.41884i	0.133172	−	0.230661i	−0.791725	−	0.610877i	$-0.790817\pi$
$367$	2.55122	−	4.41884i	0.133172	−	0.230661i	0.924898	+	0.380216i	$0.124150\pi$
$368$		0			0
$369$	−0.0996818	−	0.172654i	−0.00518923	−	0.00898801i
$370$		0			0
$371$	7.83017	+	2.08899i	0.406522	+	0.108455i
$372$		0			0
$373$	−2.38221	−	4.12611i	−0.123346	−	0.213642i	0.797739	−	0.603003i	$-0.206029\pi$
$373$	−2.38221	−	4.12611i	−0.123346	−	0.213642i	−0.921085	+	0.389361i	$0.872696\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.2320			−0.732987
$378$		0			0
$379$	−14.6147			−0.750707			−0.375353	−	0.926882i	$-0.622479\pi$
$379$	−14.6147			−0.750707			−0.375353	+	0.926882i	$0.622479\pi$
$380$		0			0
$381$	7.55793	−	13.0907i	0.387205	−	0.670658i
$382$		0			0
$383$	1.00672	+	1.74368i	0.0514408	+	0.0890980i	0.890599	−	0.454789i	$-0.150285\pi$
$383$	1.00672	+	1.74368i	0.0514408	+	0.0890980i	−0.839158	+	0.543887i	$0.816952\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.20095	−	10.7404i	−0.315212	−	0.545964i
$388$		0			0
$389$	0.264600	−	0.458301i	0.0134158	−	0.0232368i	−0.859240	−	0.511573i	$-0.829063\pi$
$389$	0.264600	−	0.458301i	0.0134158	−	0.0232368i	0.872655	+	0.488337i	$0.162396\pi$
$390$		0			0
$391$	−0.492125			−0.0248879
$392$		0			0
$393$	−3.87039			−0.195235
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−14.2833	−	24.7394i	−0.716857	−	1.24163i	−0.962239	−	0.272206i	$-0.912247\pi$
$397$	−14.2833	−	24.7394i	−0.716857	−	1.24163i	0.245382	−	0.969427i	$-0.421087\pi$
$398$		0			0
$399$	−0.623326	−	2.31624i	−0.0312053	−	0.115957i
$400$		0			0
$401$	−16.4945	−	28.5693i	−0.823695	−	1.42668i	−0.902913	−	0.429824i	$-0.858576\pi$
$401$	−16.4945	−	28.5693i	−0.823695	−	1.42668i	0.0792176	−	0.996857i	$-0.474758\pi$
$402$		0			0
$403$	−6.50157	+	11.2611i	−0.323866	+	0.560953i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.8065			1.08091
$408$		0			0
$409$	9.10799	−	15.7755i	0.450361	−	0.780048i	−0.548047	−	0.836447i	$-0.684629\pi$
$409$	9.10799	−	15.7755i	0.450361	−	0.780048i	0.998408	+	0.0563992i	$0.0179619\pi$
$410$		0			0
$411$	−8.49782	−	14.7187i	−0.419167	−	0.726018i
$412$		0			0
$413$	36.5432	+	9.74926i	1.79817	+	0.479730i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.09750	−	7.09708i	0.200655	−	0.347546i
$418$		0			0
$419$	−14.3665			−0.701851			−0.350925	−	0.936403i	$-0.614133\pi$
$419$	−14.3665			−0.701851			−0.350925	+	0.936403i	$0.614133\pi$
$420$		0			0
$421$	15.9374			0.776743			0.388372	−	0.921503i	$-0.373038\pi$
$421$	15.9374			0.776743			0.388372	+	0.921503i	$0.373038\pi$
$422$		0			0
$423$	5.40368	−	9.35944i	0.262736	−	0.455072i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.07259	+	4.08143i	−0.197086	+	0.197514i
$428$		0			0
$429$	−4.39362	−	7.60997i	−0.212126	−	0.367413i
$430$		0			0
$431$	−5.10420	+	8.84073i	−0.245861	+	0.425843i	−0.962373	−	0.271731i	$-0.912404\pi$
$431$	−5.10420	+	8.84073i	−0.245861	+	0.425843i	0.716513	+	0.697574i	$0.245737\pi$
$432$		0			0
$433$	−32.6618			−1.56963			−0.784814	−	0.619732i	$-0.787241\pi$
$433$	−32.6618			−1.56963			−0.784814	+	0.619732i	$0.787241\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.594751	−	1.03014i	0.0284508	−	0.0492782i
$438$		0			0
$439$	5.26181	+	9.11373i	0.251133	+	0.434974i	0.963838	−	0.266489i	$-0.0858637\pi$
$439$	5.26181	+	9.11373i	0.251133	+	0.434974i	−0.712705	+	0.701464i	$0.752530\pi$
$440$		0			0
$441$	6.06975	+	3.48685i	0.289036	+	0.166040i
$442$		0			0
$443$	−17.6022	−	30.4879i	−0.836306	−	1.44853i	−0.892962	−	0.450131i	$-0.851377\pi$
$443$	−17.6022	−	30.4879i	−0.836306	−	1.44853i	0.0566561	−	0.998394i	$-0.481956\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	11.9562			0.565511
$448$		0			0
$449$	−2.85276			−0.134630			−0.0673151	−	0.997732i	$-0.521443\pi$
