LMFDB - Embedded newform 2100.2.bi.l.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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, 3, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

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.bi (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 $ x^16 - 3x^15 + 9x^14 - 18x^13 + 32x^12 - 36x^11 + 51x^9 - 167x^8 + 153x^7 - 972x^5 + 2592x^4 - 4374x^3 + 6561x^2 - 6561*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$0.747325 - 1.56253i$ of defining polynomial
Character	$\chi$	$=$	2100.101
Dual form			2100.2.bi.l.1601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.747325 - 1.56253i) q^{3} +(0.786875 + 2.52603i) q^{7} +(-1.88301 + 2.33544i) q^{9} +O(q^{10})$	\(q+(-0.747325 - 1.56253i) q^{3} +(0.786875 + 2.52603i) q^{7} +(-1.88301 + 2.33544i) q^{9} +(-2.34474 - 1.35373i) q^{11} +1.12489i q^{13} +(3.69121 - 6.39336i) q^{17} +(-0.412264 + 0.238021i) q^{19} +(3.35895 - 3.11728i) q^{21} +(-4.84706 + 2.79845i) q^{23} +(5.05642 + 1.19693i) q^{27} +2.20372i q^{29} +(-2.07315 - 1.19693i) q^{31} +(-0.362972 + 4.67541i) q^{33} +(4.34879 + 7.53233i) q^{37} +(1.75767 - 0.840655i) q^{39} -5.42336 q^{41} +4.16209 q^{43} +(6.21227 + 10.7600i) q^{47} +(-5.76166 + 3.97534i) q^{49} +(-12.7484 - 0.989712i) q^{51} +(4.25321 + 2.45559i) q^{53} +(0.680011 + 0.466297i) q^{57} +(-1.15586 + 2.00200i) q^{59} +(-2.26895 + 1.30998i) q^{61} +(-7.38108 - 2.91884i) q^{63} +(-7.34210 + 12.7169i) q^{67} +(7.99501 + 5.48234i) q^{69} +9.89729i q^{71} +(6.29046 + 3.63180i) q^{73} +(1.57456 - 6.98810i) q^{77} +(3.47478 + 6.01850i) q^{79} +(-1.90854 - 8.79531i) q^{81} +11.3005 q^{83} +(3.44338 - 1.64689i) q^{87} +(-3.48186 - 6.03075i) q^{89} +(-2.84150 + 0.885144i) q^{91} +(-0.320929 + 4.13385i) q^{93} +8.79691i q^{97} +(7.57673 - 2.92689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9	$ 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9} - 18 q^{19} - 11 q^{21} - 18 q^{31} - 12 q^{33} + 6 q^{37} + 12 q^{39} - 4 q^{43} - 18 q^{49} - q^{51} - 6 q^{57} + 36 q^{61} - 19 q^{63} - 30 q^{67} - 54 q^{73} + 7 q^{81} - 81 q^{87} + 20 q^{91} + 34 q^{93} - 30 q^{99}+O(q^{100}) $ 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9 - 18 * q^19 - 11 * q^21 - 18 * q^31 - 12 * q^33 + 6 * q^37 + 12 * q^39 - 4 * q^43 - 18 * q^49 - q^51 - 6 * q^57 + 36 * q^61 - 19 * q^63 - 30 * q^67 - 54 * q^73 + 7 * q^81 - 81 * q^87 + 20 * q^91 + 34 * q^93 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.747325	−	1.56253i	−0.431468	−	0.902128i
$3$	−0.747325	−	1.56253i	−0.431468	−	0.902128i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.786875	+	2.52603i	0.297411	+	0.954750i
$7$	0.786875	+	2.52603i	0.297411	+	0.954750i
$8$		0			0
$9$	−1.88301	+	2.33544i	−0.627670	+	0.778479i
$10$		0			0
$11$	−2.34474	−	1.35373i	−0.706965	−	0.408166i	0.102971	−	0.994684i	$-0.467165\pi$
$11$	−2.34474	−	1.35373i	−0.706965	−	0.408166i	−0.809936	+	0.586518i	$0.800498\pi$
$12$		0			0
$13$			1.12489i			0.311987i	0.987758	+	0.155994i	$0.0498579\pi$
$13$			1.12489i			0.311987i	−0.987758	+	0.155994i	$0.950142\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.69121	−	6.39336i	0.895250	−	1.55062i	0.0617544	−	0.998091i	$-0.480330\pi$
$17$	3.69121	−	6.39336i	0.895250	−	1.55062i	0.833495	−	0.552527i	$-0.186336\pi$
$18$		0			0
$19$	−0.412264	+	0.238021i	−0.0945799	+	0.0546057i	−0.546544	−	0.837430i	$-0.684057\pi$
$19$	−0.412264	+	0.238021i	−0.0945799	+	0.0546057i	0.451964	+	0.892036i	$0.350724\pi$
$20$		0			0
$21$	3.35895	−	3.11728i	0.732983	−	0.680247i
$22$		0			0
$23$	−4.84706	+	2.79845i	−1.01068	+	0.583518i	−0.911392	−	0.411540i	$-0.864991\pi$
$23$	−4.84706	+	2.79845i	−1.01068	+	0.583518i	−0.0992913	+	0.995058i	$0.531658\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.05642	+	1.19693i	0.973108	+	0.230350i
$28$		0			0
$29$			2.20372i			0.409220i	0.978844	+	0.204610i	$0.0655926\pi$
$29$			2.20372i			0.409220i	−0.978844	+	0.204610i	$0.934407\pi$
$30$		0			0
$31$	−2.07315	−	1.19693i	−0.372348	−	0.214975i	0.302136	−	0.953265i	$-0.402300\pi$
$31$	−2.07315	−	1.19693i	−0.372348	−	0.214975i	−0.674484	+	0.738290i	$0.735634\pi$
$32$		0			0
$33$	−0.362972	+	4.67541i	−0.0631854	+	0.813884i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.34879	+	7.53233i	0.714937	+	1.23831i	0.962984	+	0.269559i	$0.0868778\pi$
$37$	4.34879	+	7.53233i	0.714937	+	1.23831i	−0.248047	+	0.968748i	$0.579789\pi$
$38$		0			0
$39$	1.75767	−	0.840655i	0.281452	−	0.134613i
$40$		0			0
$41$	−5.42336			−0.846986			−0.423493	−	0.905899i	$-0.639196\pi$
$41$	−5.42336			−0.846986			−0.423493	+	0.905899i	$0.639196\pi$
$42$		0			0
$43$	4.16209			0.634712			0.317356	−	0.948306i	$-0.397205\pi$
$43$	4.16209			0.634712			0.317356	+	0.948306i	$0.397205\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.21227	+	10.7600i	0.906153	+	1.56950i	0.819362	+	0.573277i	$0.194328\pi$
$47$	6.21227	+	10.7600i	0.906153	+	1.56950i	0.0867912	+	0.996227i	$0.472339\pi$
$48$		0			0
$49$	−5.76166	+	3.97534i	−0.823094	+	0.567905i
$50$		0			0
$51$	−12.7484	−	0.989712i	−1.78513	−	0.138587i
$52$		0			0
$53$	4.25321	+	2.45559i	0.584224	+	0.337302i	0.762810	−	0.646622i	$-0.223819\pi$
$53$	4.25321	+	2.45559i	0.584224	+	0.337302i	−0.178586	+	0.983924i	$0.557152\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.680011	+	0.466297i	0.0900696	+	0.0617626i
$58$		0			0
$59$	−1.15586	+	2.00200i	−0.150480	+	0.260638i	−0.931404	−	0.363987i	$-0.881415\pi$
$59$	−1.15586	+	2.00200i	−0.150480	+	0.260638i	0.780924	+	0.624626i	$0.214748\pi$
$60$		0			0
$61$	−2.26895	+	1.30998i	−0.290509	+	0.167726i	−0.638172	−	0.769894i	$-0.720309\pi$
$61$	−2.26895	+	1.30998i	−0.290509	+	0.167726i	0.347662	+	0.937620i	$0.386976\pi$
$62$		0			0
$63$	−7.38108	−	2.91884i	−0.929929	−	0.367740i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.34210	+	12.7169i	−0.896980	+	1.55361i	−0.0656452	+	0.997843i	$0.520911\pi$
$67$	−7.34210	+	12.7169i	−0.896980	+	1.55361i	−0.831335	+	0.555772i	$0.812423\pi$
$68$		0			0
$69$	7.99501	+	5.48234i	0.962486	+	0.659996i
$70$		0			0
$71$			9.89729i			1.17459i	0.809372	+	0.587296i	$0.199807\pi$
$71$			9.89729i			1.17459i	−0.809372	+	0.587296i	$0.800193\pi$
$72$		0			0
$73$	6.29046	+	3.63180i	0.736242	+	0.425070i	0.820701	−	0.571357i	$-0.193583\pi$
