LMFDB - Embedded newform 2100.2.bi.l.1601.5

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			1601.5
Root			$-0.404332 + 1.68420i$ of defining polynomial
Character	$\chi$	$=$	2100.1601
Dual form			2100.2.bi.l.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.404332 + 1.68420i) q^{3} +(1.60761 + 2.10133i) q^{7} +(-2.67303 + 1.36195i) q^{9} +O(q^{10})$	\(q+(0.404332 + 1.68420i) q^{3} +(1.60761 + 2.10133i) q^{7} +(-2.67303 + 1.36195i) q^{9} +(-2.05856 + 1.18851i) q^{11} +0.748179i q^{13} +(-3.77242 - 6.53402i) q^{17} +(-6.11872 - 3.53264i) q^{19} +(-2.88904 + 3.55717i) q^{21} +(-2.83006 - 1.63394i) q^{23} +(-3.37458 - 3.95123i) q^{27} +2.48504i q^{29} +(-6.84372 + 3.95123i) q^{31} +(-2.83402 - 2.98646i) q^{33} +(-2.15905 + 3.73959i) q^{37} +(-1.26008 + 0.302513i) q^{39} +10.8663 q^{41} -3.03200 q^{43} +(3.22790 - 5.59088i) q^{47} +(-1.83117 + 6.75624i) q^{49} +(9.47926 - 8.99541i) q^{51} +(-0.0935472 + 0.0540095i) q^{53} +(3.47567 - 11.7335i) q^{57} +(-6.60248 - 11.4358i) q^{59} +(6.90005 + 3.98375i) q^{61} +(-7.15910 - 3.42743i) q^{63} +(-2.94367 - 5.09859i) q^{67} +(1.60758 - 5.42703i) q^{69} +13.9589i q^{71} +(-1.35221 + 0.780701i) q^{73} +(-5.80681 - 2.41505i) q^{77} +(-1.27644 + 2.21086i) q^{79} +(5.29018 - 7.28107i) q^{81} -0.901948 q^{83} +(-4.18529 + 1.00478i) q^{87} +(-2.43223 + 4.21274i) q^{89} +(-1.57217 + 1.20278i) q^{91} +(-9.42178 - 9.92856i) q^{93} +12.9183i q^{97} +(3.88390 - 5.98057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.404332	+	1.68420i	0.233441	+	0.972371i
$3$	0.404332	+	1.68420i	0.233441	+	0.972371i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.60761	+	2.10133i	0.607620	+	0.794228i
$7$	1.60761	+	2.10133i	0.607620	+	0.794228i
$8$		0			0
$9$	−2.67303	+	1.36195i	−0.891010	+	0.453983i
$10$		0			0
$11$	−2.05856	+	1.18851i	−0.620679	+	0.358349i	−0.777133	−	0.629336i	$-0.783327\pi$
$11$	−2.05856	+	1.18851i	−0.620679	+	0.358349i	0.156455	+	0.987685i	$0.449994\pi$
$12$		0			0
$13$			0.748179i			0.207508i	0.994603	+	0.103754i	$0.0330854\pi$
$13$			0.748179i			0.207508i	−0.994603	+	0.103754i	$0.966915\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.77242	−	6.53402i	−0.914946	−	1.58473i	−0.806980	−	0.590578i	$-0.798900\pi$
$17$	−3.77242	−	6.53402i	−0.914946	−	1.58473i	−0.107966	−	0.994155i	$-0.534434\pi$
$18$		0			0
$19$	−6.11872	−	3.53264i	−1.40373	−	0.810444i	−0.408957	−	0.912553i	$-0.634108\pi$
$19$	−6.11872	−	3.53264i	−1.40373	−	0.810444i	−0.994773	+	0.102109i	$0.967441\pi$
$20$		0			0
$21$	−2.88904	+	3.55717i	−0.630440	+	0.776238i
$22$		0			0
$23$	−2.83006	−	1.63394i	−0.590109	−	0.340699i	0.175032	−	0.984563i	$-0.443997\pi$
$23$	−2.83006	−	1.63394i	−0.590109	−	0.340699i	−0.765141	+	0.643863i	$0.777331\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.37458	−	3.95123i	−0.649439	−	0.760414i
$28$		0			0
$29$			2.48504i			0.461460i	0.973018	+	0.230730i	$0.0741114\pi$
$29$			2.48504i			0.461460i	−0.973018	+	0.230730i	$0.925889\pi$
$30$		0			0
$31$	−6.84372	+	3.95123i	−1.22917	+	0.709661i	−0.966856	−	0.255322i	$-0.917819\pi$
$31$	−6.84372	+	3.95123i	−1.22917	+	0.709661i	−0.262313	+	0.964983i	$0.584485\pi$
$32$		0			0
$33$	−2.83402	−	2.98646i	−0.493340	−	0.519876i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.15905	+	3.73959i	−0.354946	+	0.614784i	−0.987109	−	0.160051i	$-0.948834\pi$
$37$	−2.15905	+	3.73959i	−0.354946	+	0.614784i	0.632163	+	0.774835i	$0.282167\pi$
$38$		0			0
$39$	−1.26008	+	0.302513i	−0.201774	+	0.0484409i
$40$		0			0
$41$	10.8663			1.69703			0.848514	−	0.529173i	$-0.177498\pi$
$41$	10.8663			1.69703			0.848514	+	0.529173i	$0.177498\pi$
$42$		0			0
$43$	−3.03200			−0.462375			−0.231188	−	0.972909i	$-0.574261\pi$
$43$	−3.03200			−0.462375			−0.231188	+	0.972909i	$0.574261\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.22790	−	5.59088i	0.470837	−	0.815514i	−0.528606	−	0.848867i	$-0.677285\pi$
$47$	3.22790	−	5.59088i	0.470837	−	0.815514i	0.999444	+	0.0333530i	$0.0106186\pi$
$48$		0			0
$49$	−1.83117	+	6.75624i	−0.261596	+	0.965178i
$50$		0			0
$51$	9.47926	−	8.99541i	1.32736	−	1.25961i
$52$		0			0
$53$	−0.0935472	+	0.0540095i	−0.0128497	+	0.00741878i	−0.506411	−	0.862292i	$-0.669028\pi$
$53$	−0.0935472	+	0.0540095i	−0.0128497	+	0.00741878i	0.493561	+	0.869711i	$0.335695\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.47567	−	11.7335i	0.460363	−	1.55414i
$58$		0			0
$59$	−6.60248	−	11.4358i	−0.859570	−	1.48882i	−0.872340	−	0.488900i	$-0.837398\pi$
$59$	−6.60248	−	11.4358i	−0.859570	−	1.48882i	0.0127699	−	0.999918i	$-0.495935\pi$
$60$		0			0
$61$	6.90005	+	3.98375i	0.883461	+	0.510067i	0.871798	−	0.489865i	$-0.162954\pi$
$61$	6.90005	+	3.98375i	0.883461	+	0.510067i	0.0116632	+	0.999932i	$0.496287\pi$
$62$		0			0
$63$	−7.15910	−	3.42743i	−0.901962	−	0.431816i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.94367	−	5.09859i	−0.359627	−	0.622892i	0.628272	−	0.777994i	$-0.283763\pi$
$67$	−2.94367	−	5.09859i	−0.359627	−	0.622892i	−0.987898	+	0.155102i	$0.950429\pi$
$68$		0			0
$69$	1.60758	−	5.42703i	0.193530	−	0.653338i
$70$		0			0
$71$			13.9589i			1.65662i	0.560273	+	0.828308i	$0.310696\pi$
$71$			13.9589i			1.65662i	−0.560273	+	0.828308i	$0.689304\pi$
$72$		0			0
$73$	−1.35221	+	0.780701i	−0.158265	+	0.0913742i	−0.577041	−	0.816715i	$-0.695793\pi$
$73$	−1.35221	+	0.780701i	−0.158265	+	0.0913742i	0.418776	+	0.908090i	$0.362459\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.80681	−	2.41505i	−0.661747	−	0.275220i
$78$		0			0
$79$	−1.27644	+	2.21086i	−0.143611	+	0.248742i	−0.928854	−	0.370446i	$-0.879205\pi$
$79$	−1.27644	+	2.21086i	−0.143611	+	0.248742i	0.785243	+	0.619188i	$0.212538\pi$
$80$		0			0
$81$	5.29018	−	7.28107i	0.587798	−	0.809008i
$82$		0			0
$83$	−0.901948			−0.0990016			−0.0495008	−	0.998774i	$-0.515763\pi$
$83$	−0.901948			−0.0990016			−0.0495008	+	0.998774i	$0.515763\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.18529	+	1.00478i	−0.448710	+	0.107724i
$88$		0			0
$89$	−2.43223	+	4.21274i	−0.257816	+	0.446550i	−0.965656	−	0.259822i	$-0.916336\pi$
$89$	−2.43223	+	4.21274i	−0.257816	+	0.446550i	0.707841	+	0.706372i	$0.249669\pi$
