LMFDB - Embedded newform 2100.2.bi.l.101.2

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			101.2
Root			$1.25639 + 1.19226i$ of defining polynomial
Character	$\chi$	$=$	2100.101
Dual form			2100.2.bi.l.1601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25639 + 1.19226i) q^{3} +(1.60761 - 2.10133i) q^{7} +(0.157032 - 2.99589i) q^{9} +O(q^{10})$	\(q+(-1.25639 + 1.19226i) q^{3} +(1.60761 - 2.10133i) q^{7} +(0.157032 - 2.99589i) q^{9} +(2.05856 + 1.18851i) q^{11} -0.748179i q^{13} +(3.77242 - 6.53402i) q^{17} +(-6.11872 + 3.53264i) q^{19} +(0.485543 + 4.55678i) q^{21} +(2.83006 - 1.63394i) q^{23} +(3.37458 + 3.95123i) q^{27} +2.48504i q^{29} +(-6.84372 - 3.95123i) q^{31} +(-4.00336 + 0.961106i) q^{33} +(-2.15905 - 3.73959i) q^{37} +(0.892024 + 0.940005i) q^{39} -10.8663 q^{41} -3.03200 q^{43} +(-3.22790 - 5.59088i) q^{47} +(-1.83117 - 6.75624i) q^{49} +(3.05062 + 12.7070i) q^{51} +(0.0935472 + 0.0540095i) q^{53} +(3.47567 - 11.7335i) q^{57} +(6.60248 - 11.4358i) q^{59} +(6.90005 - 3.98375i) q^{61} +(-6.04290 - 5.14620i) q^{63} +(-2.94367 + 5.09859i) q^{67} +(-1.60758 + 5.42703i) q^{69} +13.9589i q^{71} +(-1.35221 - 0.780701i) q^{73} +(5.80681 - 2.41505i) q^{77} +(-1.27644 - 2.21086i) q^{79} +(-8.95068 - 0.940900i) q^{81} +0.901948 q^{83} +(-2.96281 - 3.12218i) q^{87} +(2.43223 + 4.21274i) q^{89} +(-1.57217 - 1.20278i) q^{91} +(13.3093 - 3.19522i) q^{93} -12.9183i q^{97} +(3.88390 - 5.98057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	−1.25639	+	1.19226i	−0.725377	+	0.688352i
$3$	−1.25639	+	1.19226i	−0.725377	+	0.688352i
$4$		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
$9$	0.157032	−	2.99589i	0.0523440	−	0.998629i
$10$		0			0
$11$	2.05856	+	1.18851i	0.620679	+	0.358349i	0.777133	−	0.629336i	$-0.216673\pi$
$11$	2.05856	+	1.18851i	0.620679	+	0.358349i	−0.156455	+	0.987685i	$0.550006\pi$
$12$		0			0
$13$		−	0.748179i		−	0.207508i	−0.994603	−	0.103754i	$-0.966915\pi$
$13$		−	0.748179i		−	0.207508i	0.994603	−	0.103754i	$-0.0330854\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.77242	−	6.53402i	0.914946	−	1.58473i	0.107966	−	0.994155i	$-0.465566\pi$
$17$	3.77242	−	6.53402i	0.914946	−	1.58473i	0.806980	−	0.590578i	$-0.201100\pi$
$18$		0			0
$19$	−6.11872	+	3.53264i	−1.40373	+	0.810444i	−0.994773	−	0.102109i	$-0.967441\pi$
$19$	−6.11872	+	3.53264i	−1.40373	+	0.810444i	−0.408957	+	0.912553i	$0.634108\pi$
$20$		0			0
$21$	0.485543	+	4.55678i	0.105954	+	0.994371i
$22$		0			0
$23$	2.83006	−	1.63394i	0.590109	−	0.340699i	−0.175032	−	0.984563i	$-0.556003\pi$
$23$	2.83006	−	1.63394i	0.590109	−	0.340699i	0.765141	+	0.643863i	$0.222669\pi$
$24$		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	−0.262313	−	0.964983i	$-0.584485\pi$
$31$	−6.84372	−	3.95123i	−1.22917	−	0.709661i	−0.966856	+	0.255322i	$0.917819\pi$
$32$		0			0
$33$	−4.00336	+	0.961106i	−0.696896	+	0.167307i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.15905	−	3.73959i	−0.354946	−	0.614784i	0.632163	−	0.774835i	$-0.282167\pi$
$37$	−2.15905	−	3.73959i	−0.354946	−	0.614784i	−0.987109	+	0.160051i	$0.948834\pi$
$38$		0			0
$39$	0.892024	+	0.940005i	0.142838	+	0.150521i
$40$		0			0
$41$	−10.8663			−1.69703			−0.848514	−	0.529173i	$-0.822502\pi$
$41$	−10.8663			−1.69703			−0.848514	+	0.529173i	$0.822502\pi$
$42$		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	$-0.322715\pi$
$47$	−3.22790	−	5.59088i	−0.470837	−	0.815514i	−0.999444	+	0.0333530i	$0.989381\pi$
$48$		0			0
$49$	−1.83117	−	6.75624i	−0.261596	−	0.965178i
$50$		0			0
$51$	3.05062	+	12.7070i	0.427173	+	1.77933i
$52$		0			0
$53$	0.0935472	+	0.0540095i	0.0128497	+	0.00741878i	0.506411	−	0.862292i	$-0.330972\pi$
$53$	0.0935472	+	0.0540095i	0.0128497	+	0.00741878i	−0.493561	+	0.869711i	$0.664305\pi$
$54$		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	−0.0127699	−	0.999918i	$-0.504065\pi$
$59$	6.60248	−	11.4358i	0.859570	−	1.48882i	0.872340	−	0.488900i	$-0.162602\pi$
$60$		0			0
$61$	6.90005	−	3.98375i	0.883461	−	0.510067i	0.0116632	−	0.999932i	$-0.496287\pi$
$61$	6.90005	−	3.98375i	0.883461	−	0.510067i	0.871798	+	0.489865i	$0.162954\pi$
$62$		0			0