$73$	6.29046	+	3.63180i	0.736242	+	0.425070i	−0.0844591	+	0.996427i	$0.526916\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.57456	−	6.98810i	0.179438	−	0.796368i
$78$		0			0
$79$	3.47478	+	6.01850i	0.390944	+	0.677134i	0.992574	−	0.121640i	$-0.0388154\pi$
$79$	3.47478	+	6.01850i	0.390944	+	0.677134i	−0.601631	+	0.798774i	$0.705482\pi$
$80$		0			0
$81$	−1.90854	−	8.79531i	−0.212060	−	0.977257i
$82$		0			0
$83$	11.3005			1.24040			0.620198	−	0.784446i	$-0.287052\pi$
$83$	11.3005			1.24040			0.620198	+	0.784446i	$0.287052\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.44338	−	1.64689i	0.369169	−	0.176566i
$88$		0			0
$89$	−3.48186	−	6.03075i	−0.369076	−	0.639258i	0.620345	−	0.784329i	$-0.286992\pi$
$89$	−3.48186	−	6.03075i	−0.369076	−	0.639258i	−0.989421	+	0.145070i	$0.953659\pi$
$90$		0			0
$91$	−2.84150	+	0.885144i	−0.297870	+	0.0927883i
$92$		0			0
$93$	−0.320929	+	4.13385i	−0.0332788	+	0.428661i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			8.79691i			0.893190i	0.894736	+	0.446595i	$0.147364\pi$
$97$			8.79691i			0.893190i	−0.894736	+	0.446595i	$0.852636\pi$
$98$		0			0
$99$	7.57673	−	2.92689i	0.761490	−	0.294164i
$100$		0			0
$101$	5.23274	−	9.06338i	0.520677	−	0.901840i	−0.479034	−	0.877797i	$-0.659013\pi$
$101$	5.23274	−	9.06338i	0.520677	−	0.901840i	0.999711	−	0.0240431i	$-0.00765389\pi$
$102$		0			0
$103$	−2.83087	+	1.63440i	−0.278934	+	0.161042i	−0.632941	−	0.774200i	$-0.718152\pi$
$103$	−2.83087	+	1.63440i	−0.278934	+	0.161042i	0.354007	+	0.935243i	$0.384819\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.31809	−	2.49305i	0.417445	−	0.241012i	−0.276538	−	0.961003i	$-0.589187\pi$
$107$	4.31809	−	2.49305i	0.417445	−	0.241012i	0.693984	+	0.719991i	$0.255854\pi$
$108$		0			0
$109$	−2.40043	+	4.15767i	−0.229920	+	0.398232i	−0.957784	−	0.287489i	$-0.907180\pi$
$109$	−2.40043	+	4.15767i	−0.229920	+	0.398232i	0.727864	+	0.685721i	$0.240513\pi$
$110$		0			0
$111$	8.51954	−	12.4242i	0.808639	−	1.17925i
$112$		0			0
$113$		−	18.8874i		−	1.77678i	−0.459094	−	0.888388i	$-0.651826\pi$
$113$		−	18.8874i		−	1.77678i	0.459094	−	0.888388i	$-0.348174\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.62710	−	2.11817i	−0.242876	−	0.195825i
$118$		0			0
$119$	19.0543	+	4.29333i	1.74671	+	0.393569i
$120$		0			0
$121$	−1.83480	−	3.17797i	−0.166800	−	0.288907i
$122$		0			0
$123$	4.05301	+	8.47417i	0.365448	+	0.764090i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.77289			−0.689732			−0.344866	−	0.938652i	$-0.612076\pi$
$127$	−7.77289			−0.689732			−0.344866	+	0.938652i	$0.612076\pi$
$128$		0			0
$129$	−3.11043	−	6.50339i	−0.273858	−	0.572592i
$130$		0			0
$131$	2.32600	+	4.02875i	0.203224	+	0.351994i	0.949565	−	0.313569i	$-0.101525\pi$
$131$	2.32600	+	4.02875i	0.203224	+	0.351994i	−0.746342	+	0.665563i	$0.768191\pi$
$132$		0			0
$133$	−0.925648	−	0.854100i	−0.0802639	−	0.0740598i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.53654	+	5.50592i	0.814762	+	0.470403i	0.848607	−	0.529024i	$-0.177442\pi$
$137$	9.53654	+	5.50592i	0.814762	+	0.470403i	−0.0338451	+	0.999427i	$0.510775\pi$
$138$		0			0
$139$			20.5928i			1.74665i	0.487134	+	0.873327i	$0.338042\pi$
$139$			20.5928i			1.74665i	−0.487134	+	0.873327i	$0.661958\pi$
$140$		0			0
$141$	12.1702	−	17.7481i	1.02492	−	1.49466i
$142$		0			0
$143$	1.52280	−	2.63756i	0.127343	−	0.220564i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	10.5174	+	6.03190i	0.867462	+	0.497503i
$148$		0			0
$149$	14.8906	−	8.59708i	1.21988	−	0.704300i	0.254991	−	0.966943i	$-0.417928\pi$
$149$	14.8906	−	8.59708i	1.21988	−	0.704300i	0.964893	+	0.262643i	$0.0845942\pi$
$150$		0			0
$151$	−1.00060	+	1.73309i	−0.0814279	+	0.141037i	−0.903863	−	0.427821i	$-0.859281\pi$
$151$	−1.00060	+	1.73309i	−0.0814279	+	0.141037i	0.822436	+	0.568858i	$0.192615\pi$
$152$		0			0
$153$	7.98072	+	20.6594i	0.645203	+	1.67021i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	15.7938	+	9.11856i	1.26048	+	0.727741i	0.973168	−	0.230095i	$-0.0739038\pi$
$157$	15.7938	+	9.11856i	1.26048	+	0.727741i	0.287316	+	0.957836i	$0.407237\pi$
$158$		0			0
$159$	0.658410	−	8.48091i	0.0522153	−	0.672580i
$160$		0			0
$161$	−10.8830	−	10.0418i	−0.857701	−	0.791405i
$162$		0			0
$163$	−9.90522	−	17.1563i	−0.775837	−	1.34379i	−0.934323	−	0.356427i	$-0.883995\pi$
$163$	−9.90522	−	17.1563i	−0.775837	−	1.34379i	0.158487	−	0.987361i	$-0.449339\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.5257			−0.969269			−0.484634	−	0.874717i	$-0.661047\pi$
$167$	−12.5257			−0.969269			−0.484634	+	0.874717i	$0.661047\pi$
$168$		0			0
$169$	11.7346			0.902664
$170$		0			0
$171$	0.220415	−	1.41101i	0.0168555	−	0.107903i
$172$		0			0
$173$	7.36813	+	12.7620i	0.560188	+	0.970275i	0.997480	+	0.0709548i	$0.0226046\pi$
$173$	7.36813	+	12.7620i	0.560188	+	0.970275i	−0.437291	+	0.899320i	$0.644062\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.99199	+	0.309916i	0.300056	+	0.0232947i
$178$		0			0
$179$	−1.18770	−	0.685720i	−0.0887730	−	0.0512531i	0.454956	−	0.890514i	$-0.349655\pi$
$179$	−1.18770	−	0.685720i	−0.0887730	−	0.0512531i	−0.543729	+	0.839261i	$0.682988\pi$
$180$		0			0
$181$			21.3843i			1.58949i	0.606947	+	0.794743i	$0.292394\pi$
$181$			21.3843i			1.58949i	−0.606947	+	0.794743i	$0.707606\pi$
$182$		0			0
$183$	3.74253	+	2.56633i	0.276656	+	0.189708i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−17.3098	+	9.99384i	−1.26582	+	0.730822i
$188$		0			0
$189$	0.955280	+	13.7145i	0.0694864	+	0.997583i
$190$		0			0
$191$	−14.9775	+	8.64724i	−1.08373	+	0.625692i	−0.931900	−	0.362714i	$-0.881850\pi$
$191$	−14.9775	+	8.64724i	−1.08373	+	0.625692i	−0.151830	+	0.988407i	$0.548517\pi$
$192$		0			0
$193$	6.40401	−	11.0921i	0.460971	−	0.798425i	−0.538039	−	0.842920i	$-0.680835\pi$
$193$	6.40401	−	11.0921i	0.460971	−	0.798425i	0.999010	+	0.0444950i	$0.0141679\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			9.17207i			0.653483i	0.945114	+	0.326741i	$0.105951\pi$
$197$			9.17207i			0.653483i	−0.945114	+	0.326741i	$0.894049\pi$
$198$		0			0
$199$	7.16818	+	4.13855i	0.508139	+	0.293374i	0.732068	−	0.681231i	$-0.238555\pi$
$199$	7.16818	+	4.13855i	0.508139	+	0.293374i	−0.223930	+	0.974605i	$0.571889\pi$
$200$		0			0
$201$	25.3575	+	1.96861i	1.78858	+	0.138855i
$202$		0			0
$203$	−5.56666	+	1.73405i	−0.390703	+	0.121706i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.59146	−	16.5895i	0.180119	−	1.15305i