$90$		0			0
$91$	−1.57217	+	1.20278i	−0.164808	+	0.126086i
$92$		0			0
$93$	−9.42178	−	9.92856i	−0.976993	−	1.02954i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			12.9183i			1.31166i	0.754909	+	0.655829i	$0.227681\pi$
$97$			12.9183i			1.31166i	−0.754909	+	0.655829i	$0.772319\pi$
$98$		0			0
$99$	3.88390	−	5.98057i	0.390346	−	0.601070i
$100$		0			0
$101$	1.56718	+	2.71443i	0.155940	+	0.270096i	0.933401	−	0.358835i	$-0.116826\pi$
$101$	1.56718	+	2.71443i	0.155940	+	0.270096i	−0.777461	+	0.628931i	$0.783493\pi$
$102$		0			0
$103$	13.6667	+	7.89048i	1.34662	+	0.777472i	0.987769	−	0.155922i	$-0.0498349\pi$
$103$	13.6667	+	7.89048i	1.34662	+	0.777472i	0.358852	+	0.933394i	$0.383168\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.9952	−	6.92544i	−1.15962	−	0.669508i	−0.208408	−	0.978042i	$-0.566828\pi$
$107$	−11.9952	−	6.92544i	−1.15962	−	0.669508i	−0.951213	+	0.308534i	$0.900161\pi$
$108$		0			0
$109$	0.863166	+	1.49505i	0.0826763	+	0.143200i	0.904399	−	0.426688i	$-0.140320\pi$
$109$	0.863166	+	1.49505i	0.0826763	+	0.143200i	−0.821722	+	0.569888i	$0.806987\pi$
$110$		0			0
$111$	−7.17117	−	2.12423i	−0.680657	−	0.201623i
$112$		0			0
$113$		−	4.93811i		−	0.464539i	−0.972652	−	0.232269i	$-0.925385\pi$
$113$		−	4.93811i		−	0.464539i	0.972652	−	0.232269i	$-0.0746151\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.01898	−	1.99991i	−0.0942050	−	0.184891i
$118$		0			0
$119$	7.66554	−	18.4313i	0.702699	−	1.68959i
$120$		0			0
$121$	−2.67489	+	4.63305i	−0.243172	+	0.421186i
$122$		0			0
$123$	4.39359	+	18.3009i	0.396157	+	1.65014i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−15.9416			−1.41458			−0.707292	−	0.706921i	$-0.750083\pi$
$127$	−15.9416			−1.41458			−0.707292	+	0.706921i	$0.750083\pi$
$128$		0			0
$129$	−1.22593	−	5.10648i	−0.107938	−	0.449600i
$130$		0			0
$131$	−4.17025	+	7.22309i	−0.364357	+	0.631084i	−0.988673	−	0.150087i	$-0.952044\pi$
$131$	−4.17025	+	7.22309i	−0.364357	+	0.631084i	0.624316	+	0.781172i	$0.285378\pi$
$132$		0			0
$133$	−2.41328	−	18.5366i	−0.209258	−	1.60732i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.94718	−	4.01096i	0.593537	−	0.342679i	−0.172958	−	0.984929i	$-0.555332\pi$
$137$	6.94718	−	4.01096i	0.593537	−	0.342679i	0.766495	+	0.642250i	$0.221999\pi$
$138$		0			0
$139$			4.61654i			0.391570i	0.980647	+	0.195785i	$0.0627254\pi$
$139$			4.61654i			0.391570i	−0.980647	+	0.195785i	$0.937275\pi$
$140$		0			0
$141$	10.7213	+	3.17584i	0.902895	+	0.267454i
$142$		0			0
$143$	−0.889218	−	1.54017i	−0.0743601	−	0.128796i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−12.1192	−	0.352278i	−0.999578	−	0.0290554i
$148$		0			0
$149$	−15.6215	−	9.01906i	−1.27976	−	0.738870i	−0.302956	−	0.953004i	$-0.597974\pi$
$149$	−15.6215	−	9.01906i	−1.27976	−	0.738870i	−0.976804	+	0.214134i	$0.931307\pi$
$150$		0			0
$151$	2.12850	+	3.68667i	0.173215	+	0.300017i	0.939542	−	0.342434i	$-0.111251\pi$
$151$	2.12850	+	3.68667i	0.173215	+	0.300017i	−0.766327	+	0.642451i	$0.777918\pi$
$152$		0			0
$153$	18.9828	+	12.3278i	1.53467	+	0.996643i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−14.4250	+	8.32830i	−1.15124	+	0.664671i	−0.949190	−	0.314703i	$-0.898095\pi$
$157$	−14.4250	+	8.32830i	−1.15124	+	0.664671i	−0.202054	+	0.979374i	$0.564762\pi$
$158$		0			0
$159$	−0.128787	−	0.135714i	−0.0102135	−	0.0107628i
$160$		0			0
$161$	−1.11620	−	8.57363i	−0.0879690	−	0.675697i
$162$		0			0
$163$	8.07999	−	13.9950i	0.632874	−	1.09617i	−0.354087	−	0.935212i	$-0.615208\pi$
$163$	8.07999	−	13.9950i	0.632874	−	1.09617i	0.986961	−	0.160957i	$-0.0514582\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.4029			−1.34668			−0.673338	−	0.739335i	$-0.735140\pi$
$167$	−17.4029			−1.34668			−0.673338	+	0.739335i	$0.735140\pi$
$168$		0			0
$169$	12.4402			0.956941
$170$		0			0
$171$	21.1668	+	1.10948i	1.61867	+	0.0848438i
$172$		0			0
$173$	9.83038	−	17.0267i	0.747390	−	1.29452i	−0.201680	−	0.979451i	$-0.564640\pi$
$173$	9.83038	−	17.0267i	0.747390	−	1.29452i	0.949070	−	0.315066i	$-0.102027\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	16.5906	−	15.7437i	1.24702	−	1.18337i
$178$		0			0
$179$	−5.84722	+	3.37589i	−0.437042	+	0.252326i	−0.702342	−	0.711840i	$-0.747862\pi$
$179$	−5.84722	+	3.37589i	−0.437042	+	0.252326i	0.265300	+	0.964166i	$0.414529\pi$
$180$		0			0
$181$			7.71256i			0.573270i	0.958040	+	0.286635i	$0.0925367\pi$
$181$			7.71256i			0.573270i	−0.958040	+	0.286635i	$0.907463\pi$
$182$		0			0
$183$	−3.91950	+	13.2318i	−0.289737	+	0.978123i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	15.5315	+	8.96711i	1.13577	+	0.655740i
$188$		0			0
$189$	2.87781	−	13.4431i	0.209330	−	0.977845i
$190$		0			0
$191$	−12.7009	−	7.33284i	−0.919001	−	0.530586i	−0.0356850	−	0.999363i	$-0.511361\pi$
$191$	−12.7009	−	7.33284i	−0.919001	−	0.530586i	−0.883316	+	0.468777i	$0.844695\pi$
$192$		0			0
$193$	−5.32299	−	9.21969i	−0.383157	−	0.663648i	0.608354	−	0.793666i	$-0.291830\pi$
$193$	−5.32299	−	9.21969i	−0.383157	−	0.663648i	−0.991512	+	0.130018i	$0.958497\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	7.53462i		−	0.536820i	−0.963305	−	0.268410i	$-0.913502\pi$
$197$		−	7.53462i		−	0.536820i	0.963305	−	0.268410i	$-0.0864982\pi$
$198$		0			0
$199$	0.993782	−	0.573760i	0.0704473	−	0.0406728i	−0.464363	−	0.885645i	$-0.653717\pi$
$199$	0.993782	−	0.573760i	0.0704473	−	0.0406728i	0.534810	+	0.844972i	$0.320383\pi$
$200$		0			0
$201$	7.39680	−	7.01924i	0.521730	−	0.495099i
$202$		0			0
$203$	−5.22188	+	3.99497i	−0.366504	+	0.280392i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	9.79018	+	0.513161i	0.680465	+	0.0356671i
$208$		0			0
$209$	16.7943			1.16169
$210$		0			0
$211$	−11.1248			−0.765862			−0.382931	−	0.923777i	$-0.625085\pi$
$211$	−11.1248			−0.765862			−0.382931	+	0.923777i	$0.625085\pi$
$212$		0			0
$213$	−23.5095	+	5.64404i	−1.61085	+	0.386723i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−19.3049	−	8.02888i	−1.31050	−	0.545036i
$218$		0			0
$219$	−1.86160	−	1.96173i	−0.125795	−	0.132561i
$220$		0			0
$221$	4.88862	−	2.82245i	0.328844	−	0.189858i
$222$		0			0
$223$		−	10.6904i		−	0.715883i	−0.933744	−	0.357942i	$-0.883479\pi$