$63$	−6.04290	−	5.14620i	−0.761334	−	0.648360i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.94367	+	5.09859i	−0.359627	+	0.622892i	−0.987898	−	0.155102i	$-0.950429\pi$
$67$	−2.94367	+	5.09859i	−0.359627	+	0.622892i	0.628272	+	0.777994i	$0.283763\pi$
$68$		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	0.418776	−	0.908090i	$-0.362459\pi$
$73$	−1.35221	−	0.780701i	−0.158265	−	0.0913742i	−0.577041	+	0.816715i	$0.695793\pi$
$74$		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	0.785243	−	0.619188i	$-0.212538\pi$
$79$	−1.27644	−	2.21086i	−0.143611	−	0.248742i	−0.928854	+	0.370446i	$0.879205\pi$
$80$		0			0
$81$	−8.95068	−	0.940900i	−0.994520	−	0.104544i
$82$		0			0
$83$	0.901948			0.0990016			0.0495008	−	0.998774i	$-0.484237\pi$
$83$	0.901948			0.0990016			0.0495008	+	0.998774i	$0.484237\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.96281	−	3.12218i	−0.317647	−	0.334732i
$88$		0			0
$89$	2.43223	+	4.21274i	0.257816	+	0.446550i	0.965656	−	0.259822i	$-0.0836640\pi$
$89$	2.43223	+	4.21274i	0.257816	+	0.446550i	−0.707841	+	0.706372i	$0.750331\pi$
$90$		0			0
$91$	−1.57217	−	1.20278i	−0.164808	−	0.126086i
$92$		0			0
$93$	13.3093	−	3.19522i	1.38011	−	0.331329i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	12.9183i		−	1.31166i	−0.754909	−	0.655829i	$-0.772319\pi$
$97$		−	12.9183i		−	1.31166i	0.754909	−	0.655829i	$-0.227681\pi$
$98$		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	$-0.883174\pi$
$101$	−1.56718	+	2.71443i	−0.155940	+	0.270096i	0.777461	+	0.628931i	$0.216507\pi$
$102$		0			0
$103$	13.6667	−	7.89048i	1.34662	−	0.777472i	0.358852	−	0.933394i	$-0.383168\pi$
$103$	13.6667	−	7.89048i	1.34662	−	0.777472i	0.987769	+	0.155922i	$0.0498349\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.9952	−	6.92544i	1.15962	−	0.669508i	0.208408	−	0.978042i	$-0.433172\pi$
$107$	11.9952	−	6.92544i	1.15962	−	0.669508i	0.951213	+	0.308534i	$0.0998385\pi$
$108$		0			0
$109$	0.863166	−	1.49505i	0.0826763	−	0.143200i	−0.821722	−	0.569888i	$-0.806987\pi$
$109$	0.863166	−	1.49505i	0.0826763	−	0.143200i	0.904399	+	0.426688i	$0.140320\pi$
$110$		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
$117$	−2.24146	−	0.117488i	−0.207223	−	0.0108618i
$118$		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
$123$	13.6523	−	12.9554i	1.23099	−	1.16815i
$124$		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
$129$	3.80937	−	3.61493i	0.335396	−	0.318277i
$130$		0			0
$131$	4.17025	+	7.22309i	0.364357	+	0.631084i	0.988673	−	0.150087i	$-0.0479555\pi$
$131$	4.17025	+	7.22309i	0.364357	+	0.631084i	−0.624316	+	0.781172i	$0.714622\pi$
$132$		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	$-0.444668\pi$
$137$	−6.94718	−	4.01096i	−0.593537	−	0.342679i	−0.766495	+	0.642250i	$0.778001\pi$
$138$		0			0
$139$		−	4.61654i		−	0.391570i	−0.980647	−	0.195785i	$-0.937275\pi$
$139$		−	4.61654i		−	0.391570i	0.980647	−	0.195785i	$-0.0627254\pi$
$140$		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
$147$	10.3559	+	6.30525i	0.854137	+	0.520048i
$148$		0			0
$149$	15.6215	−	9.01906i	1.27976	−	0.738870i	0.302956	−	0.953004i	$-0.402026\pi$
$149$	15.6215	−	9.01906i	1.27976	−	0.738870i	0.976804	+	0.214134i	$0.0686931\pi$
$150$		0			0
$151$	2.12850	−	3.68667i	0.173215	−	0.300017i	−0.766327	−	0.642451i	$-0.777918\pi$
$151$	2.12850	−	3.68667i	0.173215	−	0.300017i	0.939542	+	0.342434i	$0.111251\pi$
$152$		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	−0.202054	−	0.979374i	$-0.564762\pi$
$157$	−14.4250	−	8.32830i	−1.15124	−	0.664671i	−0.949190	+	0.314703i	$0.898095\pi$
$158$		0			0
$159$	−0.181925	+	0.0436756i	−0.0144276	+	0.00346370i
$160$		0			0
$161$	1.11620	−	8.57363i	0.0879690	−	0.675697i
$162$		0			0
$163$	8.07999	+	13.9950i	0.632874	+	1.09617i	0.986961	+	0.160957i	$0.0514582\pi$
$163$	8.07999	+	13.9950i	0.632874	+	1.09617i	−0.354087	+	0.935212i	$0.615208\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	17.4029			1.34668			0.673338	−	0.739335i	$-0.264860\pi$
$167$	17.4029			1.34668			0.673338	+	0.739335i	$0.264860\pi$
$168$		0			0
$169$	12.4402			0.956941
$170$		0			0
$171$	9.62257	+	18.8857i	0.735856	+	1.44423i
$172$		0			0
$173$	−9.83038	−	17.0267i	−0.747390	−	1.29452i	−0.949070	−	0.315066i	$-0.897973\pi$