$449$	−2.85276			−0.134630			−0.0673151	+	0.997732i	$0.521443\pi$
$450$		0			0
$451$	−0.378854	+	0.656195i	−0.0178396	+	0.0308990i
$452$		0			0
$453$	−9.02305	−	15.6284i	−0.423940	−	0.734286i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.0929842	−	0.161053i	−0.00434962	−	0.00753376i	0.863842	−	0.503762i	$-0.168051\pi$
$457$	−0.0929842	−	0.161053i	−0.00434962	−	0.00753376i	−0.868192	+	0.496228i	$0.834718\pi$
$458$		0			0
$459$	−0.187541	+	0.324831i	−0.00875368	+	0.0151618i
$460$		0			0
$461$	−7.00484			−0.326248			−0.163124	−	0.986606i	$-0.552157\pi$
$461$	−7.00484			−0.326248			−0.163124	+	0.986606i	$0.552157\pi$
$462$		0			0
$463$	38.3435			1.78198			0.890988	−	0.454027i	$-0.150013\pi$
$463$	38.3435			1.78198			0.890988	+	0.454027i	$0.150013\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.26912	−	16.0546i	−0.428924	−	0.742917i	0.567854	−	0.823129i	$-0.307774\pi$
$467$	−9.26912	−	16.0546i	−0.428924	−	0.742917i	−0.996778	+	0.0802117i	$0.974440\pi$
$468$		0			0
$469$	14.2181	+	3.79320i	0.656529	+	0.175154i
$470$		0			0
$471$	11.2455	+	19.4777i	0.518164	+	0.897486i
$472$		0			0
$473$	−23.5676	+	40.8202i	−1.08364	+	1.87692i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.06304			0.140247
$478$		0			0
$479$	17.0983	−	29.6152i	0.781243	−	1.35315i	−0.149974	−	0.988690i	$-0.547919\pi$
$479$	17.0983	−	29.6152i	0.781243	−	1.35315i	0.931218	−	0.364463i	$-0.118748\pi$
$480$		0			0
$481$	−6.63279	−	11.4883i	−0.302429	−	0.523823i
$482$		0			0
$483$	0.902085	+	3.35208i	0.0410463	+	0.152525i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−7.39831	+	12.8143i	−0.335250	+	0.580669i	−0.983533	−	0.180730i	$-0.942154\pi$
$487$	−7.39831	+	12.8143i	−0.335250	+	0.580669i	0.648283	+	0.761399i	$0.275487\pi$
$488$		0			0
$489$	10.3514			0.468108
$490$		0			0
$491$	−5.47873			−0.247252			−0.123626	−	0.992329i	$-0.539452\pi$
$491$	−5.47873			−0.247252			−0.123626	+	0.992329i	$0.539452\pi$
$492$		0			0
$493$	1.15443	−	1.99953i	0.0519930	−	0.0900545i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.79494	+	25.2495i	0.304795	+	1.13260i
$498$		0			0
$499$	−3.21395	−	5.56673i	−0.143876	−	0.249201i	0.785077	−	0.619398i	$-0.212623\pi$
$499$	−3.21395	−	5.56673i	−0.143876	−	0.249201i	−0.928953	+	0.370197i	$0.879290\pi$
$500$		0			0
$501$	−1.04042	+	1.80205i	−0.0464823	+	0.0805098i
$502$		0			0
$503$	−33.5288			−1.49498			−0.747489	−	0.664274i	$-0.768741\pi$
$503$	−33.5288			−1.49498			−0.747489	+	0.664274i	$0.768741\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.82722	−	6.62895i	0.169973	−	0.294402i
$508$		0			0
$509$	16.5079	+	28.5925i	0.731699	+	1.26734i	0.956157	+	0.292856i	$0.0946055\pi$
$509$	16.5079	+	28.5925i	0.731699	+	1.26734i	−0.224458	+	0.974484i	$0.572061\pi$
$510$		0			0
$511$	16.3655	+	4.36610i	0.723965	+	0.193145i
$512$		0			0
$513$	−0.453301	−	0.785140i	−0.0200137	−	0.0346648i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−41.0748			−1.80647
$518$		0			0
$519$	23.8704			1.04779
$520$		0			0
$521$	7.49884	−	12.9884i	0.328530	−	0.569031i	−0.653690	−	0.756762i	$-0.726780\pi$
$521$	7.49884	−	12.9884i	0.328530	−	0.569031i	0.982220	+	0.187731i	$0.0601134\pi$
$522$		0			0
$523$	10.1695	+	17.6140i	0.444679	+	0.770207i	0.998030	−	0.0627415i	$-0.0199844\pi$
$523$	10.1695	+	17.6140i	0.444679	+	0.770207i	−0.553351	+	0.832948i	$0.686651\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.05475	−	1.82688i	−0.0459456	−	0.0795801i
$528$		0			0
$529$	10.6393	−	18.4278i	0.462577	−	0.801207i
$530$		0			0
$531$	14.2951			0.620355
$532$		0			0
$533$	0.460938			0.0199654
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−6.40544	−	11.0946i	−0.276415	−	0.478765i
$538$		0			0
$539$	−0.0576935	−	26.6044i	−0.00248504	−	1.14593i
$540$		0			0