$223$		−	10.6904i		−	0.715883i	0.933744	−	0.357942i	$-0.116521\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.69603	+	11.5979i	0.444431	+	0.769777i	0.998012	−	0.0630180i	$-0.0200725\pi$
$227$	6.69603	+	11.5979i	0.444431	+	0.769777i	−0.553581	+	0.832795i	$0.686739\pi$
$228$		0			0
$229$	8.32905	+	4.80878i	0.550399	+	0.317773i	0.749283	−	0.662250i	$-0.230398\pi$
$229$	8.32905	+	4.80878i	0.550399	+	0.317773i	−0.198884	+	0.980023i	$0.563732\pi$
$230$		0			0
$231$	1.71953	−	10.7563i	0.113137	−	0.707712i
$232$		0			0
$233$	−18.5481	−	10.7087i	−1.21512	−	0.701552i	−0.251253	−	0.967921i	$-0.580843\pi$
$233$	−18.5481	−	10.7087i	−1.21512	−	0.701552i	−0.963871	+	0.266369i	$0.914176\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.23964	−	1.25586i	−0.275394	−	0.0815766i
$238$		0			0
$239$			25.2806i			1.63527i	0.575738	+	0.817634i	$0.304715\pi$
$239$			25.2806i			1.63527i	−0.575738	+	0.817634i	$0.695285\pi$
$240$		0			0
$241$	−19.7291	+	11.3906i	−1.27086	+	0.733733i	−0.975150	−	0.221543i	$-0.928891\pi$
$241$	−19.7291	+	11.3906i	−1.27086	+	0.733733i	−0.295713	+	0.955277i	$0.595557\pi$
$242$		0			0
$243$	14.4017	+	5.96573i	0.923872	+	0.382702i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.64305	−	4.57790i	0.168173	−	0.291285i
$248$		0			0
$249$	−0.364687	−	1.51906i	−0.0231111	−	0.0962663i
$250$		0			0
$251$	16.4201			1.03643			0.518215	−	0.855251i	$-0.326597\pi$
$251$	16.4201			1.03643			0.518215	+	0.855251i	$0.326597\pi$
$252$		0			0
$253$	7.76780			0.488357
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.92452	−	10.2616i	0.369562	−	0.640100i	−0.619935	−	0.784653i	$-0.712841\pi$
$257$	5.92452	−	10.2616i	0.369562	−	0.640100i	0.989497	+	0.144553i	$0.0461745\pi$
$258$		0			0
$259$	−11.3290	+	1.47493i	−0.703951	+	0.0916474i
$260$		0			0
$261$	−3.38450	−	6.64258i	−0.209495	−	0.411165i
$262$		0			0
$263$	−4.79507	+	2.76844i	−0.295677	+	0.170709i	−0.640499	−	0.767959i	$-0.721273\pi$
$263$	−4.79507	+	2.76844i	−0.295677	+	0.170709i	0.344822	+	0.938668i	$0.387939\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−8.07851	−	2.39300i	−0.494397	−	0.146449i
$268$		0			0
$269$	0.504112	+	0.873148i	0.0307363	+	0.0532368i	0.880984	−	0.473145i	$-0.156881\pi$
$269$	0.504112	+	0.873148i	0.0307363	+	0.0532368i	−0.850248	+	0.526382i	$0.823548\pi$
$270$		0			0
$271$	0.991979	+	0.572720i	0.0602585	+	0.0347902i	0.529827	−	0.848106i	$-0.322257\pi$
$271$	0.991979	+	0.572720i	0.0602585	+	0.0347902i	−0.469568	+	0.882896i	$0.655590\pi$
$272$		0			0
$273$	−2.66140	−	2.16152i	−0.161075	−	0.130821i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.66672	+	8.08299i	0.280396	+	0.485660i	0.971482	−	0.237112i	$-0.0762010\pi$
$277$	4.66672	+	8.08299i	0.280396	+	0.485660i	−0.691086	+	0.722772i	$0.742868\pi$
$278$		0			0
$279$	12.9121	−	19.8826i	0.773028	−	1.19034i
$280$		0			0
$281$			0.922818i			0.0550507i	0.999621	+	0.0275253i	$0.00876270\pi$
$281$			0.922818i			0.0550507i	−0.999621	+	0.0275253i	$0.991237\pi$
$282$		0			0
$283$	−6.54162	+	3.77681i	−0.388859	+	0.224508i	−0.681666	−	0.731664i	$-0.738744\pi$
$283$	−6.54162	+	3.77681i	−0.388859	+	0.224508i	0.292807	+	0.956172i	$0.405411\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	17.4688	+	22.8336i	1.03115	+	1.34783i
$288$		0			0
$289$	−19.9623	+	34.5757i	−1.17425	+	2.03386i
$290$		0			0
$291$	−21.7570	+	5.22330i	−1.27542	+	0.306195i
$292$		0			0
$293$	21.3909			1.24967			0.624834	−	0.780758i	$-0.285167\pi$
$293$	21.3909			1.24967			0.624834	+	0.780758i	$0.285167\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	11.6428	+	4.12310i	0.675586	+	0.239247i
$298$		0			0
$299$	1.22248	−	2.11739i	0.0706977	−	0.122452i
$300$		0			0
$301$	−4.87427	−	6.37122i	−0.280949	−	0.367231i
$302$		0			0
$303$	−3.93797	+	3.73696i	−0.226230	+	0.214683i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			16.7500i			0.955972i	0.878368	+	0.477986i	$0.158633\pi$
$307$			16.7500i			0.955972i	−0.878368	+	0.477986i	$0.841367\pi$
$308$		0			0
$309$	−7.76322	+	26.2078i	−0.441634	+	1.49091i
$310$		0			0
$311$	2.52577	+	4.37477i	0.143224	+	0.248070i	0.928709	−	0.370810i	$-0.120920\pi$
$311$	2.52577	+	4.37477i	0.143224	+	0.248070i	−0.785485	+	0.618880i	$0.787587\pi$
$312$		0			0
$313$	12.9998	+	7.50546i	0.734795	+	0.424234i	0.820174	−	0.572115i	$-0.193877\pi$
$313$	12.9998	+	7.50546i	0.734795	+	0.424234i	−0.0853790	+	0.996349i	$0.527210\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.0531	+	12.7324i	1.23863	+	0.715121i	0.968813	−	0.247792i	$-0.0797051\pi$
$317$	22.0531	+	12.7324i	1.23863	+	0.715121i	0.269812	+	0.962913i	$0.413038\pi$
$318$		0			0
$319$	−2.95349	−	5.11559i	−0.165364	−	0.286418i
$320$		0			0
$321$	6.81374	−	23.0025i	0.380306	−	1.28387i
$322$		0			0
$323$			53.3065i			2.96605i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.16895	+	2.05824i	−0.119943	+	0.113821i
$328$		0			0
$329$	16.9375	−	2.20509i	0.933794	−	0.121571i
$330$		0			0
$331$	−5.45134	+	9.44199i	−0.299633	+	0.518979i	−0.976052	−	0.217538i	$-0.930197\pi$
$331$	−5.45134	+	9.44199i	−0.299633	+	0.518979i	0.676419	+	0.736517i	$0.263531\pi$
$332$		0			0
$333$	0.678080	−	12.9365i	0.0371585	−	0.708918i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	18.4210			1.00345			0.501727	−	0.865026i	$-0.332698\pi$
$337$	18.4210			1.00345			0.501727	+	0.865026i	$0.332698\pi$
$338$		0			0
$339$	8.31675	−	1.99664i	0.451704	−	0.108443i
$340$		0			0
$341$	9.39213	−	16.2677i	0.508613	−	0.880943i
$342$		0			0
$343$	−17.1409	+	7.01353i	−0.925522	+	0.378695i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.30010	+	4.79206i	−0.445573	+	0.257252i	−0.705959	−	0.708253i	$-0.749484\pi$
$347$	−8.30010	+	4.79206i	−0.445573	+	0.257252i	0.260386	+	0.965505i	$0.416150\pi$
$348$		0			0
$349$		−	16.5601i		−	0.886441i	−0.896413	−	0.443220i	$-0.853836\pi$
$349$		−	16.5601i		−	0.886441i	0.896413	−	0.443220i	$-0.146164\pi$
$350$		0			0
$351$	2.95623	−	2.52479i	0.157792	−	0.134764i
$352$		0			0
$353$	9.00574	+	15.5984i	0.479327	+	0.830219i	0.999719	−	0.0237089i	$-0.00754747\pi$