$173$	−9.83038	−	17.0267i	−0.747390	−	1.29452i	0.201680	−	0.979451i	$-0.435360\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.33920	+	22.2397i	0.401318	+	1.67164i
$178$		0			0
$179$	5.84722	+	3.37589i	0.437042	+	0.252326i	0.702342	−	0.711840i	$-0.252138\pi$
$179$	5.84722	+	3.37589i	0.437042	+	0.252326i	−0.265300	+	0.964166i	$0.585471\pi$
$180$		0			0
$181$		−	7.71256i		−	0.573270i	−0.958040	−	0.286635i	$-0.907463\pi$
$181$		−	7.71256i		−	0.573270i	0.958040	−	0.286635i	$-0.0925367\pi$
$182$		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
$189$	13.7278	−	0.739073i	0.998554	−	0.0537597i
$190$		0			0
$191$	12.7009	−	7.33284i	0.919001	−	0.530586i	0.0356850	−	0.999363i	$-0.488639\pi$
$191$	12.7009	−	7.33284i	0.919001	−	0.530586i	0.883316	+	0.468777i	$0.155305\pi$
$192$		0			0
$193$	−5.32299	+	9.21969i	−0.383157	+	0.663648i	−0.991512	−	0.130018i	$-0.958497\pi$
$193$	−5.32299	+	9.21969i	−0.383157	+	0.663648i	0.608354	+	0.793666i	$0.291830\pi$
$194$		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	0.534810	−	0.844972i	$-0.320383\pi$
$199$	0.993782	+	0.573760i	0.0704473	+	0.0406728i	−0.464363	+	0.885645i	$0.653717\pi$
$200$		0			0
$201$	−2.38044	−	9.91544i	−0.167904	−	0.699381i
$202$		0			0
$203$	5.22188	+	3.99497i	0.366504	+	0.280392i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.45068	−	8.73513i	−0.309344	−	0.607133i
$208$		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
$213$	−16.6426	−	17.5378i	−1.14033	−	1.20167i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−19.3049	+	8.02888i	−1.31050	+	0.545036i
$218$		0			0
$219$	2.62971	−	0.631326i	0.177699	−	0.0426610i
$220$		0			0
$221$	−4.88862	−	2.82245i	−0.328844	−	0.189858i
$222$		0			0
$223$			10.6904i			0.715883i	0.933744	+	0.357942i	$0.116521\pi$
$223$			10.6904i			0.715883i	−0.933744	+	0.357942i	$0.883479\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.69603	+	11.5979i	−0.444431	+	0.769777i	−0.998012	−	0.0630180i	$-0.979927\pi$
$227$	−6.69603	+	11.5979i	−0.444431	+	0.769777i	0.553581	+	0.832795i	$0.313261\pi$
$228$		0			0
$229$	8.32905	−	4.80878i	0.550399	−	0.317773i	−0.198884	−	0.980023i	$-0.563732\pi$
$229$	8.32905	−	4.80878i	0.550399	−	0.317773i	0.749283	+	0.662250i	$0.230398\pi$
$230$		0			0
$231$	−4.41626	+	9.95747i	−0.290568	+	0.655153i
$232$		0			0
$233$	18.5481	−	10.7087i	1.21512	−	0.701552i	0.251253	−	0.967921i	$-0.419157\pi$
$233$	18.5481	−	10.7087i	1.21512	−	0.701552i	0.963871	+	0.266369i	$0.0858240\pi$
$234$		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	−0.295713	−	0.955277i	$-0.595557\pi$
$241$	−19.7291	−	11.3906i	−1.27086	−	0.733733i	−0.975150	+	0.221543i	$0.928891\pi$
$242$		0			0
$243$	12.3673	−	9.48940i	0.793366	−	0.608746i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.64305	+	4.57790i	0.168173	+	0.291285i
$248$		0			0
$249$	−1.13320	+	1.07536i	−0.0718135	+	0.0681479i
$250$		0			0
$251$	−16.4201			−1.03643			−0.518215	−	0.855251i	$-0.673403\pi$
$251$	−16.4201			−1.03643			−0.518215	+	0.855251i	$0.673403\pi$
$252$		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	$-0.287159\pi$
$257$	−5.92452	−	10.2616i	−0.369562	−	0.640100i	−0.989497	+	0.144553i	$0.953825\pi$
$258$		0			0
$259$	−11.3290	−	1.47493i	−0.703951	−	0.0916474i
$260$		0			0
$261$	7.44489	+	0.390230i	0.460827	+	0.0241546i
$262$		0			0
$263$	4.79507	+	2.76844i	0.295677	+	0.170709i	0.640499	−	0.767959i	$-0.278727\pi$
$263$	4.79507	+	2.76844i	0.295677	+	0.170709i	−0.344822	+	0.938668i	$0.612061\pi$
$264$		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	$-0.843119\pi$
$269$	−0.504112	+	0.873148i	−0.0307363	+	0.0532368i	0.850248	+	0.526382i	$0.176452\pi$
$270$		0			0
$271$	0.991979	−	0.572720i	0.0602585	−	0.0347902i	−0.469568	−	0.882896i	$-0.655590\pi$
$271$	0.991979	−	0.572720i	0.0602585	−	0.0347902i	0.529827	+	0.848106i	$0.322257\pi$
$272$		0			0
$273$	3.40929	−	0.363274i	0.206340	−	0.0219863i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.66672	−	8.08299i	0.280396	−	0.485660i	−0.691086	−	0.722772i	$-0.742868\pi$
$277$	4.66672	−	8.08299i	0.280396	−	0.485660i	0.971482	+	0.237112i	$0.0762010\pi$
$278$		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	0.292807	−	0.956172i	$-0.405411\pi$
$283$	−6.54162	−	3.77681i	−0.388859	−	0.224508i	−0.681666	+	0.731664i	$0.738744\pi$