$541$	−8.38064	−	14.5157i	−0.360312	−	0.624078i	0.627700	−	0.778455i	$-0.283996\pi$
$541$	−8.38064	−	14.5157i	−0.360312	−	0.624078i	−0.988012	+	0.154377i	$0.950663\pi$
$542$		0			0
$543$	1.52305	−	2.63801i	0.0653605	−	0.113208i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	4.58552			0.196063			0.0980314	−	0.995183i	$-0.468745\pi$
$547$	4.58552			0.196063			0.0980314	+	0.995183i	$0.468745\pi$
$548$		0			0
$549$	−1.08963	+	1.88729i	−0.0465041	+	0.0805475i
$550$		0			0
$551$	2.79034	+	4.83302i	0.118873	+	0.205893i
$552$		0			0
$553$	28.4672	−	28.5290i	1.21055	−	1.21318i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.4734	−	19.8726i	0.486145	−	0.842028i	−0.513728	−	0.857953i	$-0.671736\pi$
$557$	11.4734	−	19.8726i	0.486145	−	0.842028i	0.999873	+	0.0159254i	$0.00506942\pi$
$558$		0			0
$559$	28.6738			1.21277
$560$		0			0
$561$	1.42555			0.0601869
$562$		0			0
$563$	10.9764	−	19.0116i	0.462598	−	0.801244i	−0.536491	−	0.843906i	$-0.680251\pi$
$563$	10.9764	−	19.0116i	0.462598	−	0.801244i	0.999090	+	0.0426622i	$0.0135839\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.55634	+	0.681999i	0.107356	+	0.0286413i
$568$		0			0
$569$	−19.3554	−	33.5245i	−0.811421	−	1.40542i	−0.911870	−	0.410480i	$-0.865361\pi$
$569$	−19.3554	−	33.5245i	−0.811421	−	1.40542i	0.100449	−	0.994942i	$-0.467972\pi$
$570$		0			0
$571$	−10.9478	+	18.9621i	−0.458150	+	0.793540i	−0.998863	−	0.0476675i	$-0.984821\pi$
$571$	−10.9478	+	18.9621i	−0.458150	+	0.793540i	0.540713	+	0.841207i	$0.318155\pi$
$572$		0			0
$573$	−17.1623			−0.716966
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−17.0997	+	29.6175i	−0.711870	+	1.23299i	0.252285	+	0.967653i	$0.418818\pi$
$577$	−17.0997	+	29.6175i	−0.711870	+	1.23299i	−0.964154	+	0.265342i	$0.914515\pi$
$578$		0			0
$579$	−7.06816	−	12.2424i	−0.293743	−	0.508777i
$580$		0			0
$581$	6.18730	+	22.9916i	0.256693	+	0.953852i
$582$		0			0
$583$	−5.82075	−	10.0818i	−0.241071	−	0.417547i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	24.2455			1.00072			0.500359	−	0.865818i	$-0.333201\pi$
$587$	24.2455			1.00072			0.500359	+	0.865818i	$0.333201\pi$
$588$		0			0
$589$	5.09881			0.210093
$590$		0			0
$591$	−0.904090	+	1.56593i	−0.0371893	+	0.0644137i
$592$		0			0
$593$	7.17238	+	12.4229i	0.294534	+	0.510148i	0.974876	−	0.222746i	$-0.0715021\pi$
$593$	7.17238	+	12.4229i	0.294534	+	0.510148i	−0.680342	+	0.732895i	$0.738169\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	9.11645	+	15.7902i	0.373112	+	0.646248i
$598$		0			0
$599$	5.35992	−	9.28365i	0.219000	−	0.379320i	−0.735502	−	0.677522i	$-0.763054\pi$
$599$	5.35992	−	9.28365i	0.219000	−	0.379320i	0.954503	+	0.298202i	$0.0963871\pi$
$600$		0			0
$601$	12.4069			0.506089			0.253045	−	0.967455i	$-0.418568\pi$
$601$	12.4069			0.506089			0.253045	+	0.967455i	$0.418568\pi$
$602$		0			0
$603$	5.56188			0.226497
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−17.2124	−	29.8127i	−0.698629	−	1.21006i	−0.968942	−	0.247288i	$-0.920461\pi$
$607$	−17.2124	−	29.8127i	−0.698629	−	1.21006i	0.270313	−	0.962773i	$-0.412873\pi$
$608$		0			0
$609$	−15.7358	−	4.19812i	−0.637648	−	0.170116i
$610$		0			0
$611$	12.4935	+	21.6394i	0.505435	+	0.875438i
$612$		0			0
$613$	−24.3511	+	42.1774i	−0.983533	+	1.70353i	−0.335249	+	0.942130i	$0.608821\pi$
$613$	−24.3511	+	42.1774i	−0.983533	+	1.70353i	−0.648284	+	0.761399i	$0.724513\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.6164			0.870242			0.435121	−	0.900372i	$-0.356706\pi$
$617$	21.6164			0.870242			0.435121	+	0.900372i	$0.356706\pi$
$618$		0			0
$619$	1.89437	−	3.28114i	0.0761410	−	0.131880i	−0.825441	−	0.564489i	$-0.809073\pi$
$619$	1.89437	−	3.28114i	0.0761410	−	0.131880i	0.901582	+	0.432609i	$0.142407\pi$
$620$		0			0
$621$	0.656022	+	1.13626i	0.0263253	+	0.0455967i