$353$	9.00574	+	15.5984i	0.479327	+	0.830219i	−0.520392	+	0.853928i	$0.674214\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	34.1413	+	5.45792i	1.80695	+	0.288864i
$358$		0			0
$359$	3.47735	+	2.00765i	0.183527	+	0.105960i	0.588949	−	0.808170i	$-0.299542\pi$
$359$	3.47735	+	2.00765i	0.183527	+	0.105960i	−0.405422	+	0.914130i	$0.632875\pi$
$360$		0			0
$361$	15.4592	+	26.7760i	0.813640	+	1.40927i
$362$		0			0
$363$	−8.88451	−	2.63175i	−0.466316	−	0.138131i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	29.4897	−	17.0259i	1.53935	−	0.888744i	0.540473	−	0.841361i	$-0.318245\pi$
$367$	29.4897	−	17.0259i	1.53935	−	0.888744i	0.998877	−	0.0473832i	$-0.0150882\pi$
$368$		0			0
$369$	−29.0459	+	14.7993i	−1.51207	+	0.770423i
$370$		0			0
$371$	−0.263879	−	0.109747i	−0.0136999	−	0.00569779i
$372$		0			0
$373$	6.70705	−	11.6169i	0.347278	−	0.601503i	−0.638487	−	0.769632i	$-0.720439\pi$
$373$	6.70705	−	11.6169i	0.347278	−	0.601503i	0.985765	+	0.168130i	$0.0537728\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.85925			−0.0957564
$378$		0			0
$379$	−15.3945			−0.790764			−0.395382	−	0.918517i	$-0.629388\pi$
$379$	−15.3945			−0.790764			−0.395382	+	0.918517i	$0.629388\pi$
$380$		0			0
$381$	−6.44569	−	26.8487i	−0.330223	−	1.37550i
$382$		0			0
$383$	−12.2065	+	21.1422i	−0.623722	+	1.08032i	0.365065	+	0.930982i	$0.381047\pi$
$383$	−12.2065	+	21.1422i	−0.623722	+	1.08032i	−0.988787	+	0.149336i	$0.952287\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.10462	−	4.12943i	0.411981	−	0.209911i
$388$		0			0
$389$	−30.1938	+	17.4324i	−1.53089	+	0.883857i	−0.531564	+	0.847018i	$0.678396\pi$
$389$	−30.1938	+	17.4324i	−1.53089	+	0.883857i	−0.999321	+	0.0368391i	$0.988271\pi$
$390$		0			0
$391$			24.6556i			1.24689i
$392$		0			0
$393$	−13.8513	−	4.10299i	−0.698704	−	0.206969i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−19.5083	−	11.2631i	−0.979095	−	0.565281i	−0.0770980	−	0.997024i	$-0.524565\pi$
$397$	−19.5083	−	11.2631i	−0.979095	−	0.565281i	−0.901997	+	0.431743i	$0.857899\pi$
$398$		0			0
$399$	30.2434	−	11.5594i	1.51407	−	0.578692i
$400$		0			0
$401$	−15.8774	−	9.16683i	−0.792881	−	0.457770i	0.0480950	−	0.998843i	$-0.484685\pi$
$401$	−15.8774	−	9.16683i	−0.792881	−	0.457770i	−0.840976	+	0.541073i	$0.818018\pi$
$402$		0			0
$403$	−2.95623	−	5.12033i	−0.147260	−	0.255062i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	10.2642i		−	0.508778i
$408$		0			0
$409$	9.37130	−	5.41052i	0.463381	−	0.267533i	−0.250084	−	0.968224i	$-0.580458\pi$
$409$	9.37130	−	5.41052i	0.463381	−	0.267533i	0.713465	+	0.700691i	$0.247125\pi$
$410$		0			0
$411$	9.56420	+	10.0786i	0.471767	+	0.497143i
$412$		0			0
$413$	13.4162	−	32.2584i	0.660169	−	1.58733i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−7.77516	+	1.86662i	−0.380751	+	0.0914086i
$418$		0			0
$419$	34.1164			1.66670			0.833348	−	0.552749i	$-0.186421\pi$
$419$	34.1164			1.66670			0.833348	+	0.552749i	$0.186421\pi$
$420$		0			0
$421$	−29.9892			−1.46158			−0.730792	−	0.682600i	$-0.760849\pi$
$421$	−29.9892			−1.46158			−0.730792	+	0.682600i	$0.760849\pi$
$422$		0			0
$423$	−1.01377	+	19.3408i	−0.0492910	+	0.940384i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.72144	+	20.9036i	0.131700	+	1.01160i
$428$		0			0
$429$	2.23441	−	2.12036i	0.107878	−	0.102372i
$430$		0			0
$431$	−32.6954	+	18.8767i	−1.57488	+	0.909258i	−0.579324	+	0.815097i	$0.696684\pi$
$431$	−32.6954	+	18.8767i	−1.57488	+	0.909258i	−0.995557	+	0.0941612i	$0.969983\pi$
$432$		0			0
$433$			0.221375i			0.0106386i	0.999986	+	0.00531930i	$0.00169319\pi$
$433$			0.221375i			0.0106386i	−0.999986	+	0.00531930i	$0.998307\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.5442	+	19.9952i	0.552236	+	0.956501i
$438$		0			0
$439$	−12.5292	−	7.23374i	−0.597987	−	0.345248i	0.170262	−	0.985399i	$-0.445538\pi$
$439$	−12.5292	−	7.23374i	−0.597987	−	0.345248i	−0.768249	+	0.640151i	$0.778872\pi$
$440$		0			0
$441$	−4.30690	−	20.5536i	−0.205090	−	0.978743i
$442$		0			0
$443$	−9.61783	−	5.55285i	−0.456957	−	0.263824i	0.253807	−	0.967255i	$-0.418317\pi$
$443$	−9.61783	−	5.55285i	−0.456957	−	0.263824i	−0.710764	+	0.703431i	$0.751651\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.87359	−	29.9563i	0.419707	−	1.41688i
$448$		0			0
$449$			31.1416i			1.46966i	0.678250	+	0.734831i	$0.262739\pi$
$449$			31.1416i			1.46966i	−0.678250	+	0.734831i	$0.737261\pi$
$450$		0			0
$451$	−22.3689	+	12.9147i	−1.05331	+	0.608128i
$452$		0			0
$453$	−5.34845	+	5.07545i	−0.251292	+	0.238466i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.47844	+	16.4171i	−0.443383	+	0.767962i	−0.997938	−	0.0641853i	$-0.979555\pi$
$457$	−9.47844	+	16.4171i	−0.443383	+	0.767962i	0.554555	+	0.832147i	$0.312888\pi$
$458$		0			0
$459$	−13.0871	+	36.9553i	−0.610851	+	1.72492i
$460$		0			0
$461$	−15.1960			−0.707746			−0.353873	−	0.935293i	$-0.615136\pi$
$461$	−15.1960			−0.707746			−0.353873	+	0.935293i	$0.615136\pi$
$462$		0			0
$463$	29.3400			1.36355			0.681773	−	0.731564i	$-0.261209\pi$
$463$	29.3400			1.36355			0.681773	+	0.731564i	$0.261209\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.39365	+	14.5382i	−0.388412	+	0.672749i	−0.992236	−	0.124369i	$-0.960309\pi$
$467$	−8.39365	+	14.5382i	−0.388412	+	0.672749i	0.603824	+	0.797117i	$0.293643\pi$
$468$		0			0
$469$	5.98153	−	14.3822i	0.276201	−	0.664107i
$470$		0			0
$471$	−19.8590	−	20.9272i	−0.915055	−	0.964274i
$472$		0			0
$473$	6.24154	−	3.60356i	0.286986	−	0.165692i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.176496	−	0.271776i	0.00808121	−	0.0124438i
$478$		0			0
$479$	1.07579	+	1.86333i	0.0491542	+	0.0851376i	0.889556	−	0.456827i	$-0.151014\pi$
$479$	1.07579	+	1.86333i	0.0491542	+	0.0851376i	−0.840401	+	0.541964i	$0.817681\pi$
$480$		0			0
$481$	−2.79788	−	1.61536i	−0.127572	−	0.0736540i
$482$		0			0
$483$	13.9884	−	5.34650i	0.636492	−	0.243274i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.74460	−	3.02174i	−0.0790555	−	0.136928i	0.823787	−	0.566899i	$-0.191857\pi$
$487$	−1.74460	−	3.02174i	−0.0790555	−	0.136928i	−0.902843	+	0.429971i	$0.858524\pi$
$488$		0			0
$489$	26.8373	+	7.94967i	1.21362	+	0.359497i
$490$		0			0
$491$		−	26.1361i		−	1.17950i	−0.807584	−	0.589752i	$-0.799225\pi$