$208$		0			0
$209$	1.28887			0.0891529
$210$		0			0
$211$	−8.50872			−0.585765			−0.292882	−	0.956148i	$-0.594614\pi$
$211$	−8.50872			−0.585765			−0.292882	+	0.956148i	$0.594614\pi$
$212$		0			0
$213$	15.4648	−	7.39649i	1.05963	−	0.506799i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.39218	−	6.17867i	0.0945073	−	0.419435i
$218$		0			0
$219$	0.973782	−	12.5432i	0.0658021	−	0.847589i
$220$		0			0
$221$	7.19180	+	4.15219i	0.483773	+	0.279306i
$222$		0			0
$223$			5.54451i			0.371288i	0.982617	+	0.185644i	$0.0594371\pi$
$223$			5.54451i			0.371288i	−0.982617	+	0.185644i	$0.940563\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.09736	+	5.36478i	−0.205579	+	0.356073i	−0.950317	−	0.311284i	$-0.899241\pi$
$227$	−3.09736	+	5.36478i	−0.205579	+	0.356073i	0.744738	+	0.667357i	$0.232574\pi$
$228$		0			0
$229$	−0.307553	+	0.177566i	−0.0203237	+	0.0117339i	−0.510127	−	0.860099i	$-0.670402\pi$
$229$	−0.307553	+	0.177566i	−0.0203237	+	0.0117339i	0.489804	+	0.871833i	$0.337068\pi$
$230$		0			0
$231$	−12.0958	+	2.76208i	−0.795847	+	0.181732i
$232$		0			0
$233$	−16.1652	+	9.33296i	−1.05901	+	0.611422i	−0.925160	−	0.379578i	$-0.876069\pi$
$233$	−16.1652	+	9.33296i	−1.05901	+	0.611422i	−0.133855	+	0.991001i	$0.542736\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.80730	−	9.92723i	0.442182	−	0.644843i
$238$		0			0
$239$		−	21.1914i		−	1.37076i	−0.728186	−	0.685379i	$-0.759636\pi$
$239$		−	21.1914i		−	1.37076i	0.728186	−	0.685379i	$-0.240364\pi$
$240$		0			0
$241$	−1.92350	−	1.11053i	−0.123903	−	0.0715356i	0.436767	−	0.899574i	$-0.356123\pi$
$241$	−1.92350	−	1.11053i	−0.123903	−	0.0715356i	−0.560671	+	0.828039i	$0.689457\pi$
$242$		0			0
$243$	−12.3166	+	9.55511i	−0.790113	+	0.612961i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.267746	−	0.463750i	−0.0170363	−	0.0295077i
$248$		0			0
$249$	−8.44517	−	17.6574i	−0.535191	−	1.11900i
$250$		0			0
$251$	18.3017			1.15519			0.577597	−	0.816322i	$-0.303990\pi$
$251$	18.3017			1.15519			0.577597	+	0.816322i	$0.303990\pi$
$252$		0			0
$253$	15.1535			0.952690
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.59968	−	9.69894i	−0.349299	−	0.605003i	0.636826	−	0.771007i	$-0.280247\pi$
$257$	−5.59968	−	9.69894i	−0.349299	−	0.605003i	−0.986125	+	0.166004i	$0.946913\pi$
$258$		0			0
$259$	−15.6049	+	16.9122i	−0.969643	+	1.05087i
$260$		0			0
$261$	−5.14665	−	4.14962i	−0.318569	−	0.256855i
$262$		0			0
$263$	−11.4450	−	6.60778i	−0.705730	−	0.407453i	0.103748	−	0.994604i	$-0.466916\pi$
$263$	−11.4450	−	6.60778i	−0.705730	−	0.407453i	−0.809478	+	0.587150i	$0.800250\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.82116	+	9.94744i	−0.417448	+	0.608774i
$268$		0			0
$269$	−12.6657	+	21.9377i	−0.772244	+	1.33757i	0.164086	+	0.986446i	$0.447532\pi$
$269$	−12.6657	+	21.9377i	−0.772244	+	1.33757i	−0.936330	+	0.351120i	$0.885801\pi$
$270$		0			0
$271$	−23.9303	+	13.8162i	−1.45366	+	0.839273i	−0.998687	−	0.0512313i	$-0.983685\pi$
$271$	−23.9303	+	13.8162i	−1.45366	+	0.839273i	−0.454976	+	0.890504i	$0.650352\pi$
$272$		0			0
$273$	3.50659	+	3.77844i	0.212228	+	0.228681i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.8309	+	20.4917i	−0.710848	+	1.23122i	0.253691	+	0.967285i	$0.418355\pi$
$277$	−11.8309	+	20.4917i	−0.710848	+	1.23122i	−0.964539	+	0.263939i	$0.914978\pi$
$278$		0			0
$279$	6.69912	−	2.58787i	0.401066	−	0.154932i
$280$		0			0
$281$		−	17.3694i		−	1.03617i	−0.855329	−	0.518085i	$-0.826645\pi$
$281$		−	17.3694i		−	1.03617i	0.855329	−	0.518085i	$-0.173355\pi$
$282$		0			0
$283$	−11.1897	−	6.46037i	−0.665158	−	0.384029i	0.129082	−	0.991634i	$-0.458797\pi$
$283$	−11.1897	−	6.46037i	−0.665158	−	0.384029i	−0.794239	+	0.607605i	$0.792130\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.26750	−	13.6996i	−0.251903	−	0.808660i
$288$		0			0
$289$	−18.7500	−	32.4760i	−1.10294	−	1.91036i
$290$		0			0
$291$	13.7454	−	6.57415i	0.805772	−	0.385383i
$292$		0			0
$293$	11.2345			0.656326			0.328163	−	0.944621i	$-0.393571\pi$
$293$	11.2345			0.656326			0.328163	+	0.944621i	$0.393571\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−10.2356	−	9.65154i	−0.593932	−	0.560039i
$298$		0			0
$299$	−3.14794	−	5.45239i	−0.182050	−	0.315320i
$300$		0			0
$301$	3.27504	+	10.5136i	0.188770	+	0.605991i
$302$		0			0
$303$	−18.0724	−	1.40304i	−1.03823	−	0.0806024i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	31.0165i		−	1.77021i	−0.465395	−	0.885103i	$-0.654088\pi$
$307$		−	31.0165i		−	1.77021i	0.465395	−	0.885103i	$-0.345912\pi$
$308$		0			0
$309$	4.66938	+	3.20189i	0.265632	+	0.182149i
$310$		0			0
$311$	−0.771357	+	1.33603i	−0.0437396	+	0.0757593i	−0.887066	−	0.461642i	$-0.847261\pi$
$311$	−0.771357	+	1.33603i	−0.0437396	+	0.0757593i	0.843327	+	0.537401i	$0.180594\pi$
$312$		0			0
$313$	22.2646	−	12.8545i	1.25847	−	0.726579i	0.285694	−	0.958321i	$-0.407776\pi$
$313$	22.2646	−	12.8545i	1.25847	−	0.726579i	0.972777	+	0.231742i	$0.0744425\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.69412	+	1.55545i	−0.151317	+	0.0873629i	−0.573747	−	0.819033i	$-0.694511\pi$
$317$	−2.69412	+	1.55545i	−0.151317	+	0.0873629i	0.422430	+	0.906396i	$0.361177\pi$
$318$		0			0
$319$	2.98325	−	5.16714i	0.167030	−	0.289304i
$320$		0			0
$321$	−7.12248	−	4.88403i	−0.397538	−	0.272600i
$322$		0			0
$323$			3.51434i			0.195543i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.29039	+	0.643619i	0.458460	+	0.0355922i
$328$		0			0
$329$	−22.2917	+	24.1591i	−1.22898	+	1.33194i
$330$		0			0
$331$	0.139978	+	0.242450i	0.00769391	+	0.0133262i	0.869847	−	0.493322i	$-0.164218\pi$
$331$	0.139978	+	0.242450i	0.00769391	+	0.0133262i	−0.862153	+	0.506648i	$0.830884\pi$
$332$		0			0
$333$	−25.7801	−	4.02712i	−1.41274	−	0.220685i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5.96891			−0.325147			−0.162574	−	0.986696i	$-0.551979\pi$
$337$	−5.96891			−0.325147			−0.162574	+	0.986696i	$0.551979\pi$
$338$		0			0
$339$	−29.5121	+	14.1150i	−1.60288	+	0.766622i
$340$		0			0
$341$	3.24066	+	5.61298i	0.175491	+	0.303960i
$342$		0			0
$343$	−14.5755	−	11.4260i	−0.787004	−	0.616947i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.41426	+	4.28063i	0.398019	+	0.229796i	0.685629	−	0.727951i	$-0.259527\pi$
$347$	7.41426	+	4.28063i	0.398019	+	0.229796i	−0.287610	+	0.957748i	$0.592861\pi$