$622$		0			0
$623$	9.36315	−	9.38348i	0.375127	−	0.375941i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.72283	+	2.98403i	−0.0688033	+	0.119171i
$628$		0			0
$629$	2.15207			0.0858088
$630$		0			0
$631$	31.2160			1.24269			0.621344	−	0.783538i	$-0.286587\pi$
$631$	31.2160			1.24269			0.621344	+	0.783538i	$0.286587\pi$
$632$		0			0
$633$	−8.09634	+	14.0233i	−0.321801	+	0.557375i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−13.9984	+	8.12253i	−0.554639	+	0.321826i
$638$		0			0
$639$	4.94148	+	8.55889i	0.195482	+	0.338585i
$640$		0			0
$641$	12.0953	−	20.9497i	0.477736	−	0.827464i	−0.521938	−	0.852983i	$-0.674791\pi$
$641$	12.0953	−	20.9497i	0.477736	−	0.827464i	0.999674	+	0.0255197i	$0.00812406\pi$
$642$		0			0
$643$	6.83519			0.269554			0.134777	−	0.990876i	$-0.456968\pi$
$643$	6.83519			0.269554			0.134777	+	0.990876i	$0.456968\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.15310	+	3.72927i	−0.0846469	+	0.146613i	−0.905241	−	0.424899i	$-0.860310\pi$
$647$	−2.15310	+	3.72927i	−0.0846469	+	0.146613i	0.820594	+	0.571512i	$0.193643\pi$
$648$		0			0
$649$	−27.1653	−	47.0516i	−1.06633	−	1.84694i
$650$		0			0
$651$	−10.5103	+	10.5331i	−0.411931	+	0.412825i
$652$		0			0
$653$	−11.7955	−	20.4305i	−0.461595	−	0.799506i	0.537446	−	0.843298i	$-0.319389\pi$
$653$	−11.7955	−	20.4305i	−0.461595	−	0.799506i	−0.999041	+	0.0437927i	$0.986056\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.40191			0.249762
$658$		0			0
$659$	−12.5231			−0.487833			−0.243916	−	0.969796i	$-0.578432\pi$
$659$	−12.5231			−0.487833			−0.243916	+	0.969796i	$0.578432\pi$
$660$		0			0
$661$	−21.2598	+	36.8231i	−0.826911	+	1.43225i	0.0735384	+	0.997292i	$0.476571\pi$
$661$	−21.2598	+	36.8231i	−0.826911	+	1.43225i	−0.900450	+	0.434960i	$0.856762\pi$
$662$		0			0
$663$	−0.433604	−	0.751024i	−0.0168398	−	0.0291674i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.03822	−	6.99440i	−0.156360	−	0.270824i
$668$		0			0
$669$	4.95707	−	8.58590i	0.191651	−	0.331950i
$670$		0			0
$671$	8.28255			0.319744
$672$		0			0
$673$	15.8140			0.609586			0.304793	−	0.952419i	$-0.401413\pi$
$673$	15.8140			0.609586			0.304793	+	0.952419i	$0.401413\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.28997	+	3.96635i	0.0880108	+	0.152439i	0.906670	−	0.421840i	$-0.138616\pi$
$677$	2.28997	+	3.96635i	0.0880108	+	0.152439i	−0.818659	+	0.574279i	$0.805282\pi$
$678$		0			0
$679$	4.37449	+	16.2553i	0.167878	+	0.623821i
$680$		0			0
$681$	−6.80986	−	11.7950i	−0.260955	−	0.451987i
$682$		0			0
$683$	−21.1330	+	36.6034i	−0.808631	+	1.40059i	0.105181	+	0.994453i	$0.466458\pi$
$683$	−21.1330	+	36.6034i	−0.808631	+	1.40059i	−0.913812	+	0.406137i	$0.866875\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	23.0537			0.879552
$688$		0			0
$689$	−3.54094	+	6.13309i	−0.134899	+	0.233652i
$690$		0			0
$691$	−12.0575	−	20.8842i	−0.458690	−	0.794474i	0.540202	−	0.841535i	$-0.318348\pi$
$691$	−12.0575	−	20.8842i	−0.458690	−	0.794474i	−0.998892	+	0.0470615i	$0.985014\pi$
$692$		0			0
$693$	−2.61309	−	9.71008i	−0.0992633	−	0.368855i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.0373889	+	0.0647596i	−0.00141621	+	0.00245294i
$698$		0			0
$699$	−30.3211			−1.14685
$700$		0			0
$701$	−7.28290			−0.275071			−0.137536	−	0.990497i	$-0.543918\pi$
$701$	−7.28290			−0.275071			−0.137536	+	0.990497i	$0.543918\pi$
$702$		0			0
$703$	−2.60086	+	4.50482i	−0.0980932	+	0.169902i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.0388	−	4.01217i	−0.565594	−	0.150893i
$708$		0			0
$709$	−3.25510	−	5.63799i	−0.122248	−	0.211739i	0.798406	−	0.602119i	$-0.205677\pi$
$709$	−3.25510	−	5.63799i	−0.122248	−	0.211739i	−0.920654	+	0.390380i	$0.872344\pi$
$710$		0			0
$711$	7.61645	−	13.1921i	0.285639	−	0.494742i