$491$		−	26.1361i		−	1.17950i	0.807584	−	0.589752i	$-0.200775\pi$
$492$		0			0
$493$	16.2373	−	9.37460i	0.731290	−	0.422211i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−29.3322	+	22.4405i	−1.31573	+	1.00659i
$498$		0			0
$499$	−7.15545	+	12.3936i	−0.320322	+	0.554814i	−0.980554	−	0.196247i	$-0.937124\pi$
$499$	−7.15545	+	12.3936i	−0.320322	+	0.554814i	0.660232	+	0.751061i	$0.270458\pi$
$500$		0			0
$501$	−7.03656	−	29.3099i	−0.314370	−	1.30947i
$502$		0			0
$503$	39.3226			1.75331			0.876653	−	0.481123i	$-0.159771\pi$
$503$	39.3226			1.75331			0.876653	+	0.481123i	$0.159771\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.02999	+	20.9518i	0.223390	+	0.930501i
$508$		0			0
$509$	−17.4284	+	30.1868i	−0.772498	+	1.33801i	0.163692	+	0.986512i	$0.447660\pi$
$509$	−17.4284	+	30.1868i	−0.772498	+	1.33801i	−0.936190	+	0.351495i	$0.885674\pi$
$510$		0			0
$511$	−3.81435	−	1.58638i	−0.168737	−	0.0701774i
$512$		0			0
$513$	6.68985	+	36.0977i	0.295364	+	1.59375i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			15.3455i			0.674896i
$518$		0			0
$519$	32.6511	+	9.67183i	1.43322	+	0.424546i
$520$		0			0
$521$	−12.3030	−	21.3094i	−0.539005	−	0.933584i	−0.998958	−	0.0456406i	$-0.985467\pi$
$521$	−12.3030	−	21.3094i	−0.539005	−	0.933584i	0.459953	−	0.887943i	$-0.347866\pi$
$522$		0			0
$523$	−23.9603	−	13.8335i	−1.04771	−	0.604897i	−0.125704	−	0.992068i	$-0.540119\pi$
$523$	−23.9603	−	13.8335i	−1.04771	−	0.604897i	−0.922008	+	0.387171i	$0.873452\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	51.6348	+	29.8114i	2.24925	+	1.29860i
$528$		0			0
$529$	−6.16050	−	10.6703i	−0.267848	−	0.463926i
$530$		0			0
$531$	33.2237	+	21.5761i	1.44178	+	0.936322i
$532$		0			0
$533$			8.12993i			0.352146i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.04989	−	8.48288i	−0.347378	−	0.366063i
$538$		0			0
$539$	−4.26029	−	16.0845i	−0.183504	−	0.692808i
$540$		0			0
$541$	7.90334	−	13.6890i	0.339791	−	0.588536i	−0.644602	−	0.764518i	$-0.722977\pi$
$541$	7.90334	−	13.6890i	0.339791	−	0.588536i	0.984393	+	0.175983i	$0.0563103\pi$
$542$		0			0
$543$	−12.9895	+	3.11844i	−0.557431	+	0.133825i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−13.9288			−0.595553			−0.297776	−	0.954636i	$-0.596245\pi$
$547$	−13.9288			−0.595553			−0.297776	+	0.954636i	$0.596245\pi$
$548$		0			0
$549$	−23.8697	−	1.25115i	−1.01873	−	0.0533978i
$550$		0			0
$551$	8.77875	−	15.2052i	0.373987	−	0.647765i
$552$		0			0
$553$	−6.69778	+	0.871984i	−0.284818	+	0.0370805i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	29.9559	−	17.2950i	1.26927	−	0.732814i	0.294421	−	0.955676i	$-0.404873\pi$
$557$	29.9559	−	17.2950i	1.26927	−	0.732814i	0.974850	+	0.222862i	$0.0715398\pi$
$558$		0			0
$559$		−	2.26848i		−	0.0959464i
$560$		0			0
$561$	−8.82248	+	29.7838i	−0.372485	+	1.25747i
$562$		0			0
$563$	−14.4793	−	25.0789i	−0.610229	−	1.05695i	−0.991202	−	0.132361i	$-0.957744\pi$
$563$	−14.4793	−	25.0789i	−0.610229	−	1.05695i	0.380972	−	0.924586i	$-0.375589\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	23.8045	−	0.588712i	0.999694	−	0.0247236i
$568$		0			0
$569$	−10.1544	−	5.86266i	−0.425696	−	0.245775i	0.271816	−	0.962349i	$-0.412376\pi$
$569$	−10.1544	−	5.86266i	−0.425696	−	0.245775i	−0.697511	+	0.716574i	$0.745709\pi$
$570$		0			0
$571$	17.5541	+	30.4045i	0.734614	+	1.27239i	0.954892	+	0.296952i	$0.0959703\pi$
$571$	17.5541	+	30.4045i	0.734614	+	1.27239i	−0.220278	+	0.975437i	$0.570696\pi$
$572$		0			0
$573$	7.21457	−	24.3556i	0.301393	−	1.01747i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	17.3937	−	10.0423i	0.724110	−	0.418065i	−0.0921536	−	0.995745i	$-0.529375\pi$
$577$	17.3937	−	10.0423i	0.724110	−	0.418065i	0.816263	+	0.577680i	$0.196042\pi$
$578$		0			0
$579$	13.3755	−	12.6928i	0.555867	−	0.527494i
$580$		0			0
$581$	−1.44998	−	1.89529i	−0.0601554	−	0.0786298i
$582$		0			0
$583$	0.128382	−	0.222363i	0.00531702	−	0.00920935i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−32.7111			−1.35013			−0.675066	−	0.737757i	$-0.735885\pi$
$587$	−32.7111			−1.35013			−0.675066	+	0.737757i	$0.735885\pi$
$588$		0			0
$589$	55.8331			2.30056
$590$		0			0
$591$	12.6898	−	3.04649i	0.521988	−	0.125316i
$592$		0			0
$593$	−2.23240	+	3.86664i	−0.0916738	+	0.158784i	−0.908216	−	0.418503i	$-0.862555\pi$
$593$	−2.23240	+	3.86664i	−0.0916738	+	0.158784i	0.816542	+	0.577286i	$0.195888\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.36814	+	1.44173i	0.0559944	+	0.0590062i
$598$		0			0
$599$	31.6126	−	18.2515i	1.29165	−	0.745737i	0.312707	−	0.949850i	$-0.398764\pi$
$599$	31.6126	−	18.2515i	1.29165	−	0.745737i	0.978947	+	0.204112i	$0.0654308\pi$
$600$		0			0
$601$		−	32.4566i		−	1.32393i	−0.749534	−	0.661966i	$-0.769722\pi$
$601$		−	32.4566i		−	1.32393i	0.749534	−	0.661966i	$-0.230278\pi$
$602$		0			0
$603$	14.8125	+	9.61955i	0.603213	+	0.391738i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	18.1187	+	10.4608i	0.735416	+	0.424593i	0.820400	−	0.571790i	$-0.193751\pi$
$607$	18.1187	+	10.4608i	0.735416	+	0.424593i	−0.0849841	+	0.996382i	$0.527084\pi$
$608$		0			0
$609$	−8.83970	−	7.17937i	−0.358203	−	0.290923i
$610$		0			0
$611$	4.18298	+	2.41505i	0.169225	+	0.0977023i
$612$		0			0
$613$	19.4442	+	33.6783i	0.785343	+	1.36025i	0.928794	+	0.370596i	$0.120847\pi$
$613$	19.4442	+	33.6783i	0.785343	+	1.36025i	−0.143451	+	0.989657i	$0.545820\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	12.8874i		−	0.518828i	−0.965766	−	0.259414i	$-0.916471\pi$
$617$		−	12.8874i		−	0.518828i	0.965766	−	0.259414i	$-0.0835294\pi$
$618$		0			0
$619$	8.89767	−	5.13707i	0.357628	−	0.206476i	−0.310412	−	0.950602i	$-0.600467\pi$
$619$	8.89767	−	5.13707i	0.357628	−	0.206476i	0.668040	+	0.744126i	$0.267134\pi$
$620$		0			0
$621$	3.09423	+	16.6961i	0.124167	+	0.669990i
$622$		0			0
$623$	−12.7624	+	1.66154i	−0.511316	+	0.0665683i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.79049	+	28.2849i	0.271186	+	1.12959i
$628$		0			0
$629$	32.5794			1.29902
$630$		0			0
$631$	44.9308			1.78866			0.894332	−	0.447403i	$-0.147651\pi$
$631$	44.9308			1.78866			0.894332	+	0.447403i	$0.147651\pi$