$284$		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
$291$	15.4020	+	16.2305i	0.902882	+	0.951447i
$292$		0			0
$293$	−21.3909			−1.24967			−0.624834	−	0.780758i	$-0.714833\pi$
$293$	−21.3909			−1.24967			−0.624834	+	0.780758i	$0.714833\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.25071	+	12.1446i	0.130599	+	0.704698i
$298$		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
$303$	−1.26732	−	5.27886i	−0.0728056	−	0.303263i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	16.7500i		−	0.955972i	−0.878368	−	0.477986i	$-0.841367\pi$
$307$		−	16.7500i		−	0.955972i	0.878368	−	0.477986i	$-0.158633\pi$
$308$		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	$-0.879080\pi$
$311$	−2.52577	+	4.37477i	−0.143224	+	0.248070i	0.785485	+	0.618880i	$0.212413\pi$
$312$		0			0
$313$	12.9998	−	7.50546i	0.734795	−	0.424234i	−0.0853790	−	0.996349i	$-0.527210\pi$
$313$	12.9998	−	7.50546i	0.734795	−	0.424234i	0.820174	+	0.572115i	$0.193877\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.0531	+	12.7324i	−1.23863	+	0.715121i	−0.968813	−	0.247792i	$-0.920295\pi$
$317$	−22.0531	+	12.7324i	−1.23863	+	0.715121i	−0.269812	+	0.962913i	$0.586962\pi$
$318$		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
$327$	0.698012	+	2.90748i	0.0386002	+	0.160784i
$328$		0			0
$329$	−16.9375	−	2.20509i	−0.933794	−	0.121571i
$330$		0			0
$331$	−5.45134	−	9.44199i	−0.299633	−	0.518979i	0.676419	−	0.736517i	$-0.263531\pi$
$331$	−5.45134	−	9.44199i	−0.299633	−	0.518979i	−0.976052	+	0.217538i	$0.930197\pi$
$332$		0			0
$333$	−11.5424	+	5.88104i	−0.632521	+	0.322279i
$334$		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
$339$	5.88751	+	6.20420i	0.319766	+	0.336966i
$340$		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	$-0.250516\pi$
$347$	8.30010	+	4.79206i	0.445573	+	0.257252i	−0.260386	+	0.965505i	$0.583850\pi$
$348$		0			0
$349$			16.5601i			0.886441i	0.896413	+	0.443220i	$0.146164\pi$
$349$			16.5601i			0.886441i	−0.896413	+	0.443220i	$0.853836\pi$
$350$		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	$-0.992453\pi$
$353$	−9.00574	+	15.5984i	−0.479327	+	0.830219i	0.520392	+	0.853928i	$0.325786\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	31.6058	+	14.0175i	1.67275	+	0.741887i
$358$		0			0
$359$	−3.47735	+	2.00765i	−0.183527	+	0.105960i	−0.588949	−	0.808170i	$-0.700458\pi$
$359$	−3.47735	+	2.00765i	−0.183527	+	0.105960i	0.405422	+	0.914130i	$0.367125\pi$
$360$		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	0.998877	+	0.0473832i	$0.0150882\pi$
$367$	29.4897	+	17.0259i	1.53935	+	0.888744i	0.540473	+	0.841361i	$0.318245\pi$
$368$		0			0
$369$	−1.70635	+	32.5542i	−0.0888292	+	1.69470i
$370$		0			0
$371$	0.263879	−	0.109747i	0.0136999	−	0.00569779i
$372$		0			0
$373$	6.70705	+	11.6169i	0.347278	+	0.601503i	0.985765	−	0.168130i	$-0.0537728\pi$
$373$	6.70705	+	11.6169i	0.347278	+	0.601503i	−0.638487	+	0.769632i	$0.720439\pi$
$374$		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
$381$	20.0288	−	19.0065i	1.02611	−	0.973731i
$382$		0			0
$383$	12.2065	+	21.1422i	0.623722	+	1.08032i	0.988787	+	0.149336i	$0.0477135\pi$
$383$	12.2065	+	21.1422i	0.623722	+	1.08032i	−0.365065	+	0.930982i	$0.618953\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.476120	+	9.08352i	−0.0242026	+	0.461741i
$388$		0			0
$389$	30.1938	+	17.4324i	1.53089	+	0.883857i	0.999321	+	0.0368391i	$0.0117289\pi$
$389$	30.1938	+	17.4324i	1.53089	+	0.883857i	0.531564	+	0.847018i	$0.321604\pi$
$390$		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	−0.901997	−	0.431743i	$-0.857899\pi$
$397$	−19.5083	+	11.2631i	−0.979095	+	0.565281i	−0.0770980	+	0.997024i	$0.524565\pi$
$398$		0			0
$399$	−19.0684	−	26.1664i	−0.954614	−	1.30996i
$400$		0			0
$401$	15.8774	−	9.16683i	0.792881	−	0.457770i	−0.0480950	−	0.998843i	$-0.515315\pi$
$401$	15.8774	−	9.16683i	0.792881	−	0.457770i	0.840976	+	0.541073i	$0.181982\pi$
$402$		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	0.713465	−	0.700691i	$-0.247125\pi$
$409$	9.37130	+	5.41052i	0.463381	+	0.267533i	−0.250084	+	0.968224i	$0.580458\pi$
$410$		0			0
$411$	13.5105	−	3.24352i	0.666422	−	0.159991i
$412$		0			0