$712$		0			0
$713$	−7.37906			−0.276348
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−5.51636	+	9.55461i	−0.206012	+	0.356823i
$718$		0			0
$719$	22.3725	+	38.7503i	0.834353	+	1.44514i	0.894556	+	0.446956i	$0.147492\pi$
$719$	22.3725	+	38.7503i	0.834353	+	1.44514i	−0.0602031	+	0.998186i	$0.519175\pi$
$720$		0			0
$721$	−23.6862	+	23.7376i	−0.882120	+	0.884035i
$722$		0			0
$723$	−3.16021	−	5.47364i	−0.117529	−	0.203567i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	23.7510			0.880877			0.440438	−	0.897783i	$-0.354823\pi$
$727$	23.7510			0.880877			0.440438	+	0.897783i	$0.354823\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.32587	+	4.02853i	−0.0860255	+	0.149000i
$732$		0			0
$733$	−7.31516	−	12.6702i	−0.270192	−	0.467986i	0.698719	−	0.715396i	$-0.253754\pi$
$733$	−7.31516	−	12.6702i	−0.270192	−	0.467986i	−0.968911	+	0.247410i	$0.920420\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.5693	−	18.3066i	−0.389327	−	0.674334i
$738$		0			0
$739$	0.403658	−	0.699156i	0.0148488	−	0.0257189i	−0.858506	−	0.512804i	$-0.828607\pi$
$739$	0.403658	−	0.699156i	0.0148488	−	0.0257189i	0.873354	+	0.487085i	$0.161940\pi$
$740$		0			0
$741$	2.09610			0.0770023
$742$		0			0
$743$	−2.34476			−0.0860208			−0.0430104	−	0.999075i	$-0.513695\pi$
$743$	−2.34476			−0.0860208			−0.0430104	+	0.999075i	$0.513695\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.49959	+	7.79351i	0.164631	+	0.285150i
$748$		0			0
$749$	4.70587	−	4.71608i	0.171949	−	0.172322i
$750$		0			0
$751$	−10.1746	−	17.6229i	−0.371275	−	0.643067i	0.618487	−	0.785795i	$-0.287746\pi$
$751$	−10.1746	−	17.6229i	−0.371275	−	0.643067i	−0.989762	+	0.142728i	$0.954413\pi$
$752$		0			0
$753$	−9.65803	+	16.7282i	−0.351958	+	0.609609i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−4.83602			−0.175768			−0.0878841	−	0.996131i	$-0.528011\pi$
$757$	−4.83602			−0.175768			−0.0878841	+	0.996131i	$0.528011\pi$
$758$		0			0
$759$	2.49330	−	4.31853i	0.0905011	−	0.156753i
$760$		0			0
$761$	20.7725	+	35.9790i	0.753002	+	1.30424i	0.946362	+	0.323109i	$0.104728\pi$
$761$	20.7725	+	35.9790i	0.753002	+	1.30424i	−0.193360	+	0.981128i	$0.561939\pi$
$762$		0			0
$763$	28.9346	+	7.71939i	1.04750	+	0.279461i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.5255	+	28.6230i	−0.596700	+	1.03352i
$768$		0			0
$769$	−15.9814			−0.576305			−0.288152	−	0.957585i	$-0.593041\pi$
$769$	−15.9814			−0.576305			−0.288152	+	0.957585i	$0.593041\pi$
$770$		0			0
$771$	−14.3448			−0.516614
$772$		0			0
$773$	4.85456	−	8.40834i	0.174606	−	0.302427i	−0.765419	−	0.643533i	$-0.777468\pi$
$773$	4.85456	−	8.40834i	0.174606	−	0.302427i	0.940025	+	0.341106i	$0.110801\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.94484	−	14.6587i	−0.141520	−	0.525879i
$778$		0			0
$779$	−0.0903717	−	0.156528i	−0.00323790	−	0.00560821i
$780$		0			0
$781$	18.7808	−	32.5292i	0.672029	−	1.16399i
$782$		0			0
$783$	−6.15561			−0.219983
$784$		0			0
$785$		0			0
$786$		0			0
$787$	13.4247	−	23.2523i	0.478540	−	0.828855i	−0.521157	−	0.853461i	$-0.674500\pi$
$787$	13.4247	−	23.2523i	0.478540	−	0.828855i	0.999697	+	0.0246053i	$0.00783291\pi$
$788$		0			0
$789$	−4.53329	−	7.85188i	−0.161389	−	0.279534i
$790$		0			0
$791$	−10.6398	−	39.5369i	−0.378309	−	1.40577i
$792$		0			0
$793$	−2.51927	−	4.36350i	−0.0894617	−	0.154952i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.6365			−0.624716			−0.312358	−	0.949964i	$-0.601119\pi$
$797$	−17.6365			−0.624716			−0.312358	+	0.949964i	$0.601119\pi$
$798$		0			0
$799$	−4.05365			−0.143408
$800$		0			0
$801$	2.50512	−	4.33900i	0.0885142	−	0.153311i
$802$		0			0
$803$	−12.1657	−	21.0715i	−0.429317	−	0.743599i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.33309	+	9.23719i	0.187734	+	0.325165i