$632$		0			0
$633$	−4.49811	−	18.7363i	−0.178784	−	0.744701i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.05488	−	1.37004i	−0.200282	−	0.0542831i
$638$		0			0
$639$	−19.0113	−	37.3126i	−0.752076	−	1.47606i
$640$		0			0
$641$	33.7953	−	19.5118i	1.33484	−	0.770668i	0.348799	−	0.937197i	$-0.386589\pi$
$641$	33.7953	−	19.5118i	1.33484	−	0.770668i	0.986036	+	0.166529i	$0.0532561\pi$
$642$		0			0
$643$			12.2206i			0.481932i	0.970534	+	0.240966i	$0.0774642\pi$
$643$			12.2206i			0.481932i	−0.970534	+	0.240966i	$0.922536\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.43406	+	14.6082i	0.331577	+	0.574308i	0.982821	−	0.184560i	$-0.0590860\pi$
$647$	8.43406	+	14.6082i	0.331577	+	0.574308i	−0.651244	+	0.758868i	$0.725753\pi$
$648$		0			0
$649$	27.1832	+	15.6942i	1.06703	+	0.616052i
$650$		0			0
$651$	5.71662	−	35.7595i	0.224052	−	1.40153i
$652$		0			0
$653$	−18.7980	−	10.8531i	−0.735624	−	0.424713i	0.0848520	−	0.996394i	$-0.472958\pi$
$653$	−18.7980	−	10.8531i	−0.735624	−	0.424713i	−0.820476	+	0.571681i	$0.806292\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.55123	−	3.92849i	0.0995331	−	0.153265i
$658$		0			0
$659$			36.3752i			1.41698i	0.705722	+	0.708489i	$0.250623\pi$
$659$			36.3752i			1.41698i	−0.705722	+	0.708489i	$0.749377\pi$
$660$		0			0
$661$	12.9940	−	7.50207i	0.505407	−	0.291797i	−0.225537	−	0.974235i	$-0.572414\pi$
$661$	12.9940	−	7.50207i	0.505407	−	0.291797i	0.730944	+	0.682438i	$0.239080\pi$
$662$		0			0
$663$	6.73018	+	7.09219i	0.261379	+	0.275438i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.06039	−	7.03281i	0.157219	−	0.272311i
$668$		0			0
$669$	18.0048	−	4.32248i	0.696104	−	0.167117i
$670$		0			0
$671$	−18.9389			−0.731127
$672$		0			0
$673$	0.119232			0.00459606			0.00229803	−	0.999997i	$-0.499269\pi$
$673$	0.119232			0.00459606			0.00229803	+	0.999997i	$0.499269\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.9293	+	20.6622i	−0.458482	+	0.794114i	−0.998881	−	0.0472948i	$-0.984940\pi$
$677$	−11.9293	+	20.6622i	−0.458482	+	0.794114i	0.540399	+	0.841409i	$0.318273\pi$
$678$		0			0
$679$	−27.1457	+	20.7677i	−1.04176	+	0.796990i
$680$		0			0
$681$	−16.8256	+	15.9668i	−0.644760	+	0.611850i
$682$		0			0
$683$	−25.3022	+	14.6082i	−0.968161	+	0.558968i	−0.898675	−	0.438615i	$-0.855469\pi$
$683$	−25.3022	+	14.6082i	−0.968161	+	0.558968i	−0.0694856	+	0.997583i	$0.522136\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−4.73122	+	15.9721i	−0.180507	+	0.609374i
$688$		0			0
$689$	−0.0404088	−	0.0699901i	−0.00153945	−	0.00266641i
$690$		0			0
$691$	−36.0356	−	20.8052i	−1.37086	−	0.791465i	−0.379822	−	0.925059i	$-0.624015\pi$
$691$	−36.0356	−	20.8052i	−1.37086	−	0.791465i	−0.991036	+	0.133594i	$0.957348\pi$
$692$		0			0
$693$	18.8110	−	1.45309i	0.714569	−	0.0551984i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−40.9922	−	71.0005i	−1.55269	−	2.68934i
$698$		0			0
$699$	10.5360	−	35.5685i	0.398509	−	1.34532i
$700$		0			0
$701$			14.6976i			0.555122i	0.960708	+	0.277561i	$0.0895261\pi$
$701$			14.6976i			0.555122i	−0.960708	+	0.277561i	$0.910474\pi$
$702$		0			0
$703$	26.4213	−	15.2543i	0.996497	−	0.575328i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.18450	+	7.65690i	−0.119765	+	0.287967i
$708$		0			0
$709$	18.6403	−	32.2859i	0.700050	−	1.21252i	−0.268398	−	0.963308i	$-0.586494\pi$
$709$	18.6403	−	32.2859i	0.700050	−	1.21252i	0.968448	−	0.249214i	$-0.0801723\pi$
$710$		0			0
$711$	0.400885	−	7.64816i	0.0150343	−	0.286828i
$712$		0			0
$713$	25.8242			0.967125
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−42.5776	+	10.2218i	−1.59009	+	0.381740i
$718$		0			0
$719$	15.8612	−	27.4724i	0.591522	−	1.02455i	−0.402505	−	0.915418i	$-0.631861\pi$
$719$	15.8612	−	27.4724i	0.591522	−	1.02455i	0.994028	−	0.109129i	$-0.0348061\pi$
$720$		0			0
$721$	5.39027	+	41.4031i	0.200744	+	1.54193i
$722$		0			0
$723$	−27.1611	−	28.6221i	−1.01013	−	1.06447i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			30.3126i			1.12423i	0.827058	+	0.562117i	$0.190013\pi$
$727$			30.3126i			1.12423i	−0.827058	+	0.562117i	$0.809987\pi$
$728$		0			0
$729$	−4.22437	+	26.6675i	−0.156458	+	0.987685i
$730$		0			0
$731$	11.4380	+	19.8111i	0.423048	+	0.732741i
$732$		0			0
$733$	2.06661	+	1.19316i	0.0763321	+	0.0440703i	0.537680	−	0.843149i	$-0.319301\pi$
$733$	2.06661	+	1.19316i	0.0763321	+	0.0440703i	−0.461348	+	0.887219i	$0.652634\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.1194	+	6.99716i	0.446425	+	0.257744i
$738$		0			0
$739$	2.29721	+	3.97889i	0.0845043	+	0.146366i	0.905180	−	0.425029i	$-0.139736\pi$
$739$	2.29721	+	3.97889i	0.0845043	+	0.146366i	−0.820676	+	0.571394i	$0.806403\pi$
$740$		0			0
$741$	8.77875	+	2.60042i	0.322496	+	0.0955289i
$742$		0			0
$743$			12.5047i			0.458753i	0.973338	+	0.229376i	$0.0736687\pi$
$743$			12.5047i			0.458753i	−0.973338	+	0.229376i	$0.926331\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.41093	−	1.22841i	0.0882114	−	0.0449451i
$748$		0			0
$749$	−4.73102	−	36.3393i	−0.172868	−	1.32781i
$750$		0			0
$751$	−17.3708	+	30.0872i	−0.633871	+	1.09790i	0.352883	+	0.935668i	$0.385202\pi$
$751$	−17.3708	+	30.0872i	−0.633871	+	1.09790i	−0.986753	+	0.162229i	$0.948132\pi$
$752$		0			0
$753$	6.63919	+	27.6547i	0.241946	+	1.00779i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−14.5066			−0.527250			−0.263625	−	0.964625i	$-0.584918\pi$
$757$	−14.5066			−0.527250			−0.263625	+	0.964625i	$0.584918\pi$
$758$		0			0
$759$	3.14077	+	13.0825i	0.114003	+	0.474864i
$760$		0			0
$761$	−20.2457	+	35.0666i	−0.733906	+	1.27116i	0.221296	+	0.975207i	$0.428971\pi$
$761$	−20.2457	+	35.0666i	−0.733906	+	1.27116i	−0.955202	+	0.295955i	$0.904362\pi$
$762$		0			0
$763$	−1.75395	+	4.21725i	−0.0634973	+	0.152675i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.55606	−	4.93984i	0.308941	−	0.178367i
$768$		0			0
$769$			39.6907i			1.43128i	0.698468	+	0.715641i	$0.253865\pi$
$769$			39.6907i			1.43128i	−0.698468	+	0.715641i	$0.746135\pi$
$770$		0			0
$771$	19.6780	+	5.82897i	0.708685	+	0.209925i
$772$		0			0
$773$	−2.83006	−	4.90181i	−0.101790	−	0.176306i	0.810632	−	0.585556i	$-0.199124\pi$