$348$		0			0
$349$			7.23833i			0.387459i	0.981055	+	0.193729i	$0.0620584\pi$
$349$			7.23833i			0.387459i	−0.981055	+	0.193729i	$0.937942\pi$
$350$		0			0
$351$	−1.34641	+	5.68789i	−0.0718661	+	0.303597i
$352$		0			0
$353$	11.8813	−	20.5790i	0.632377	−	1.09531i	−0.354688	−	0.934985i	$-0.615413\pi$
$353$	11.8813	−	20.5790i	0.632377	−	1.09531i	0.987065	−	0.160324i	$-0.0512538\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.53132	−	32.9815i	−0.398600	−	1.74557i
$358$		0			0
$359$	−31.3993	+	18.1284i	−1.65719	+	0.956780i	−0.683188	+	0.730242i	$0.739407\pi$
$359$	−31.3993	+	18.1284i	−1.65719	+	0.956780i	−0.974003	+	0.226537i	$0.927260\pi$
$360$		0			0
$361$	−9.38669	+	16.2582i	−0.494036	+	0.855696i
$362$		0			0
$363$	−3.59449	+	5.24192i	−0.188662	+	0.275129i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.26512	+	0.730418i	0.0660387	+	0.0381275i	0.532656	−	0.846332i	$-0.321194\pi$
$367$	1.26512	+	0.730418i	0.0660387	+	0.0381275i	−0.466617	+	0.884459i	$0.654527\pi$
$368$		0			0
$369$	10.2122	−	12.6659i	0.531628	−	0.659361i
$370$		0			0
$371$	−2.85616	+	12.6760i	−0.148284	+	0.658105i
$372$		0			0
$373$	−10.5919	−	18.3457i	−0.548429	−	0.949907i	−0.998382	−	0.0568547i	$-0.981893\pi$
$373$	−10.5919	−	18.3457i	−0.548429	−	0.949907i	0.449954	−	0.893052i	$-0.351441\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.47893			−0.127671
$378$		0			0
$379$	24.3581			1.25119			0.625596	−	0.780147i	$-0.284856\pi$
$379$	24.3581			1.25119			0.625596	+	0.780147i	$0.284856\pi$
$380$		0			0
$381$	5.80887	+	12.1454i	0.297598	+	0.622227i
$382$		0			0
$383$	12.5964	+	21.8176i	0.643647	+	1.11483i	0.984612	+	0.174754i	$0.0559129\pi$
$383$	12.5964	+	21.8176i	0.643647	+	1.11483i	−0.340965	+	0.940076i	$0.610754\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.83725	+	9.72030i	−0.398390	+	0.494110i
$388$		0			0
$389$	−10.9380	−	6.31508i	−0.554581	−	0.320187i	0.196387	−	0.980527i	$-0.437079\pi$
$389$	−10.9380	−	6.31508i	−0.554581	−	0.320187i	−0.750967	+	0.660339i	$0.770413\pi$
$390$		0			0
$391$			41.3187i			2.08958i
$392$		0			0
$393$	4.55677	−	6.64524i	0.229859	−	0.335208i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.3269	−	8.27166i	0.719048	−	0.415143i	−0.0953542	−	0.995443i	$-0.530398\pi$
$397$	14.3269	−	8.27166i	0.719048	−	0.415143i	0.814402	+	0.580301i	$0.197065\pi$
$398$		0			0
$399$	−0.642797	+	2.08465i	−0.0321801	+	0.104363i
$400$		0			0
$401$	9.72834	−	5.61666i	0.485810	−	0.280482i	−0.237025	−	0.971504i	$-0.576172\pi$
$401$	9.72834	−	5.61666i	0.485810	−	0.280482i	0.722835	+	0.691021i	$0.242839\pi$
$402$		0			0
$403$	1.34641	−	2.33205i	0.0670695	−	0.116168i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	23.5484i		−	1.16725i
$408$		0			0
$409$	−31.6764	−	18.2884i	−1.56630	−	0.904303i	−0.996595	−	0.0824520i	$-0.973725\pi$
$409$	−31.6764	−	18.2884i	−1.56630	−	0.904303i	−0.569703	−	0.821851i	$-0.692942\pi$
$410$		0			0
$411$	1.47628	−	19.0159i	0.0728198	−	0.937983i
$412$		0			0
$413$	−5.96663	−	1.34440i	−0.293599	−	0.0661537i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	32.1768	−	15.3895i	1.57571	−	0.753626i
$418$		0			0
$419$	8.29006			0.404996			0.202498	−	0.979283i	$-0.435094\pi$
$419$	8.29006			0.404996			0.202498	+	0.979283i	$0.435094\pi$
$420$		0			0
$421$	23.8826			1.16397			0.581984	−	0.813200i	$-0.302277\pi$
$421$	23.8826			1.16397			0.581984	+	0.813200i	$0.302277\pi$
$422$		0			0
$423$	−36.8270	−	5.75276i	−1.79059	−	0.279709i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.09443	−	4.70065i	−0.246537	−	0.227480i
$428$		0			0
$429$	−5.25930	−	0.408303i	−0.253921	−	0.0197130i
$430$		0			0
$431$	−9.93859	−	5.73805i	−0.478725	−	0.276392i	0.241160	−	0.970485i	$-0.422472\pi$
$431$	−9.93859	−	5.73805i	−0.478725	−	0.276392i	−0.719885	+	0.694093i	$0.755806\pi$
$432$		0			0
$433$		−	3.31657i		−	0.159384i	−0.996820	−	0.0796920i	$-0.974606\pi$
$433$		−	3.31657i		−	0.159384i	0.996820	−	0.0796920i	$-0.0253937\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.33218	−	2.30741i	0.0637269	−	0.110378i
$438$		0			0
$439$	23.6144	−	13.6338i	1.12705	−	0.650705i	0.183862	−	0.982952i	$-0.441140\pi$
$439$	23.6144	−	13.6338i	1.12705	−	0.650705i	0.943192	+	0.332247i	$0.107807\pi$
$440$		0			0
$441$	1.56510	−	20.9416i	0.0745287	−	0.997219i
$442$		0			0
$443$	−35.4300	+	20.4555i	−1.68333	+	0.971872i	−0.723911	+	0.689893i	$0.757657\pi$
$443$	−35.4300	+	20.4555i	−1.68333	+	0.971872i	−0.959421	+	0.281979i	$0.909009\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−24.5613	−	16.8422i	−1.16171	−	0.796608i
$448$		0			0
$449$		−	19.6734i		−	0.928446i	−0.885718	−	0.464223i	$-0.846334\pi$
$449$		−	19.6734i		−	0.928446i	0.885718	−	0.464223i	$-0.153666\pi$
$450$		0			0
$451$	12.7164	+	7.34179i	0.598790	+	0.345711i
$452$		0			0
$453$	3.45579	+	0.268288i	0.162367	+	0.0126053i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.59563	+	7.95987i	0.214975	+	0.372347i	0.953265	−	0.302136i	$-0.0976998\pi$
$457$	4.59563	+	7.95987i	0.214975	+	0.372347i	−0.738290	+	0.674483i	$0.764366\pi$
$458$		0			0
$459$	26.3167	−	27.9094i	1.22836	−	1.30270i
$460$		0			0
$461$	28.7958			1.34115			0.670577	−	0.741840i	$-0.266047\pi$
$461$	28.7958			1.34115			0.670577	+	0.741840i	$0.266047\pi$
$462$		0			0
$463$	25.0825			1.16568			0.582841	−	0.812586i	$-0.301941\pi$
$463$	25.0825			1.16568			0.582841	+	0.812586i	$0.301941\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.6675	+	20.2087i	0.539907	+	0.935145i	0.998908	+	0.0467103i	$0.0148737\pi$
$467$	11.6675	+	20.2087i	0.539907	+	0.935145i	−0.459002	+	0.888435i	$0.651793\pi$
$468$		0			0
$469$	−37.9005	−	8.53977i	−1.75008	−	0.394330i
$470$		0			0
$471$	2.44493	−	31.4929i	0.112656	−	1.45111i
$472$		0			0
$473$	−9.75900	−	5.63436i	−0.448719	−	0.259068i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−13.7437	+	5.30921i	−0.629282	+	0.243092i
$478$		0			0
$479$	8.12075	−	14.0655i	0.371046	−	0.642671i	−0.618680	−	0.785643i	$-0.712332\pi$
$479$	8.12075	−	14.0655i	0.371046	−	0.642671i	0.989727	+	0.142971i	$0.0456657\pi$
$480$		0			0
$481$	−8.47301	+	4.89189i	−0.386336	+	0.223051i
$482$		0			0
$483$	−7.55748	+	24.5095i	−0.343877	+	1.11522i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.07733	−	8.79420i	0.230076	−	0.398503i	−0.727754	−	0.685838i	$-0.759436\pi$