$413$	−13.4162	−	32.2584i	−0.660169	−	1.58733i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.50412	+	5.80018i	0.269538	+	0.284036i
$418$		0			0
$419$	−34.1164			−1.66670			−0.833348	−	0.552749i	$-0.813579\pi$
$419$	−34.1164			−1.66670			−0.833348	+	0.552749i	$0.813579\pi$
$420$		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
$423$	−17.2565	+	8.79247i	−0.839042	+	0.427505i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.72144	−	20.9036i	0.131700	−	1.01160i
$428$		0			0
$429$	0.719079	+	2.99523i	0.0347175	+	0.144611i
$430$		0			0
$431$	32.6954	+	18.8767i	1.57488	+	0.909258i	0.995557	+	0.0941612i	$0.0300169\pi$
$431$	32.6954	+	18.8767i	1.57488	+	0.909258i	0.579324	+	0.815097i	$0.303316\pi$
$432$		0			0
$433$		−	0.221375i		−	0.0106386i	−0.999986	−	0.00531930i	$-0.998307\pi$
$433$		−	0.221375i		−	0.0106386i	0.999986	−	0.00531930i	$-0.00169319\pi$
$434$		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	−0.768249	−	0.640151i	$-0.778872\pi$
$439$	−12.5292	+	7.23374i	−0.597987	+	0.345248i	0.170262	+	0.985399i	$0.445538\pi$
$440$		0			0
$441$	−20.5285	+	4.42503i	−0.977547	+	0.210716i
$442$		0			0
$443$	9.61783	−	5.55285i	0.456957	−	0.263824i	−0.253807	−	0.967255i	$-0.581683\pi$
$443$	9.61783	−	5.55285i	0.456957	−	0.263824i	0.710764	+	0.703431i	$0.248349\pi$
$444$		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
$453$	1.72124	+	7.16962i	0.0808711	+	0.336858i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.47844	−	16.4171i	−0.443383	−	0.767962i	0.554555	−	0.832147i	$-0.312888\pi$
$457$	−9.47844	−	16.4171i	−0.443383	−	0.767962i	−0.997938	+	0.0641853i	$0.979555\pi$
$458$		0			0
$459$	38.5477	−	7.14392i	1.79925	−	0.333450i
$460$		0			0
$461$	15.1960			0.707746			0.353873	−	0.935293i	$-0.384864\pi$
$461$	15.1960			0.707746			0.353873	+	0.935293i	$0.384864\pi$
$462$		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	$-0.0396905\pi$
$467$	8.39365	+	14.5382i	0.388412	+	0.672749i	−0.603824	+	0.797117i	$0.706357\pi$
$468$		0			0
$469$	5.98153	+	14.3822i	0.276201	+	0.664107i
$470$		0			0
$471$	28.0530	−	6.73481i	1.29261	−	0.310324i
$472$		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	$-0.848986\pi$
$479$	−1.07579	+	1.86333i	−0.0491542	+	0.0851376i	0.840401	+	0.541964i	$0.182319\pi$
$480$		0			0
$481$	−2.79788	+	1.61536i	−0.127572	+	0.0736540i
$482$		0			0
$483$	8.81961	+	12.1026i	0.401306	+	0.550689i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.74460	+	3.02174i	−0.0790555	+	0.136928i	−0.902843	−	0.429971i	$-0.858524\pi$
$487$	−1.74460	+	3.02174i	−0.0790555	+	0.136928i	0.823787	+	0.566899i	$0.191857\pi$
$488$		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	0.660232	−	0.751061i	$-0.270458\pi$
$499$	−7.15545	−	12.3936i	−0.320322	−	0.554814i	−0.980554	+	0.196247i	$0.937124\pi$
$500$		0			0
$501$	−21.8648	+	20.7488i	−0.976848	+	0.926987i
$502$		0			0
$503$	−39.3226			−1.75331			−0.876653	−	0.481123i	$-0.840229\pi$
$503$	−39.3226			−1.75331			−0.876653	+	0.481123i	$0.840229\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−15.6298	+	14.8320i	−0.694143	+	0.658712i
$508$		0			0
$509$	17.4284	+	30.1868i	0.772498	+	1.33801i	0.936190	+	0.351495i	$0.114326\pi$
$509$	17.4284	+	30.1868i	0.772498	+	1.33801i	−0.163692	+	0.986512i	$0.552340\pi$
$510$		0			0
$511$	−3.81435	+	1.58638i	−0.168737	+	0.0701774i
$512$		0			0
$513$	−34.6064	−	12.2552i	−1.52791	−	0.541082i
$514$		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	−0.459953	−	0.887943i	$-0.652134\pi$
$521$	12.3030	−	21.3094i	0.539005	−	0.933584i	0.998958	−	0.0456406i	$-0.0145329\pi$
$522$		0			0
$523$	−23.9603	+	13.8335i	−1.04771	+	0.604897i	−0.922008	−	0.387171i	$-0.873452\pi$
$523$	−23.9603	+	13.8335i	−1.04771	+	0.604897i	−0.125704	+	0.992068i	$0.540119\pi$
$524$		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
$537$	−11.3713	+	2.72997i	−0.490709	+	0.117807i
$538$		0			0
$539$	4.26029	−	16.0845i	0.183504	−	0.692808i
$540$		0			0
$541$	7.90334	+	13.6890i	0.339791	+	0.588536i	0.984393	−	0.175983i	$-0.0563103\pi$
$541$	7.90334	+	13.6890i	0.339791	+	0.588536i	−0.644602	+	0.764518i	$0.722977\pi$
$542$		0			0
$543$	9.19537	+	9.68998i	0.394611	+	0.415837i
$544$		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