$773$	−2.83006	−	4.90181i	−0.101790	−	0.176306i	−0.912422	+	0.409250i	$0.865790\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.06475	−	18.4839i	−0.253447	−	0.663107i
$778$		0			0
$779$	−66.4877	−	38.3867i	−2.38217	−	1.37535i
$780$		0			0
$781$	−16.5903	−	28.7352i	−0.593647	−	1.02823i
$782$		0			0
$783$	9.81894	−	8.38596i	0.350900	−	0.299690i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.76237	−	1.59485i	0.0984677	−	0.0568504i	−0.449958	−	0.893050i	$-0.648561\pi$
$787$	2.76237	−	1.59485i	0.0984677	−	0.0568504i	0.548425	+	0.836200i	$0.315228\pi$
$788$		0			0
$789$	−6.60139	−	6.95647i	−0.235016	−	0.247657i
$790$		0			0
$791$	10.3766	−	7.93857i	0.368949	−	0.282263i
$792$		0			0
$793$	−2.98056	+	5.16248i	−0.105843	+	0.183325i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.7853			−0.665410			−0.332705	−	0.943031i	$-0.607961\pi$
$797$	−18.7853			−0.665410			−0.332705	+	0.943031i	$0.607961\pi$
$798$		0			0
$799$	−48.7079			−1.72316
$800$		0			0
$801$	0.763875	−	14.5734i	0.0269902	−	0.514924i
$802$		0			0
$803$	1.85574	−	3.21424i	0.0654877	−	0.113428i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.26672	+	1.20207i	−0.0445908	+	0.0423147i
$808$		0			0
$809$	−24.5995	+	14.2025i	−0.864873	+	0.499335i	−0.865641	−	0.500665i	$-0.833089\pi$
$809$	−24.5995	+	14.2025i	−0.864873	+	0.499335i	0.000767968		1.00000i	$0.499756\pi$
$810$		0			0
$811$		−	46.9628i		−	1.64909i	−0.565799	−	0.824543i	$-0.691432\pi$
$811$		−	46.9628i		−	1.64909i	0.565799	−	0.824543i	$-0.308568\pi$
$812$		0			0
$813$	−0.563482	+	1.90226i	−0.0197622	+	0.0667151i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	18.5519	+	10.7110i	0.649050	+	0.374729i
$818$		0			0
$819$	2.56433	−	5.35629i	0.0896050	−	0.187164i
$820$		0			0
$821$	16.9019	+	9.75831i	0.589880	+	0.340567i	0.765050	−	0.643971i	$-0.222714\pi$
$821$	16.9019	+	9.75831i	0.589880	+	0.340567i	−0.175170	+	0.984538i	$0.556048\pi$
$822$		0			0
$823$	−12.5304	−	21.7033i	−0.436782	−	0.756529i	0.560657	−	0.828048i	$-0.310549\pi$
$823$	−12.5304	−	21.7033i	−0.436782	−	0.756529i	−0.997439	+	0.0715193i	$0.977215\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	40.2141i		−	1.39838i	−0.714935	−	0.699191i	$-0.753544\pi$
$827$		−	40.2141i		−	1.39838i	0.714935	−	0.699191i	$-0.246456\pi$
$828$		0			0
$829$	5.52711	−	3.19108i	0.191964	−	0.110831i	−0.400937	−	0.916105i	$-0.631316\pi$
$829$	5.52711	−	3.19108i	0.191964	−	0.110831i	0.592902	+	0.805275i	$0.297982\pi$
$830$		0			0
$831$	−11.7264	+	11.1279i	−0.406785	+	0.386022i
$832$		0			0
$833$	51.0534	−	13.5225i	1.76889	−	0.468526i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	38.7069	+	13.7074i	1.33791	+	0.473796i
$838$		0			0
$839$	15.2513			0.526534			0.263267	−	0.964723i	$-0.415200\pi$
$839$	15.2513			0.526534			0.263267	+	0.964723i	$0.415200\pi$
$840$		0			0
$841$	22.8246			0.787055
$842$		0			0
$843$	−1.55421	+	0.373125i	−0.0535297	+	0.0128511i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.0358	+	1.82732i	−0.482274	+	0.0627873i
$848$		0			0
$849$	−9.00587	−	9.49028i	−0.309081	−	0.325706i
$850$		0			0
$851$	12.2205	−	7.05551i	0.418913	−	0.241860i
$852$		0			0
$853$		−	16.7815i		−	0.574586i	−0.957843	−	0.287293i	$-0.907245\pi$
$853$		−	16.7815i		−	0.574586i	0.957843	−	0.287293i	$-0.0927554\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.68551	−	16.7758i	−0.330851	−	0.573050i	0.651828	−	0.758367i	$-0.274002\pi$
$857$	−9.68551	−	16.7758i	−0.330851	−	0.573050i	−0.982679	+	0.185317i	$0.940669\pi$
$858$		0			0
$859$	42.4714	+	24.5208i	1.44910	+	0.836641i	0.998428	−	0.0560471i	$-0.0178497\pi$
$859$	42.4714	+	24.5208i	1.44910	+	0.836641i	0.450676	+	0.892688i	$0.351183\pi$
$860$		0			0
$861$	−31.3931	+	38.6532i	−1.06987	+	1.31730i
$862$		0			0
$863$	19.4609	+	11.2358i	0.662458	+	0.382470i	0.793213	−	0.608944i	$-0.208407\pi$
$863$	19.4609	+	11.2358i	0.662458	+	0.382470i	−0.130755	+	0.991415i	$0.541740\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−66.3036	−	19.6403i	−2.25179	−	0.667020i
$868$		0			0
$869$		−	6.06826i		−	0.205851i
$870$		0			0
$871$	3.81466	−	2.20239i	0.129255	−	0.0746253i
$872$		0			0
$873$	−17.5941	−	34.5311i	−0.595471	−	1.16870i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	15.5087	−	26.8618i	0.523691	−	0.907059i	−0.475929	−	0.879484i	$-0.657888\pi$
$877$	15.5087	−	26.8618i	0.523691	−	0.907059i	0.999620	−	0.0275755i	$-0.00877866\pi$
$878$		0			0
$879$	8.64902	+	36.0264i	0.291724	+	1.21514i
$880$		0			0
$881$	21.8713			0.736864			0.368432	−	0.929655i	$-0.379895\pi$
$881$	21.8713			0.736864			0.368432	+	0.929655i	$0.379895\pi$
$882$		0			0
$883$	−34.3430			−1.15573			−0.577867	−	0.816131i	$-0.696115\pi$
$883$	−34.3430			−1.15573			−0.577867	+	0.816131i	$0.696115\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.9903	−	48.4807i	0.939824	−	1.62782i	0.174027	−	0.984741i	$-0.444322\pi$
$887$	27.9903	−	48.4807i	0.939824	−	1.62782i	0.765797	−	0.643082i	$-0.222345\pi$
$888$		0			0
$889$	−25.6278	−	33.4985i	−0.859530	−	1.12350i
$890$		0			0
$891$	−2.23654	+	21.2759i	−0.0749268	+	0.712771i
$892$		0			0
$893$	−39.5012	+	22.8060i	−1.32186	+	0.763175i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	4.06039	+	1.20276i	0.135573	+	0.0401590i
$898$		0			0
$899$	−9.81894	−	17.0069i	−0.327480	−	0.567212i
$900$		0			0
$901$	0.705799	+	0.407493i	0.0235136	+	0.0135756i
$902$		0			0
$903$	8.75956	−	10.7853i	0.291500	−	0.358913i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.494450	−	0.856413i	−0.0164180	−	0.0284367i	0.857700	−	0.514151i	$-0.171893\pi$
$907$	−0.494450	−	0.856413i	−0.0164180	−	0.0284367i	−0.874118	+	0.485714i	$0.838560\pi$
$908$		0			0
$909$	−7.88602	−	5.12133i	−0.261563	−	0.169864i
$910$		0			0
$911$			28.5096i			0.944567i	0.881447	+	0.472283i	$0.156570\pi$
$911$			28.5096i			0.944567i	−0.881447	+	0.472283i	$0.843430\pi$
$912$		0			0
$913$	1.85671	−	1.07197i	0.0614482	−	0.0354771i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.8822	+	2.84885i	−0.722615	+	0.0940774i
$918$		0			0
$919$	1.40350	−	2.43093i	0.0462971	−	0.0801889i	−0.841948	−	0.539558i	$-0.818591\pi$