$487$	5.07733	−	8.79420i	0.230076	−	0.398503i	0.957830	+	0.287335i	$0.0927692\pi$
$488$		0			0
$489$	−19.4049	+	28.2986i	−0.877520	+	1.27971i
$490$		0			0
$491$		−	25.5734i		−	1.15411i	−0.816704	−	0.577057i	$-0.804201\pi$
$491$		−	25.5734i		−	1.15411i	0.816704	−	0.577057i	$-0.195799\pi$
$492$		0			0
$493$	14.0892	+	8.13438i	0.634544	+	0.366354i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.0008	+	7.78792i	−1.12144	+	0.349336i
$498$		0			0
$499$	−4.80838	−	8.32836i	−0.215253	−	0.372829i	0.738098	−	0.674693i	$-0.235724\pi$
$499$	−4.80838	−	8.32836i	−0.215253	−	0.372829i	−0.953351	+	0.301865i	$0.902391\pi$
$500$		0			0
$501$	9.36078	+	19.5718i	0.418209	+	0.874405i
$502$		0			0
$503$	−6.82743			−0.304420			−0.152210	−	0.988348i	$-0.548639\pi$
$503$	−6.82743			−0.304420			−0.152210	+	0.988348i	$0.548639\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.76958	−	18.3357i	−0.389471	−	0.814319i
$508$		0			0
$509$	7.02977	+	12.1759i	0.311589	+	0.539688i	0.978707	−	0.205265i	$-0.0658055\pi$
$509$	7.02977	+	12.1759i	0.311589	+	0.539688i	−0.667118	+	0.744952i	$0.732472\pi$
$510$		0			0
$511$	−4.22423	+	18.7477i	−0.186869	+	0.829347i
$512$		0			0
$513$	−2.36948	+	0.710081i	−0.104615	+	0.0313508i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	33.6391i		−	1.47945i
$518$		0			0
$519$	14.4346	−	21.0503i	0.633609	−	0.924005i
$520$		0			0
$521$	−13.6122	+	23.5771i	−0.596363	+	1.03293i	0.396990	+	0.917823i	$0.370055\pi$
$521$	−13.6122	+	23.5771i	−0.596363	+	1.03293i	−0.993353	+	0.115109i	$0.963278\pi$
$522$		0			0
$523$	−0.916202	+	0.528969i	−0.0400627	+	0.0231302i	−0.519898	−	0.854229i	$-0.674030\pi$
$523$	−0.916202	+	0.528969i	−0.0400627	+	0.0231302i	0.479835	+	0.877359i	$0.340697\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.3048	+	8.83625i	−0.666689	+	0.384913i
$528$		0			0
$529$	4.16269	−	7.20999i	0.180987	−	0.313478i
$530$		0			0
$531$	−2.49906	−	6.46922i	−0.108450	−	0.280740i
$532$		0			0
$533$		−	6.10066i		−	0.264249i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.183860	+	2.36828i	−0.00793414	+	0.102199i
$538$		0			0
$539$	18.8911	−	1.52137i	0.813698	−	0.0655300i
$540$		0			0
$541$	13.1032	+	22.6953i	0.563349	+	0.975748i	0.997201	+	0.0747644i	$0.0238205\pi$
$541$	13.1032	+	22.6953i	0.563349	+	0.975748i	−0.433853	+	0.900984i	$0.642846\pi$
$542$		0			0
$543$	33.4137	−	15.9810i	1.43392	−	0.685812i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−36.6385			−1.56655			−0.783275	−	0.621675i	$-0.786452\pi$
$547$	−36.6385			−1.56655			−0.783275	+	0.621675i	$0.786452\pi$
$548$		0			0
$549$	1.21308	−	7.76570i	0.0517731	−	0.331432i
$550$		0			0
$551$	−0.524531	−	0.908514i	−0.0223458	−	0.0387040i
$552$		0			0
$553$	−12.4687	+	13.5132i	−0.530223	+	0.574640i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−29.6236	−	17.1032i	−1.25519	−	0.724685i	−0.283055	−	0.959104i	$-0.591348\pi$
$557$	−29.6236	−	17.1032i	−1.25519	−	0.724685i	−0.972136	+	0.234419i	$0.924681\pi$
$558$		0			0
$559$			4.68187i			0.198022i
$560$		0			0
$561$	28.5518	+	19.5785i	1.20546	+	0.826606i
$562$		0			0
$563$	−11.9319	+	20.6666i	−0.502868	+	0.870993i	0.497127	+	0.867678i	$0.334388\pi$
$563$	−11.9319	+	20.6666i	−0.502868	+	0.870993i	−0.999995	+	0.00331483i	$0.998945\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	20.7154	−	11.7418i	0.869966	−	0.493111i
$568$		0			0
$569$	−27.8326	+	16.0692i	−1.16680	+	0.673655i	−0.952925	−	0.303205i	$-0.901943\pi$
$569$	−27.8326	+	16.0692i	−1.16680	+	0.673655i	−0.213879	+	0.976860i	$0.568610\pi$
$570$		0			0
$571$	9.85333	−	17.0665i	0.412349	−	0.714209i	−0.582797	−	0.812618i	$-0.698042\pi$
$571$	9.85333	−	17.0665i	0.412349	−	0.714209i	0.995146	+	0.0984083i	$0.0313751\pi$
$572$		0			0
$573$	24.7046	+	16.9405i	1.03205	+	0.707697i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	10.7514	+	6.20731i	0.447586	+	0.258414i	0.706810	−	0.707403i	$-0.250134\pi$
$577$	10.7514	+	6.20731i	0.447586	+	0.258414i	−0.259224	+	0.965817i	$0.583467\pi$
$578$		0			0
$579$	−22.1176	−	1.71709i	−0.919176	−	0.0713597i
$580$		0			0
$581$	8.89211	+	28.5455i	0.368907	+	1.18427i
$582$		0			0
$583$	−6.64845	−	11.5154i	−0.275351	−	0.476921i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−30.6227			−1.26394			−0.631968	−	0.774995i	$-0.717753\pi$
$587$	−30.6227			−1.26394			−0.631968	+	0.774995i	$0.717753\pi$
$588$		0			0
$589$	1.13958			0.0469556
$590$		0			0
$591$	14.3316	−	6.85452i	0.589525	−	0.281957i
$592$		0			0
$593$	−21.7660	−	37.6999i	−0.893823	−	1.54815i	−0.835254	−	0.549864i	$-0.814679\pi$
$593$	−21.7660	−	37.6999i	−0.893823	−	1.54815i	−0.0585693	−	0.998283i	$-0.518654\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.10966	−	14.2933i	0.0454152	−	0.584988i
$598$		0			0
$599$	−22.8060	−	13.1670i	−0.931827	−	0.537991i	−0.0444381	−	0.999012i	$-0.514150\pi$
$599$	−22.8060	−	13.1670i	−0.931827	−	0.537991i	−0.887389	+	0.461022i	$0.847483\pi$
$600$		0			0
$601$			18.8846i			0.770317i	0.922850	+	0.385159i	$0.125853\pi$
$601$			18.8846i			0.770317i	−0.922850	+	0.385159i	$0.874147\pi$
$602$		0			0
$603$	−15.8743	−	41.0930i	−0.646450	−	1.67344i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	12.4123	−	7.16622i	0.503798	−	0.290868i	−0.226482	−	0.974015i	$-0.572723\pi$
$607$	12.4123	−	7.16622i	0.503798	−	0.290868i	0.730281	+	0.683147i	$0.239389\pi$
$608$		0			0
$609$	6.86961	+	7.40218i	0.278371	+	0.299951i
$610$		0			0
$611$	−12.1037	+	6.98810i	−0.489665	+	0.282708i
$612$		0			0
$613$	9.26188	−	16.0421i	0.374084	−	0.647932i	−0.616106	−	0.787664i	$-0.711291\pi$
$613$	9.26188	−	16.0421i	0.374084	−	0.647932i	0.990189	+	0.139731i	$0.0446239\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			46.6900i			1.87967i	0.341633	+	0.939833i	$0.389020\pi$
$617$			46.6900i			1.87967i	−0.341633	+	0.939833i	$0.610980\pi$
$618$		0			0
$619$	33.0066	+	19.0564i	1.32665	+	0.765940i	0.984780	−	0.173808i	$-0.0556073\pi$
$619$	33.0066	+	19.0564i	1.32665	+	0.765940i	0.341868	+	0.939748i	$0.388941\pi$
$620$		0			0
$621$	−27.8583	+	8.34854i	−1.11792	+	0.335016i
$622$		0			0
$623$	12.4941	−	13.5407i	0.500565	−	0.542498i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.963204	−	2.01390i	−0.0384667	−	0.0804274i
$628$		0			0
$629$	64.2092			2.56019
$630$		0			0
$631$	−17.1097			−0.681128			−0.340564	−	0.940221i	$-0.610618\pi$