$549$	−10.8513	−	21.2974i	−0.463123	−	0.908949i
$550$		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	$-0.595127\pi$
$557$	−29.9559	−	17.2950i	−1.26927	−	0.732814i	−0.974850	+	0.222862i	$0.928460\pi$
$558$		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	−0.380972	−	0.924586i	$-0.624411\pi$
$563$	14.4793	−	25.0789i	0.610229	−	1.05695i	0.991202	−	0.132361i	$-0.0422560\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−16.3664	+	17.2957i	−0.687323	+	0.726352i
$568$		0			0
$569$	10.1544	−	5.86266i	0.425696	−	0.245775i	−0.271816	−	0.962349i	$-0.587624\pi$
$569$	10.1544	−	5.86266i	0.425696	−	0.245775i	0.697511	+	0.716574i	$0.254291\pi$
$570$		0			0
$571$	17.5541	−	30.4045i	0.734614	−	1.27239i	−0.220278	−	0.975437i	$-0.570696\pi$
$571$	17.5541	−	30.4045i	0.734614	−	1.27239i	0.954892	−	0.296952i	$-0.0959703\pi$
$572$		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	0.816263	−	0.577680i	$-0.196042\pi$
$577$	17.3937	+	10.0423i	0.724110	+	0.418065i	−0.0921536	+	0.995745i	$0.529375\pi$
$578$		0			0
$579$	−4.30452	−	17.9299i	−0.178890	−	0.745142i
$580$		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	$-0.264115\pi$
$587$	32.7111			1.35013			0.675066	+	0.737757i	$0.264115\pi$
$588$		0			0
$589$	55.8331			2.30056
$590$		0			0
$591$	8.98323	+	9.46643i	0.369521	+	0.389397i
$592$		0			0
$593$	2.23240	+	3.86664i	0.0916738	+	0.158784i	0.908216	−	0.418503i	$-0.137445\pi$
$593$	2.23240	+	3.86664i	0.0916738	+	0.158784i	−0.816542	+	0.577286i	$0.804112\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.93265	+	0.463980i	−0.0790981	+	0.0189894i
$598$		0			0
$599$	−31.6126	−	18.2515i	−1.29165	−	0.745737i	−0.312707	−	0.949850i	$-0.601236\pi$
$599$	−31.6126	−	18.2515i	−1.29165	−	0.745737i	−0.978947	+	0.204112i	$0.934569\pi$
$600$		0			0
$601$			32.4566i			1.32393i	0.749534	+	0.661966i	$0.230278\pi$
$601$			32.4566i			1.32393i	−0.749534	+	0.661966i	$0.769722\pi$
$602$		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	−0.0849841	−	0.996382i	$-0.527084\pi$
$607$	18.1187	−	10.4608i	0.735416	−	0.424593i	0.820400	+	0.571790i	$0.193751\pi$
$608$		0			0
$609$	−11.3238	+	1.20659i	−0.458862	+	0.0488936i
$610$		0			0
$611$	−4.18298	+	2.41505i	−0.169225	+	0.0977023i
$612$		0			0
$613$	19.4442	−	33.6783i	0.785343	−	1.36025i	−0.143451	−	0.989657i	$-0.545820\pi$
$613$	19.4442	−	33.6783i	0.785343	−	1.36025i	0.928794	−	0.370596i	$-0.120847\pi$
$614$		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	0.668040	−	0.744126i	$-0.267134\pi$
$619$	8.89767	+	5.13707i	0.357628	+	0.206476i	−0.310412	+	0.950602i	$0.600467\pi$
$620$		0			0
$621$	16.0063	+	5.66836i	0.642312	+	0.227463i
$622$		0			0
$623$	12.7624	+	1.66154i	0.511316	+	0.0665683i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	21.1002	−	20.0232i	0.842661	−	0.799649i
$628$		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
$633$	13.9771	−	13.2636i	0.555538	−	0.527182i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.05488	+	1.37004i	−0.200282	+	0.0542831i
$638$		0			0
$639$	41.8193	+	2.19199i	1.65435	+	0.0867139i
$640$		0			0
$641$	−33.7953	−	19.5118i	−1.33484	−	0.770668i	−0.348799	−	0.937197i	$-0.613411\pi$
$641$	−33.7953	−	19.5118i	−1.33484	−	0.770668i	−0.986036	+	0.166529i	$0.946744\pi$
$642$		0			0
$643$		−	12.2206i		−	0.481932i	−0.970534	−	0.240966i	$-0.922536\pi$
$643$		−	12.2206i		−	0.481932i	0.970534	−	0.240966i	$-0.0774642\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.43406	+	14.6082i	−0.331577	+	0.574308i	−0.982821	−	0.184560i	$-0.940914\pi$
$647$	−8.43406	+	14.6082i	−0.331577	+	0.574308i	0.651244	+	0.758868i	$0.274247\pi$
$648$		0			0
$649$	27.1832	−	15.6942i	1.06703	−	0.616052i
$650$		0			0
$651$	14.6819	−	33.1038i	0.575431	−	1.29744i
$652$		0			0
$653$	18.7980	−	10.8531i	0.735624	−	0.424713i	−0.0848520	−	0.996394i	$-0.527042\pi$
$653$	18.7980	−	10.8531i	0.735624	−	0.424713i	0.820476	+	0.571681i	$0.193708\pi$
$654$		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	0.730944	−	0.682438i	$-0.239080\pi$
$661$	12.9940	+	7.50207i	0.505407	+	0.291797i	−0.225537	+	0.974235i	$0.572414\pi$
$662$		0			0
$663$	9.50710	−	2.28241i	0.369225	−	0.0886416i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.06039	+	7.03281i	0.157219	+	0.272311i