$808$		0			0
$809$	−14.0251	+	24.2921i	−0.493095	+	0.854065i	−0.999968	−	0.00795514i	$-0.997468\pi$
$809$	−14.0251	+	24.2921i	−0.493095	+	0.854065i	0.506874	+	0.862020i	$0.330801\pi$
$810$		0			0
$811$	−41.3801			−1.45305			−0.726527	−	0.687138i	$-0.758867\pi$
$811$	−41.3801			−1.45305			−0.726527	+	0.687138i	$0.758867\pi$
$812$		0			0
$813$	−20.5441			−0.720514
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.62180	−	9.73724i	−0.196682	−	0.340663i
$818$		0			0
$819$	−4.32075	+	4.33013i	−0.150979	+	0.151307i
$820$		0			0
$821$	9.42516	+	16.3249i	0.328940	+	0.569741i	0.982302	−	0.187305i	$-0.0599752\pi$
$821$	9.42516	+	16.3249i	0.328940	+	0.569741i	−0.653362	+	0.757046i	$0.726642\pi$
$822$		0			0
$823$	−4.89435	+	8.47726i	−0.170606	+	0.295499i	−0.938632	−	0.344920i	$-0.887906\pi$
$823$	−4.89435	+	8.47726i	−0.170606	+	0.295499i	0.768026	+	0.640419i	$0.221239\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.6206			0.647500			0.323750	−	0.946143i	$-0.395056\pi$
$827$	18.6206			0.647500			0.323750	+	0.946143i	$0.395056\pi$
$828$		0			0
$829$	−22.6558	+	39.2411i	−0.786870	+	1.36290i	0.141005	+	0.990009i	$0.454966\pi$
$829$	−22.6558	+	39.2411i	−0.786870	+	1.36290i	−0.927876	+	0.372890i	$0.878367\pi$
$830$		0			0
$831$	6.55593	+	11.3552i	0.227423	+	0.393907i
$832$		0			0
$833$	−0.00569375	−	2.62557i	−0.000197277	−	0.0909707i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.81204	+	4.87060i	−0.0971985	+	0.168353i
$838$		0			0
$839$	2.31727			0.0800010			0.0400005	−	0.999200i	$-0.487264\pi$
$839$	2.31727			0.0800010			0.0400005	+	0.999200i	$0.487264\pi$
$840$		0			0
$841$	8.89152			0.306604
$842$		0			0
$843$	6.18503	−	10.7128i	0.213024	−	0.368968i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−6.43771	+	6.45168i	−0.221202	+	0.221682i
$848$		0			0
$849$	9.64932	+	16.7131i	0.331164	+	0.573593i
$850$		0			0
$851$	3.76399	−	6.51943i	0.129028	−	0.223483i
$852$		0			0
$853$	12.6273			0.432350			0.216175	−	0.976355i	$-0.430642\pi$
$853$	12.6273			0.432350			0.216175	+	0.976355i	$0.430642\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.05970	+	15.6919i	−0.309473	+	0.536024i	−0.978247	−	0.207442i	$-0.933486\pi$
$857$	−9.05970	+	15.6919i	−0.309473	+	0.536024i	0.668774	+	0.743466i	$0.266819\pi$
$858$		0			0
$859$	8.92380	+	15.4565i	0.304476	+	0.527368i	0.977145	−	0.212576i	$-0.0681852\pi$
$859$	8.92380	+	15.4565i	0.304476	+	0.527368i	−0.672668	+	0.739944i	$0.734852\pi$
$860$		0			0
$861$	0.509641	+	0.135966i	0.0173685	+	0.00463371i
$862$		0			0
$863$	−6.51989	−	11.2928i	−0.221940	−	0.384411i	0.733457	−	0.679736i	$-0.237905\pi$
$863$	−6.51989	−	11.2928i	−0.221940	−	0.384411i	−0.955397	+	0.295325i	$0.904572\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−16.8593			−0.572572
$868$		0			0
$869$	−57.8947			−1.96394
$870$		0			0
$871$	−6.42966	+	11.1365i	−0.217861	+	0.377346i
$872$		0			0
$873$	3.18126	+	5.51010i	0.107669	+	0.186489i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.2691	+	19.5187i	0.380531	+	0.659099i	0.991138	−	0.132835i	$-0.0424079\pi$
$877$	11.2691	+	19.5187i	0.380531	+	0.659099i	−0.610607	+	0.791934i	$0.709075\pi$
$878$		0			0
$879$	−9.31699	+	16.1375i	−0.314254	+	0.544305i
$880$		0			0
$881$	−25.3761			−0.854944			−0.427472	−	0.904029i	$-0.640596\pi$
$881$	−25.3761			−0.854944			−0.427472	+	0.904029i	$0.640596\pi$
$882$		0			0
$883$	−15.1504			−0.509852			−0.254926	−	0.966961i	$-0.582051\pi$
$883$	−15.1504			−0.509852			−0.254926	+	0.966961i	$0.582051\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.6145	−	35.7054i	−0.692167	−	1.19887i	−0.971126	−	0.238566i	$-0.923323\pi$
$887$	−20.6145	−	35.7054i	−0.692167	−	1.19887i	0.278959	−	0.960303i	$-0.410011\pi$
$888$		0			0
$889$	10.3928	+	38.6188i	0.348563	+	1.29523i