$631$	−17.1097			−0.681128			−0.340564	+	0.940221i	$0.610618\pi$
$632$		0			0
$633$	6.35878	+	13.2952i	0.252739	+	0.528435i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.47180	−	6.48121i	−0.177179	−	0.256795i
$638$		0			0
$639$	−23.1145	−	18.6367i	−0.914395	−	0.737256i
$640$		0			0
$641$	18.2874	+	10.5583i	0.722310	+	0.417026i	0.815602	−	0.578613i	$-0.196406\pi$
$641$	18.2874	+	10.5583i	0.722310	+	0.417026i	−0.0932922	+	0.995639i	$0.529739\pi$
$642$		0			0
$643$			6.86538i			0.270744i	0.990795	+	0.135372i	$0.0432230\pi$
$643$			6.86538i			0.270744i	−0.990795	+	0.135372i	$0.956777\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.90522	+	15.4243i	−0.350100	+	0.606391i	−0.986267	−	0.165161i	$-0.947186\pi$
$647$	−8.90522	+	15.4243i	−0.350100	+	0.606391i	0.636167	+	0.771552i	$0.280519\pi$
$648$		0			0
$649$	5.42036	−	3.12944i	0.212768	−	0.122841i
$650$		0			0
$651$	−10.6948	+	2.44215i	−0.419161	+	0.0957153i
$652$		0			0
$653$	39.5964	−	22.8610i	1.54953	−	0.894619i	0.551348	−	0.834275i	$-0.314114\pi$
$653$	39.5964	−	22.8610i	1.54953	−	0.894619i	0.998178	−	0.0603437i	$-0.0192197\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−20.3268	+	7.85226i	−0.793025	+	0.306346i
$658$		0			0
$659$		−	6.74688i		−	0.262821i	−0.991328	−	0.131411i	$-0.958049\pi$
$659$		−	6.74688i		−	0.262821i	0.991328	−	0.131411i	$-0.0419506\pi$
$660$		0			0
$661$	−43.2369	−	24.9628i	−1.68172	−	0.970942i	−0.960518	−	0.278218i	$-0.910256\pi$
$661$	−43.2369	−	24.9628i	−1.68172	−	0.970942i	−0.721203	−	0.692724i	$-0.756410\pi$
$662$		0			0
$663$	1.11331	−	14.3405i	0.0432375	−	0.556937i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.16700	−	10.6816i	−0.238787	−	0.413592i
$668$		0			0
$669$	8.66348	−	4.14355i	0.334949	−	0.160199i
$670$		0			0
$671$	7.09346			0.273840
$672$		0			0
$673$	20.0600			0.773257			0.386628	−	0.922236i	$-0.373640\pi$
$673$	20.0600			0.773257			0.386628	+	0.922236i	$0.373640\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.4751	−	21.6076i	−0.479458	−	0.830446i	0.520264	−	0.854005i	$-0.325833\pi$
$677$	−12.4751	−	21.6076i	−0.479458	−	0.830446i	−0.999722	+	0.0235594i	$0.992500\pi$
$678$		0			0
$679$	−22.2212	+	6.92206i	−0.852773	+	0.265644i
$680$		0			0
$681$	10.6974	+	0.830484i	0.409924	+	0.0318242i
$682$		0			0
$683$	26.7156	+	15.4243i	1.02225	+	0.590194i	0.914754	−	0.404012i	$-0.132385\pi$
$683$	26.7156	+	15.4243i	1.02225	+	0.590194i	0.107492	+	0.994206i	$0.465718\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	0.507294	+	0.347862i	0.0193545	+	0.0132718i
$688$		0			0
$689$	−2.76226	+	4.78438i	−0.105234	+	0.182270i
$690$		0			0
$691$	15.5472	−	8.97619i	0.591444	−	0.341470i	−0.174224	−	0.984706i	$-0.555742\pi$
$691$	15.5472	−	8.97619i	0.591444	−	0.341470i	0.765668	+	0.643236i	$0.222408\pi$
$692$		0			0
$693$	13.3554	+	16.8360i	0.507328	+	0.639545i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−20.0188	+	34.6735i	−0.758264	+	1.31335i
$698$		0			0
$699$	26.6637	+	18.2838i	1.00851	+	0.691557i
$700$		0			0
$701$		−	31.7744i		−	1.20010i	−0.799961	−	0.600052i	$-0.795147\pi$
$701$		−	31.7744i		−	1.20010i	0.799961	−	0.600052i	$-0.204853\pi$
$702$		0			0
$703$	−3.58570	−	2.07021i	−0.135237	−	0.0780793i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	27.0119	+	6.08633i	1.01589	+	0.228900i
$708$		0			0
$709$	−13.2201	−	22.8978i	−0.496490	−	0.859946i	0.503502	−	0.863994i	$-0.332045\pi$
$709$	−13.2201	−	22.8978i	−0.496490	−	0.859946i	−0.999992	+	0.00404829i	$0.998711\pi$
$710$		0			0
$711$	−20.5989	−	3.21776i	−0.772518	−	0.120675i
$712$		0			0
$713$	13.3982			0.501768
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−33.1123	+	15.8369i	−1.23660	+	0.591439i
$718$		0			0
$719$	−12.2625	−	21.2393i	−0.457314	−	0.792092i	0.541504	−	0.840698i	$-0.317855\pi$
$719$	−12.2625	−	21.2393i	−0.457314	−	0.792092i	−0.998818	+	0.0486066i	$0.984522\pi$
$720$		0			0
$721$	−6.35608	−	5.86478i	−0.236713	−	0.218416i
$722$		0			0
$723$	−0.297763	+	3.83545i	−0.0110739	+	0.142642i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	49.4804i		−	1.83513i	−0.397589	−	0.917564i	$-0.630153\pi$
$727$		−	49.4804i		−	1.83513i	0.397589	−	0.917564i	$-0.369847\pi$
$728$		0			0
$729$	24.1347	+	12.1044i	0.893878	+	0.448310i
$730$		0			0
$731$	15.3631	−	26.6097i	0.568226	−	0.984196i
$732$		0			0
$733$	−14.3352	+	8.27642i	−0.529482	+	0.305697i	−0.740805	−	0.671720i	$-0.765556\pi$
$733$	−14.3352	+	8.27642i	−0.529482	+	0.305697i	0.211324	+	0.977416i	$0.432223\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	34.4306	−	19.8785i	1.26827	−	0.732234i
$738$		0			0
$739$	−8.41010	+	14.5667i	−0.309371	+	0.535846i	−0.978225	−	0.207548i	$-0.933452\pi$
$739$	−8.41010	+	14.5667i	−0.309371	+	0.535846i	0.668854	+	0.743394i	$0.266785\pi$
$740$		0			0
$741$	−0.524531	+	0.764935i	−0.0192691	+	0.0281006i
$742$		0			0
$743$		−	4.76463i		−	0.174797i	−0.996173	−	0.0873987i	$-0.972145\pi$
$743$		−	4.76463i		−	0.174797i	0.996173	−	0.0873987i	$-0.0278554\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−21.2790	+	26.3917i	−0.778559	+	0.965622i
$748$		0			0
$749$	9.69531	+	8.94590i	0.354259	+	0.326876i
$750$		0			0
$751$	−4.11749	−	7.13171i	−0.150249	−	0.260240i	0.781070	−	0.624444i	$-0.214674\pi$
$751$	−4.11749	−	7.13171i	−0.150249	−	0.260240i	−0.931319	+	0.364204i	$0.881341\pi$
$752$		0			0
$753$	−13.6773	−	28.5970i	−0.498430	−	1.04213i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−3.01624			−0.109627			−0.0548136	−	0.998497i	$-0.517456\pi$
$757$	−3.01624			−0.109627			−0.0548136	+	0.998497i	$0.517456\pi$
$758$		0			0
$759$	−11.3246	−	23.6778i	−0.411055	−	0.859448i
$760$		0			0
$761$	−7.59504	−	13.1550i	−0.275320	−	0.476868i	0.694896	−	0.719110i	$-0.255450\pi$
$761$	−7.59504	−	13.1550i	−0.275320	−	0.476868i	−0.970216	+	0.242242i	$0.922117\pi$
$762$		0			0
$763$	−12.3912	−	2.79200i	−0.448593	−	0.101077i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.25202	−	1.30021i	−0.0813158	−	0.0469477i
$768$		0			0
$769$			33.1611i			1.19582i	0.801563	+	0.597910i	$0.204002\pi$
$769$			33.1611i			1.19582i	−0.801563	+	0.597910i	$0.795998\pi$
$770$		0			0
$771$	−10.9701	+	15.9979i	−0.395079	+	0.576152i
$772$		0			0
$773$	−4.84706	+	8.39536i	−0.174337	+	0.301960i	−0.939932	−	0.341363i	$-0.889111\pi$
$773$	−4.84706	+	8.39536i	−0.174337	+	0.301960i	0.765595	+	0.643323i	$0.222445\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	38.0878	+	11.7443i	1.36639	+	0.421325i