$668$		0			0
$669$	−12.7458	−	13.4313i	−0.492779	−	0.519285i
$670$		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	$-0.0150600\pi$
$677$	11.9293	+	20.6622i	0.458482	+	0.794114i	−0.540399	+	0.841409i	$0.681727\pi$
$678$		0			0
$679$	−27.1457	−	20.7677i	−1.04176	−	0.796990i
$680$		0			0
$681$	−5.41484	−	22.5548i	−0.207497	−	0.864304i
$682$		0			0
$683$	25.3022	+	14.6082i	0.968161	+	0.558968i	0.898675	−	0.438615i	$-0.144531\pi$
$683$	25.3022	+	14.6082i	0.968161	+	0.558968i	0.0694856	+	0.997583i	$0.477864\pi$
$684$		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	−0.991036	−	0.133594i	$-0.957348\pi$
$691$	−36.0356	+	20.8052i	−1.37086	+	0.791465i	−0.379822	+	0.925059i	$0.624015\pi$
$692$		0			0
$693$	−6.32335	−	17.7758i	−0.240204	−	0.675246i
$694$		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	0.968448	+	0.249214i	$0.0801723\pi$
$709$	18.6403	+	32.2859i	0.700050	+	1.21252i	−0.268398	+	0.963308i	$0.586494\pi$
$710$		0			0
$711$	−6.82394	+	3.47690i	−0.255918	+	0.130394i
$712$		0			0
$713$	−25.8242			−0.967125
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−30.1411	−	31.7624i	−1.12564	−	1.18619i
$718$		0			0
$719$	−15.8612	−	27.4724i	−0.591522	−	1.02455i	−0.994028	−	0.109129i	$-0.965194\pi$
$719$	−15.8612	−	27.4724i	−0.591522	−	1.02455i	0.402505	−	0.915418i	$-0.368139\pi$
$720$		0			0
$721$	5.39027	−	41.4031i	0.200744	−	1.54193i
$722$		0			0
$723$	38.3680	−	9.21118i	1.42692	−	0.342568i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	30.3126i		−	1.12423i	−0.827058	−	0.562117i	$-0.809987\pi$
$727$		−	30.3126i		−	1.12423i	0.827058	−	0.562117i	$-0.190013\pi$
$728$		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	−0.461348	−	0.887219i	$-0.652634\pi$
$733$	2.06661	−	1.19316i	0.0763321	−	0.0440703i	0.537680	+	0.843149i	$0.319301\pi$
$734$		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	−0.820676	−	0.571394i	$-0.806403\pi$
$739$	2.29721	−	3.97889i	0.0845043	−	0.146366i	0.905180	+	0.425029i	$0.139736\pi$
$740$		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
$747$	0.141635	−	2.70213i	0.00518214	−	0.0988659i
$748$		0			0
$749$	4.73102	−	36.3393i	0.172868	−	1.32781i
$750$		0			0
$751$	−17.3708	−	30.0872i	−0.633871	−	1.09790i	−0.986753	−	0.162229i	$-0.948132\pi$
$751$	−17.3708	−	30.0872i	−0.633871	−	1.09790i	0.352883	−	0.935668i	$-0.385202\pi$
$752$		0			0
$753$	20.6301	−	19.5771i	0.751802	−	0.713428i
$754$		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
$759$	−9.75938	+	9.26123i	−0.354243	+	0.336161i
$760$		0			0
$761$	20.2457	+	35.0666i	0.733906	+	1.27116i	0.955202	+	0.295955i	$0.0956379\pi$
$761$	20.2457	+	35.0666i	0.733906	+	1.27116i	−0.221296	+	0.975207i	$0.571029\pi$
$762$		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	$-0.746135\pi$
$769$		−	39.6907i		−	1.43128i	0.698468	−	0.715641i	$-0.253865\pi$
$770$		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	$-0.800876\pi$
$773$	2.83006	−	4.90181i	0.101790	−	0.176306i	0.912422	+	0.409250i	$0.134210\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	15.9922	−	11.6541i	0.573715	−	0.418087i
$778$		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	0.548425	−	0.836200i	$-0.315228\pi$
$787$	2.76237	+	1.59485i	0.0984677	+	0.0568504i	−0.449958	+	0.893050i	$0.648561\pi$
$788$		0			0
$789$	−9.32518	+	2.23874i	−0.331985	+	0.0797012i
$790$		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	$-0.392039\pi$
$797$	18.7853			0.665410			0.332705	+	0.943031i	$0.392039\pi$
$798$		0			0
$799$	−48.7079			−1.72316
$800$		0			0
$801$	13.0028	−	6.62514i	0.459433	−	0.234088i
$802$		0			0
$803$	−1.85574	−	3.21424i	−0.0654877	−	0.113428i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.407658	−	1.69805i	−0.0143502	−	0.0597741i
$808$		0			0
$809$	24.5995	+	14.2025i	0.864873	+	0.499335i	0.865641	−	0.500665i	$-0.166911\pi$
$809$	24.5995	+	14.2025i	0.864873	+	0.499335i	−0.000767968		1.00000i	$0.500244\pi$
$810$		0			0
$811$			46.9628i			1.64909i	0.565799	+	0.824543i	$0.308568\pi$
$811$			46.9628i			1.64909i	−0.565799	+	0.824543i	$0.691432\pi$
$812$		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
$819$	−3.85028	+	4.52117i	−0.134540	+	0.157983i
$820$		0			0