$890$		0			0
$891$	−1.90032	−	3.29145i	−0.0636631	−	0.110268i
$892$		0			0
$893$	4.89898	−	8.48529i	0.163938	−	0.283949i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−3.03351			−0.101286
$898$		0			0
$899$	17.3098	−	29.9815i	0.577316	−	0.999940i
$900$		0			0
$901$	−0.574447	−	0.994971i	−0.0191376	−	0.0331473i
$902$		0			0
$903$	31.7035	+	8.45809i	1.05503	+	0.281468i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.50711	+	6.07450i	−0.116452	+	0.201700i	−0.918359	−	0.395748i	$-0.870485\pi$
$907$	−3.50711	+	6.07450i	−0.116452	+	0.201700i	0.801907	+	0.597448i	$0.203819\pi$
$908$		0			0
$909$	−5.88296			−0.195125
$910$		0			0
$911$	−3.78721			−0.125476			−0.0627379	−	0.998030i	$-0.519983\pi$
$911$	−3.78721			−0.125476			−0.0627379	+	0.998030i	$0.519983\pi$
$912$		0			0
$913$	17.1013	−	29.6203i	0.565970	−	0.980289i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.23298	−	7.24868i	0.238854	−	0.239373i
$918$		0			0
$919$	12.6119	+	21.8444i	0.416027	+	0.720579i	0.995536	−	0.0943866i	$-0.0300890\pi$
$919$	12.6119	+	21.8444i	0.416027	+	0.720579i	−0.579509	+	0.814966i	$0.696756\pi$
$920$		0			0
$921$	−8.66390	+	15.0063i	−0.285485	+	0.494475i
$922$		0			0
$923$	−22.8498			−0.752112
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.33728	+	10.9765i	−0.208144	+	0.360515i
$928$		0			0
$929$	23.6884	+	41.0295i	0.777191	+	1.34613i	0.933555	+	0.358434i	$0.116689\pi$
$929$	23.6884	+	41.0295i	0.777191	+	1.34613i	−0.156364	+	0.987699i	$0.549977\pi$
$930$		0			0
$931$	5.50285	+	3.16118i	0.180349	+	0.103604i
$932$		0			0
$933$	0.484075	+	0.838442i	0.0158479	+	0.0274494i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.59102			−0.313325			−0.156663	−	0.987652i	$-0.550074\pi$
$937$	−9.59102			−0.313325			−0.156663	+	0.987652i	$0.550074\pi$
$938$		0			0
$939$	26.6746			0.870491
$940$		0			0
$941$	24.8312	−	43.0088i	0.809472	−	1.40205i	−0.103757	−	0.994603i	$-0.533087\pi$
$941$	24.8312	−	43.0088i	0.809472	−	1.40205i	0.913230	−	0.407445i	$-0.133580\pi$
$942$		0			0
$943$	0.130787	+	0.226530i	0.00425901	+	0.00737682i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.8989	−	41.3941i	−0.776610	−	1.34513i	−0.933885	−	0.357573i	$-0.883604\pi$
$947$	−23.8989	−	41.3941i	−0.776610	−	1.34513i	0.157275	−	0.987555i	$-0.449729\pi$
$948$		0			0
$949$	−7.40075	+	12.8185i	−0.240239	+	0.416105i
$950$		0			0
$951$	−32.0354			−1.03882
$952$		0			0
$953$	47.3018			1.53226			0.766128	−	0.642688i	$-0.222181\pi$
$953$	47.3018			1.53226			0.766128	+	0.642688i	$0.222181\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	11.6976	+	20.2609i	0.378130	+	0.654941i
$958$		0			0
$959$	43.4466	+	11.5910i	1.40297	+	0.374293i
$960$		0			0
$961$	−0.315191	−	0.545926i	−0.0101674	−	0.0176105i
$962$		0			0
$963$	1.25906	−	2.18076i	0.0405727	−	0.0702740i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	37.9613			1.22075			0.610377	−	0.792111i	$-0.291018\pi$
$967$	37.9613			1.22075			0.610377	+	0.792111i	$0.291018\pi$
$968$		0			0
$969$	−0.170025	+	0.294493i	−0.00546200	+	0.00946047i
$970$		0			0
$971$	6.51989	+	11.2928i	0.209233	+	0.362403i	0.951473	−	0.307732i	$-0.0995699\pi$
$971$	6.51989	+	11.2928i	0.209233	+	0.362403i	−0.742240	+	0.670134i	$0.766237\pi$
$972$		0			0
$973$	5.63440	+	20.9370i	0.180631	+	0.671211i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.6986	−	41.0472i	0.758185	−	1.31322i	−0.185590	−	0.982627i	$-0.559420\pi$
$977$	23.6986	−	41.0472i	0.758185	−	1.31322i	0.943775	−	0.330588i	$-0.107247\pi$
$978$		0			0
$979$	−19.0421			−0.608589
$980$		0			0
$981$	11.3188			0.361380
$982$		0			0
$983$	9.16920	−	15.8815i	0.292452	−	0.506542i	−0.681937	−	0.731411i	$-0.738862\pi$