$778$		0			0
$779$	2.23586	−	1.29087i	0.0801079	−	0.0462503i
$780$		0			0
$781$	13.3983	−	23.2065i	0.479429	−	0.830395i
$782$		0			0
$783$	−2.63770	+	11.1429i	−0.0942637	+	0.398215i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	36.3526	+	20.9882i	1.29583	+	0.748148i	0.979681	−	0.200562i	$-0.0642768\pi$
$787$	36.3526	+	20.9882i	1.29583	+	0.748148i	0.316149	+	0.948710i	$0.397610\pi$
$788$		0			0
$789$	−1.77172	+	22.8214i	−0.0630750	+	0.812462i
$790$		0			0
$791$	47.7101	−	14.8620i	1.69638	−	0.528432i
$792$		0			0
$793$	−1.47358	−	2.55231i	−0.0523283	−	0.0906352i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	29.8186			1.05623			0.528115	−	0.849173i	$-0.322899\pi$
$797$	29.8186			1.05623			0.528115	+	0.849173i	$0.322899\pi$
$798$		0			0
$799$	91.7232			3.24493
$800$		0			0
$801$	20.6408	+	3.22431i	0.729308	+	0.113925i
$802$		0			0
$803$	−9.83298	−	17.0312i	−0.346998	−	0.601019i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	43.7438	+	3.39602i	1.53985	+	0.119546i
$808$		0			0
$809$	15.5493	+	8.97739i	0.546684	+	0.315628i	0.747784	−	0.663942i	$-0.231118\pi$
$809$	15.5493	+	8.97739i	0.546684	+	0.315628i	−0.201099	+	0.979571i	$0.564451\pi$
$810$		0			0
$811$		−	4.42584i		−	0.155412i	−0.996976	−	0.0777061i	$-0.975240\pi$
$811$		−	4.42584i		−	0.155412i	0.996976	−	0.0777061i	$-0.0247596\pi$
$812$		0			0
$813$	39.4719	+	27.0667i	1.38434	+	0.949270i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.71588	+	0.990664i	−0.0600311	+	0.0346589i
$818$		0			0
$819$	3.28337	−	8.30287i	0.114730	−	0.290126i
$820$		0			0
$821$	−32.5257	+	18.7787i	−1.13515	+	0.655381i	−0.945226	−	0.326417i	$-0.894159\pi$
$821$	−32.5257	+	18.7787i	−1.13515	+	0.655381i	−0.189927	+	0.981798i	$0.560825\pi$
$822$		0			0
$823$	−18.4164	+	31.8982i	−0.641957	+	1.11190i	0.343038	+	0.939321i	$0.388544\pi$
$823$	−18.4164	+	31.8982i	−0.641957	+	1.11190i	−0.984995	+	0.172581i	$0.944789\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.9737i			0.520686i	0.965516	+	0.260343i	$0.0838357\pi$
$827$			14.9737i			0.520686i	−0.965516	+	0.260343i	$0.916164\pi$
$828$		0			0
$829$	−2.95565	−	1.70645i	−0.102654	−	0.0592674i	0.447794	−	0.894137i	$-0.352210\pi$
$829$	−2.95565	−	1.70645i	−0.102654	−	0.0592674i	−0.550448	+	0.834869i	$0.685543\pi$
$830$		0			0
$831$	40.8604	+	3.17217i	1.41743	+	0.110041i
$832$		0			0
$833$	4.14829	+	51.5102i	0.143730	+	1.78472i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−9.05005	−	8.53360i	−0.312815	−	0.294964i
$838$		0			0
$839$	−3.71578			−0.128283			−0.0641416	−	0.997941i	$-0.520431\pi$
$839$	−3.71578			−0.128283			−0.0641416	+	0.997941i	$0.520431\pi$
$840$		0			0
$841$	24.1436			0.832539
$842$		0			0
$843$	−27.1402	+	12.9806i	−0.934759	+	0.447075i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	6.58390	−	7.13544i	0.226225	−	0.245176i
$848$		0			0
$849$	−1.73220	+	22.3122i	−0.0594488	+	0.765754i
$850$		0			0
$851$	−42.1577	−	24.3398i	−1.44515	−	0.834357i
$852$		0			0
$853$			10.5549i			0.361393i	0.983539	+	0.180696i	$0.0578351\pi$
$853$			10.5549i			0.361393i	−0.983539	+	0.180696i	$0.942165\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	19.2967	−	33.4229i	0.659163	−	1.14170i	−0.321669	−	0.946852i	$-0.604244\pi$
$857$	19.2967	−	33.4229i	0.659163	−	1.14170i	0.980833	−	0.194852i	$-0.0624228\pi$
$858$		0			0
$859$	−25.9876	+	15.0039i	−0.886685	+	0.511928i	−0.872857	−	0.487977i	$-0.837735\pi$
$859$	−25.9876	+	15.0039i	−0.886685	+	0.511928i	−0.0138282	+	0.999904i	$0.504402\pi$
$860$		0			0
$861$	−18.2168	+	16.9061i	−0.620827	+	0.576160i
$862$		0			0
$863$	33.0204	−	19.0643i	1.12403	−	0.648958i	0.181602	−	0.983372i	$-0.441872\pi$
$863$	33.0204	−	19.0643i	1.12403	−	0.648958i	0.942426	+	0.334414i	$0.108538\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−36.7325	+	53.5677i	−1.24750	+	1.81925i
$868$		0			0
$869$		−	18.8157i		−	0.638280i
$870$		0			0
$871$	−14.3050	−	8.25902i	−0.484708	−	0.279846i
$872$		0			0
$873$	−20.5446	−	16.5647i	−0.695330	−	0.560629i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	16.5855	+	28.7268i	0.560051	+	0.970037i	0.997491	+	0.0707893i	$0.0225518\pi$
$877$	16.5855	+	28.7268i	0.560051	+	0.970037i	−0.437440	+	0.899247i	$0.644115\pi$
$878$		0			0
$879$	−8.39581	−	17.5542i	−0.283184	−	0.592090i
$880$		0			0
$881$	−19.8093			−0.667393			−0.333697	−	0.942681i	$-0.608296\pi$
$881$	−19.8093			−0.667393			−0.333697	+	0.942681i	$0.608296\pi$
$882$		0			0
$883$	3.37029			0.113419			0.0567096	−	0.998391i	$-0.481939\pi$
$883$	3.37029			0.113419			0.0567096	+	0.998391i	$0.481939\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18.0715	−	31.3008i	−0.606783	−	1.05098i	−0.991767	−	0.128056i	$-0.959126\pi$
$887$	−18.0715	−	31.3008i	−0.606783	−	1.05098i	0.384984	−	0.922923i	$-0.374207\pi$
$888$		0			0
$889$	−6.11629	−	19.6346i	−0.205134	−	0.658522i
$890$		0			0
$891$	−7.43148	+	23.2064i	−0.248964	+	0.777442i
$892$		0			0
$893$	−5.12220	−	2.95730i	−0.171408	−	0.0989623i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.16700	+	8.99347i	−0.205910	+	0.300283i
$898$		0			0
$899$	2.63770	−	4.56863i	0.0879722	−	0.152372i
$900$		0			0
$901$	31.3990	−	18.1282i	1.04605	−	0.603939i
$902$		0			0
$903$	13.9802	−	12.9744i	0.465233	−	0.431761i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−23.0513	+	39.9260i	−0.765405	+	1.32572i	0.174627	+	0.984635i	$0.444128\pi$
$907$	−23.0513	+	39.9260i	−0.765405	+	1.32572i	−0.940032	+	0.341086i	$0.889205\pi$
$908$		0			0
$909$	11.3136	+	29.2872i	0.375250	+	0.971394i
$910$		0			0
$911$			58.0403i			1.92296i	0.274871	+	0.961481i	$0.411365\pi$
$911$			58.0403i			1.92296i	−0.274871	+	0.961481i	$0.588635\pi$
$912$		0			0
$913$	−26.4968	−	15.2979i	−0.876916	−	0.506288i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.34648	+	9.04567i	−0.275625	+	0.298714i
$918$		0			0
$919$	−2.66148	−	4.60983i	−0.0877943	−	0.152064i	0.818784	−	0.574101i	$-0.194648\pi$
$919$	−2.66148	−	4.60983i	−0.0877943	−	0.152064i	−0.906578	+	0.422037i	$0.861315\pi$
$920$		0			0
$921$	−48.4643	+	23.1794i	−1.59695	+	0.763788i
$922$		0			0
$923$	−11.1333			−0.366458
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.51351	−	9.68891i	0.0497101	−	0.318226i
$928$		0			0
$929$	−20.7113	−	35.8731i	−0.679517	−	1.17696i	−0.975127	−	0.221649i	$-0.928856\pi$