$919$	1.40350	−	2.43093i	0.0462971	−	0.0801889i	0.888245	+	0.459369i	$0.151925\pi$
$920$		0			0
$921$	−28.2102	+	6.77256i	−0.929559	+	0.223163i
$922$		0			0
$923$	−10.4438			−0.343761
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−47.2780	−	2.47812i	−1.55281	−	0.0813920i
$928$		0			0
$929$	−6.57702	+	11.3917i	−0.215785	+	0.373751i	−0.953515	−	0.301345i	$-0.902564\pi$
$929$	−6.57702	+	11.3917i	−0.215785	+	0.373751i	0.737730	+	0.675096i	$0.235898\pi$
$930$		0			0
$931$	35.0718	−	34.8707i	1.14943	−	1.14284i
$932$		0			0
$933$	−6.34672	+	6.02276i	−0.207782	+	0.197176i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			20.2219i			0.660622i	0.943872	+	0.330311i	$0.107154\pi$
$937$			20.2219i			0.660622i	−0.943872	+	0.330311i	$0.892846\pi$
$938$		0			0
$939$	−7.38441	+	24.9290i	−0.240981	+	0.813527i
$940$		0			0
$941$	−22.8119	−	39.5113i	−0.743646	−	1.28803i	−0.950825	−	0.309729i	$-0.899762\pi$
$941$	−22.8119	−	39.5113i	−0.743646	−	1.28803i	0.207179	−	0.978303i	$-0.433572\pi$
$942$		0			0
$943$	−30.7523	−	17.7548i	−1.00143	−	0.578177i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−50.7421	−	29.2959i	−1.64890	−	0.951990i	−0.977512	−	0.210880i	$-0.932367\pi$
$947$	−50.7421	−	29.2959i	−1.64890	−	0.951990i	−0.671383	−	0.741110i	$-0.734300\pi$
$948$		0			0
$949$	−0.584105	−	1.01170i	−0.0189608	−	0.0328411i
$950$		0			0
$951$	−12.5270	+	42.2898i	−0.406216	+	1.37134i
$952$		0			0
$953$		−	26.9224i		−	0.872101i	−0.899922	−	0.436051i	$-0.856377\pi$
$953$		−	26.9224i		−	0.872101i	0.899922	−	0.436051i	$-0.143623\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7.42147	−	7.04265i	0.239902	−	0.227657i
$958$		0			0
$959$	19.5967	+	8.15025i	0.632811	+	0.263185i
$960$		0			0
$961$	15.7244	−	27.2354i	0.507238	−	0.878562i
$962$		0			0
$963$	41.4957	+	2.17503i	1.33718	+	0.0700894i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	17.4008			0.559572			0.279786	−	0.960062i	$-0.409737\pi$
$967$	17.4008			0.559572			0.279786	+	0.960062i	$0.409737\pi$
$968$		0			0
$969$	−89.7785	+	21.5535i	−2.88410	+	0.692399i
$970$		0			0
$971$	−12.6200	+	21.8585i	−0.404996	+	0.701474i	−0.994321	−	0.106422i	$-0.966060\pi$
$971$	−12.6200	+	21.8585i	−0.404996	+	0.701474i	0.589325	+	0.807896i	$0.299394\pi$
$972$		0			0
$973$	−9.70087	+	7.42160i	−0.310996	+	0.237926i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.49450	+	3.74960i	−0.207778	+	0.119960i	−0.600278	−	0.799791i	$-0.704943\pi$
$977$	−6.49450	+	3.74960i	−0.207778	+	0.119960i	0.392501	+	0.919752i	$0.371610\pi$
$978$		0			0
$979$		−	11.5629i		−	0.369552i
$980$		0			0
$981$	−4.34345	−	2.82072i	−0.138676	−	0.0900586i
$982$		0			0
$983$	−12.9037	−	22.3498i	−0.411563	−	0.712848i	0.583498	−	0.812115i	$-0.301684\pi$
$983$	−12.9037	−	22.3498i	−0.411563	−	0.712848i	−0.995061	+	0.0992666i	$0.968350\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	10.5622	+	27.6345i	0.336198	+	0.879615i
$988$		0			0
$989$	8.58074	+	4.95409i	0.272852	+	0.157531i
$990$		0			0
$991$	−11.4009	−	19.7469i	−0.362161	−	0.627280i	0.626156	−	0.779698i	$-0.284627\pi$
$991$	−11.4009	−	19.7469i	−0.362161	−	0.627280i	−0.988316	+	0.152418i	$0.951294\pi$
$992$		0			0
$993$	−18.1063	−	5.36341i	−0.574586	−	0.170203i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.2479	−	5.91662i	0.324554	−	0.187381i	−0.328867	−	0.944376i	$-0.606667\pi$
$997$	10.2479	−	5.91662i	0.324554	−	0.187381i	0.653421	+	0.756995i	$0.273333\pi$
$998$		0			0
$999$	22.0618	−	4.08865i	0.698006	−	0.129359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.l.1601.5	yes	16
3.2	odd	2	inner	2100.2.bi.l.1601.2	yes	16
5.2	odd	4		2100.2.bo.i.1349.16		32
5.3	odd	4		2100.2.bo.i.1349.1		32
5.4	even	2		2100.2.bi.m.1601.4	yes	16
7.3	odd	6	inner	2100.2.bi.l.101.2	✓	16
15.2	even	4		2100.2.bo.i.1349.6		32
15.8	even	4		2100.2.bo.i.1349.11		32
15.14	odd	2		2100.2.bi.m.1601.7	yes	16
21.17	even	6	inner	2100.2.bi.l.101.5	yes	16
35.3	even	12		2100.2.bo.i.1949.6		32
35.17	even	12		2100.2.bo.i.1949.11		32
35.24	odd	6		2100.2.bi.m.101.7	yes	16
105.17	odd	12		2100.2.bo.i.1949.1		32
105.38	odd	12		2100.2.bo.i.1949.16		32
105.59	even	6		2100.2.bi.m.101.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.2	✓	16	7.3	odd	6	inner
2100.2.bi.l.101.5	yes	16	21.17	even	6	inner
2100.2.bi.l.1601.2	yes	16	3.2	odd	2	inner
2100.2.bi.l.1601.5	yes	16	1.1	even	1	trivial
2100.2.bi.m.101.4	yes	16	105.59	even	6
2100.2.bi.m.101.7	yes	16	35.24	odd	6
2100.2.bi.m.1601.4	yes	16	5.4	even	2
2100.2.bi.m.1601.7	yes	16	15.14	odd	2
2100.2.bo.i.1349.1		32	5.3	odd	4
2100.2.bo.i.1349.6		32	15.2	even	4
2100.2.bo.i.1349.11		32	15.8	even	4
2100.2.bo.i.1349.16		32	5.2	odd	4
2100.2.bo.i.1949.1		32	105.17	odd	12
2100.2.bo.i.1949.6		32	35.3	even	12
2100.2.bo.i.1949.11		32	35.17	even	12
2100.2.bo.i.1949.16		32	105.38	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.404332 + 1.68420i) q^{3} +(1.60761 + 2.10133i) q^{7} +(-2.67303 + 1.36195i) q^{9} +O(q^{10})\)	\(q+(0.404332 + 1.68420i) q^{3} +(1.60761 + 2.10133i) q^{7} +(-2.67303 + 1.36195i) q^{9} +(-2.05856 + 1.18851i) q^{11} +0.748179i q^{13} +(-3.77242 - 6.53402i) q^{17} +(-6.11872 - 3.53264i) q^{19} +(-2.88904 + 3.55717i) q^{21} +(-2.83006 - 1.63394i) q^{23} +(-3.37458 - 3.95123i) q^{27} +2.48504i q^{29} +(-6.84372 + 3.95123i) q^{31} +(-2.83402 - 2.98646i) q^{33} +(-2.15905 + 3.73959i) q^{37} +(-1.26008 + 0.302513i) q^{39} +10.8663 q^{41} -3.03200 q^{43} +(3.22790 - 5.59088i) q^{47} +(-1.83117 + 6.75624i) q^{49} +(9.47926 - 8.99541i) q^{51} +(-0.0935472 + 0.0540095i) q^{53} +(3.47567 - 11.7335i) q^{57} +(-6.60248 - 11.4358i) q^{59} +(6.90005 + 3.98375i) q^{61} +(-7.15910 - 3.42743i) q^{63} +(-2.94367 - 5.09859i) q^{67} +(1.60758 - 5.42703i) q^{69} +13.9589i q^{71} +(-1.35221 + 0.780701i) q^{73} +(-5.80681 - 2.41505i) q^{77} +(-1.27644 + 2.21086i) q^{79} +(5.29018 - 7.28107i) q^{81} -0.901948 q^{83} +(-4.18529 + 1.00478i) q^{87} +(-2.43223 + 4.21274i) q^{89} +(-1.57217 + 1.20278i) q^{91} +(-9.42178 - 9.92856i) q^{93} +12.9183i q^{97} +(3.88390 - 5.98057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 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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