$983$	9.16920	−	15.8815i	0.292452	−	0.506542i	0.974389	+	0.224869i	$0.0721955\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	7.43050	+	27.6112i	0.236515	+	0.878875i
$988$		0			0
$989$	8.13593	+	14.0918i	0.258708	+	0.448095i
$990$		0			0
$991$	3.31968	−	5.74986i	0.105453	−	0.182650i	−0.808470	−	0.588537i	$-0.799704\pi$
$991$	3.31968	−	5.74986i	0.105453	−	0.182650i	0.913923	+	0.405887i	$0.133037\pi$
$992$		0			0
$993$	−0.687128			−0.0218053
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.138744	−	0.240312i	0.00439407	−	0.00761075i	−0.863820	−	0.503801i	$-0.831935\pi$
$997$	0.138744	−	0.240312i	0.00439407	−	0.00761075i	0.868214	+	0.496190i	$0.165268\pi$
$998$		0			0
$999$	−2.86880	−	4.96891i	−0.0907648	−	0.157209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.q.l.1201.2		8
5.2	odd	4		420.2.bb.a.109.6	yes	16
5.3	odd	4		420.2.bb.a.109.3	✓	16
5.4	even	2		2100.2.q.m.1201.3		8
7.2	even	3	inner	2100.2.q.l.1801.2		8
15.2	even	4		1260.2.bm.c.109.5		16
15.8	even	4		1260.2.bm.c.109.3		16
20.3	even	4		1680.2.di.e.529.7		16
20.7	even	4		1680.2.di.e.529.2		16
35.2	odd	12		420.2.bb.a.289.3	yes	16
35.3	even	12		2940.2.k.g.589.4		8
35.9	even	6		2100.2.q.m.1801.3		8
35.12	even	12		2940.2.bb.i.1549.6		16
35.13	even	4		2940.2.bb.i.949.6		16
35.17	even	12		2940.2.k.g.589.8		8
35.18	odd	12		2940.2.k.f.589.5		8
35.23	odd	12		420.2.bb.a.289.6	yes	16
35.27	even	4		2940.2.bb.i.949.3		16
35.32	odd	12		2940.2.k.f.589.1		8
35.33	even	12		2940.2.bb.i.1549.3		16
105.2	even	12		1260.2.bm.c.289.3		16
105.23	even	12		1260.2.bm.c.289.5		16
140.23	even	12		1680.2.di.e.289.2		16
140.107	even	12		1680.2.di.e.289.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.3	✓	16	5.3	odd	4
420.2.bb.a.109.6	yes	16	5.2	odd	4
420.2.bb.a.289.3	yes	16	35.2	odd	12
420.2.bb.a.289.6	yes	16	35.23	odd	12
1260.2.bm.c.109.3		16	15.8	even	4
1260.2.bm.c.109.5		16	15.2	even	4
1260.2.bm.c.289.3		16	105.2	even	12
1260.2.bm.c.289.5		16	105.23	even	12
1680.2.di.e.289.2		16	140.23	even	12
1680.2.di.e.289.7		16	140.107	even	12
1680.2.di.e.529.2		16	20.7	even	4
1680.2.di.e.529.7		16	20.3	even	4
2100.2.q.l.1201.2		8	1.1	even	1	trivial
2100.2.q.l.1801.2		8	7.2	even	3	inner
2100.2.q.m.1201.3		8	5.4	even	2
2100.2.q.m.1801.3		8	35.9	even	6
2940.2.k.f.589.1		8	35.32	odd	12
2940.2.k.f.589.5		8	35.18	odd	12
2940.2.k.g.589.4		8	35.3	even	12
2940.2.k.g.589.8		8	35.17	even	12
2940.2.bb.i.949.3		16	35.27	even	4
2940.2.bb.i.949.6		16	35.13	even	4
2940.2.bb.i.1549.3		16	35.33	even	12
2940.2.bb.i.1549.6		16	35.12	even	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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.687541 - 2.55486i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.687541 - 2.55486i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.90032 + 3.29145i) q^{11} +2.31204 q^{13} +(-0.187541 + 0.324831i) q^{17} +(-0.453301 - 0.785140i) q^{19} +(2.55634 + 0.681999i) q^{21} +(0.656022 + 1.13626i) q^{23} +1.00000 q^{27} -6.15561 q^{29} +(-2.81204 + 4.87060i) q^{31} +(-1.90032 - 3.29145i) q^{33} +(-2.86880 - 4.96891i) q^{37} +(-1.15602 + 2.00229i) q^{39} +0.199364 q^{41} +12.4019 q^{43} +(5.40368 + 9.35944i) q^{47} +(-6.05457 + 3.51314i) q^{49} +(-0.187541 - 0.324831i) q^{51} +(-1.53152 + 2.65267i) q^{53} +0.906602 q^{57} +(-7.14756 + 12.3799i) q^{59} +(-1.08963 - 1.88729i) q^{61} +(-1.86880 + 1.87286i) q^{63} +(-2.78094 + 4.81673i) q^{67} -1.31204 q^{69} -9.88296 q^{71} +(-3.20095 + 5.54422i) q^{73} +(9.71572 + 2.59203i) q^{77} +(7.61645 + 13.1921i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.99917 q^{83} +(3.07780 - 5.33091i) q^{87} +(2.50512 + 4.33900i) q^{89} +(-1.58963 - 5.90694i) q^{91} +(-2.81204 - 4.87060i) q^{93} -6.36252 q^{97} +3.80064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Introduction

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