$929$	−20.7113	−	35.8731i	−0.679517	−	1.17696i	0.295610	−	0.955309i	$-0.404477\pi$
$930$		0			0
$931$	1.42911	−	3.01029i	0.0468373	−	0.0986581i
$932$		0			0
$933$	2.66404	+	0.206821i	0.0872168	+	0.00677103i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			0.523249i			0.0170938i	0.999963	+	0.00854690i	$0.00272060\pi$
$937$			0.523249i			0.0170938i	−0.999963	+	0.00854690i	$0.997279\pi$
$938$		0			0
$939$	−36.7245	−	25.1827i	−1.19846	−	0.821807i
$940$		0			0
$941$	−9.58594	+	16.6033i	−0.312493	+	0.541253i	−0.978901	−	0.204333i	$-0.934497\pi$
$941$	−9.58594	+	16.6033i	−0.312493	+	0.541253i	0.666409	+	0.745587i	$0.267831\pi$
$942$		0			0
$943$	26.2874	−	15.1770i	0.856035	−	0.494232i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.0940	−	15.0654i	0.847940	−	0.489558i	−0.0120156	−	0.999928i	$-0.503825\pi$
$947$	26.0940	−	15.0654i	0.847940	−	0.489558i	0.859955	+	0.510370i	$0.170491\pi$
$948$		0			0
$949$	−4.08536	+	7.07605i	−0.132616	+	0.229698i
$950$		0			0
$951$	4.44383	+	3.04722i	0.144101	+	0.0988130i
$952$		0			0
$953$			17.4015i			0.563691i	0.959460	+	0.281846i	$0.0909466\pi$
$953$			17.4015i			0.563691i	−0.959460	+	0.281846i	$0.909053\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−10.3033	−	0.799889i	−0.333058	−	0.0258567i
$958$		0			0
$959$	−6.40407	+	28.4221i	−0.206798	+	0.917796i
$960$		0			0
$961$	−12.6347	−	21.8840i	−0.407571	−	0.705934i
$962$		0			0
$963$	−2.30864	+	14.7791i	−0.0743949	+	0.476249i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	24.9154			0.801224			0.400612	−	0.916248i	$-0.368797\pi$
$967$	24.9154			0.801224			0.400612	+	0.916248i	$0.368797\pi$
$968$		0			0
$969$	5.49127	−	2.62635i	0.176405	−	0.0843707i
$970$		0			0
$971$	−9.45293	−	16.3730i	−0.303359	−	0.525433i	0.673536	−	0.739155i	$-0.264775\pi$
$971$	−9.45293	−	16.3730i	−0.303359	−	0.525433i	−0.976895	+	0.213722i	$0.931441\pi$
$972$		0			0
$973$	−52.0179	+	16.2039i	−1.66762	+	0.519474i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	35.0586	+	20.2411i	1.12163	+	0.647571i	0.941815	−	0.336131i	$-0.109118\pi$
$977$	35.0586	+	20.2411i	1.12163	+	0.647571i	0.179810	+	0.983701i	$0.442452\pi$
$978$		0			0
$979$			18.8540i			0.602578i
$980$		0			0
$981$	−5.18994	−	13.4350i	−0.165702	−	0.428946i
$982$		0			0
$983$	−27.1552	+	47.0341i	−0.866116	+	1.50016i	−0.000180339		1.00000i	$0.500057\pi$
$983$	−27.1552	+	47.0341i	−0.866116	+	1.50016i	−0.865935	+	0.500156i	$0.833276\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	54.4086	+	16.7768i	1.73184	+	0.534012i
$988$		0			0
$989$	−20.1739	+	11.6474i	−0.641493	+	0.370366i
$990$		0			0
$991$	30.8784	−	53.4830i	0.980886	−	1.69894i	0.321929	−	0.946764i	$-0.395669\pi$
$991$	30.8784	−	53.4830i	0.980886	−	1.69894i	0.658957	−	0.752181i	$-0.270998\pi$
$992$		0			0
$993$	0.274226	−	0.399910i	0.00870230	−	0.0126907i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	17.7948	+	10.2738i	0.563566	+	0.325375i	0.754576	−	0.656213i	$-0.227843\pi$
$997$	17.7948	+	10.2738i	0.563566	+	0.325375i	−0.191009	+	0.981588i	$0.561176\pi$
$998$		0			0
$999$	12.9736	+	43.2918i	0.410467	+	1.36969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.l.101.4	yes	16
3.2	odd	2	inner	2100.2.bi.l.101.1	✓	16
5.2	odd	4		2100.2.bo.i.1949.4		32
5.3	odd	4		2100.2.bo.i.1949.13		32
5.4	even	2		2100.2.bi.m.101.5	yes	16
7.5	odd	6	inner	2100.2.bi.l.1601.1	yes	16
15.2	even	4		2100.2.bo.i.1949.9		32
15.8	even	4		2100.2.bo.i.1949.8		32
15.14	odd	2		2100.2.bi.m.101.8	yes	16
21.5	even	6	inner	2100.2.bi.l.1601.4	yes	16
35.12	even	12		2100.2.bo.i.1349.8		32
35.19	odd	6		2100.2.bi.m.1601.8	yes	16
35.33	even	12		2100.2.bo.i.1349.9		32
105.47	odd	12		2100.2.bo.i.1349.13		32
105.68	odd	12		2100.2.bo.i.1349.4		32
105.89	even	6		2100.2.bi.m.1601.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.1	✓	16	3.2	odd	2	inner
2100.2.bi.l.101.4	yes	16	1.1	even	1	trivial
2100.2.bi.l.1601.1	yes	16	7.5	odd	6	inner
2100.2.bi.l.1601.4	yes	16	21.5	even	6	inner
2100.2.bi.m.101.5	yes	16	5.4	even	2
2100.2.bi.m.101.8	yes	16	15.14	odd	2
2100.2.bi.m.1601.5	yes	16	105.89	even	6
2100.2.bi.m.1601.8	yes	16	35.19	odd	6
2100.2.bo.i.1349.4		32	105.68	odd	12
2100.2.bo.i.1349.8		32	35.12	even	12
2100.2.bo.i.1349.9		32	35.33	even	12
2100.2.bo.i.1349.13		32	105.47	odd	12
2100.2.bo.i.1949.4		32	5.2	odd	4
2100.2.bo.i.1949.8		32	15.8	even	4
2100.2.bo.i.1949.9		32	15.2	even	4
2100.2.bo.i.1949.13		32	5.3	odd	4

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.747325 - 1.56253i) q^{3} +(0.786875 + 2.52603i) q^{7} +(-1.88301 + 2.33544i) q^{9} +O(q^{10})\)	\(q+(-0.747325 - 1.56253i) q^{3} +(0.786875 + 2.52603i) q^{7} +(-1.88301 + 2.33544i) q^{9} +(-2.34474 - 1.35373i) q^{11} +1.12489i q^{13} +(3.69121 - 6.39336i) q^{17} +(-0.412264 + 0.238021i) q^{19} +(3.35895 - 3.11728i) q^{21} +(-4.84706 + 2.79845i) q^{23} +(5.05642 + 1.19693i) q^{27} +2.20372i q^{29} +(-2.07315 - 1.19693i) q^{31} +(-0.362972 + 4.67541i) q^{33} +(4.34879 + 7.53233i) q^{37} +(1.75767 - 0.840655i) q^{39} -5.42336 q^{41} +4.16209 q^{43} +(6.21227 + 10.7600i) q^{47} +(-5.76166 + 3.97534i) q^{49} +(-12.7484 - 0.989712i) q^{51} +(4.25321 + 2.45559i) q^{53} +(0.680011 + 0.466297i) q^{57} +(-1.15586 + 2.00200i) q^{59} +(-2.26895 + 1.30998i) q^{61} +(-7.38108 - 2.91884i) q^{63} +(-7.34210 + 12.7169i) q^{67} +(7.99501 + 5.48234i) q^{69} +9.89729i q^{71} +(6.29046 + 3.63180i) q^{73} +(1.57456 - 6.98810i) q^{77} +(3.47478 + 6.01850i) q^{79} +(-1.90854 - 8.79531i) q^{81} +11.3005 q^{83} +(3.44338 - 1.64689i) q^{87} +(-3.48186 - 6.03075i) q^{89} +(-2.84150 + 0.885144i) q^{91} +(-0.320929 + 4.13385i) q^{93} +8.79691i q^{97} +(7.57673 - 2.92689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9} - 18 q^{19} - 11 q^{21} - 18 q^{31} - 12 q^{33} + 6 q^{37} + 12 q^{39} - 4 q^{43} - 18 q^{49} - q^{51} - 6 q^{57} + 36 q^{61} - 19 q^{63} - 30 q^{67} - 54 q^{73} + 7 q^{81} - 81 q^{87} + 20 q^{91} + 34 q^{93} - 30 q^{99}+O(q^{100}) \) 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9 - 18 * q^19 - 11 * q^21 - 18 * q^31 - 12 * q^33 + 6 * q^37 + 12 * q^39 - 4 * q^43 - 18 * q^49 - q^51 - 6 * q^57 + 36 * q^61 - 19 * q^63 - 30 * q^67 - 54 * q^73 + 7 * q^81 - 81 * q^87 + 20 * q^91 + 34 * q^93 - 30 * q^99

Introduction

L-functions

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