$821$	−16.9019	+	9.75831i	−0.589880	+	0.340567i	−0.765050	−	0.643971i	$-0.777286\pi$
$821$	−16.9019	+	9.75831i	−0.589880	+	0.340567i	0.175170	+	0.984538i	$0.443952\pi$
$822$		0			0
$823$	−12.5304	+	21.7033i	−0.436782	+	0.756529i	−0.997439	−	0.0715193i	$-0.977215\pi$
$823$	−12.5304	+	21.7033i	−0.436782	+	0.756529i	0.560657	+	0.828048i	$0.310549\pi$
$824$		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	0.592902	−	0.805275i	$-0.297982\pi$
$829$	5.52711	+	3.19108i	0.191964	+	0.110831i	−0.400937	+	0.916105i	$0.631316\pi$
$830$		0			0
$831$	3.77381	+	15.7193i	0.130912	+	0.545297i
$832$		0			0
$833$	−51.0534	−	13.5225i	−1.76889	−	0.468526i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−7.48253	−	40.3748i	−0.258634	−	1.39556i
$838$		0			0
$839$	−15.2513			−0.526534			−0.263267	−	0.964723i	$-0.584800\pi$
$839$	−15.2513			−0.526534			−0.263267	+	0.964723i	$0.584800\pi$
$840$		0			0
$841$	22.8246			0.787055
$842$		0			0
$843$	−1.10024	−	1.15942i	−0.0378942	−	0.0399325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.0358	−	1.82732i	−0.482274	−	0.0627873i
$848$		0			0
$849$	12.7218	−	3.05417i	0.436610	−	0.104819i
$850$		0			0
$851$	−12.2205	−	7.05551i	−0.418913	−	0.241860i
$852$		0			0
$853$			16.7815i			0.574586i	0.957843	+	0.287293i	$0.0927554\pi$
$853$			16.7815i			0.574586i	−0.957843	+	0.287293i	$0.907245\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.68551	−	16.7758i	0.330851	−	0.573050i	−0.651828	−	0.758367i	$-0.725998\pi$
$857$	9.68551	−	16.7758i	0.330851	−	0.573050i	0.982679	+	0.185317i	$0.0593311\pi$
$858$		0			0
$859$	42.4714	−	24.5208i	1.44910	−	0.836641i	0.450676	−	0.892688i	$-0.351183\pi$
$859$	42.4714	−	24.5208i	1.44910	−	0.836641i	0.998428	+	0.0560471i	$0.0178497\pi$
$860$		0			0
$861$	−5.27605	−	49.5153i	−0.179807	−	1.68748i
$862$		0			0
$863$	−19.4609	+	11.2358i	−0.662458	+	0.382470i	−0.793213	−	0.608944i	$-0.791593\pi$
$863$	−19.4609	+	11.2358i	−0.662458	+	0.382470i	0.130755	+	0.991415i	$0.458260\pi$
$864$		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
$873$	−38.7019	−	2.02859i	−1.30986	−	0.0686574i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	15.5087	+	26.8618i	0.523691	+	0.907059i	0.999620	+	0.0275755i	$0.00877866\pi$
$877$	15.5087	+	26.8618i	0.523691	+	0.907059i	−0.475929	+	0.879484i	$0.657888\pi$
$878$		0			0
$879$	26.8753	−	25.5035i	0.906480	−	0.860211i
$880$		0			0
$881$	−21.8713			−0.736864			−0.368432	−	0.929655i	$-0.620105\pi$
$881$	−21.8713			−0.736864			−0.368432	+	0.929655i	$0.620105\pi$
$882$		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	−0.765797	−	0.643082i	$-0.777655\pi$
$887$	−27.9903	−	48.4807i	−0.939824	−	1.62782i	−0.174027	−	0.984741i	$-0.555678\pi$
$888$		0			0
$889$	−25.6278	+	33.4985i	−0.859530	+	1.12350i
$890$		0			0
$891$	−17.3072	−	12.5749i	−0.579814	−	0.421274i
$892$		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
$903$	−1.47217	−	13.8161i	−0.0489906	−	0.459773i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.494450	+	0.856413i	−0.0164180	+	0.0284367i	−0.874118	−	0.485714i	$-0.838560\pi$
$907$	−0.494450	+	0.856413i	−0.0164180	+	0.0284367i	0.857700	+	0.514151i	$0.171893\pi$
$908$		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	0.888245	−	0.459369i	$-0.151925\pi$
$919$	1.40350	+	2.43093i	0.0462971	+	0.0801889i	−0.841948	+	0.539558i	$0.818591\pi$
$920$		0			0
$921$	19.9703	+	21.0445i	0.658045	+	0.693440i
$922$		0			0
$923$	10.4438			0.343761
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−21.4929	−	42.1830i	−0.705919	−	1.38547i
$928$		0			0
$929$	6.57702	+	11.3917i	0.215785	+	0.373751i	0.953515	−	0.301345i	$-0.0974356\pi$
$929$	6.57702	+	11.3917i	0.215785	+	0.373751i	−0.737730	+	0.675096i	$0.764102\pi$
$930$		0			0
$931$	35.0718	+	34.8707i	1.14943	+	1.14284i
$932$		0			0
$933$	−2.04251	−	8.50780i	−0.0668686	−	0.278533i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	20.2219i		−	0.660622i	−0.943872	−	0.330311i	$-0.892846\pi$
$937$		−	20.2219i		−	0.660622i	0.943872	−	0.330311i	$-0.107154\pi$
$938$		0			0
$939$	−7.38441	+	24.9290i	−0.240981	+	0.813527i
$940$		0			0
$941$	22.8119	−	39.5113i	0.743646	−	1.28803i	−0.207179	−	0.978303i	$-0.566428\pi$
$941$	22.8119	−	39.5113i	0.743646	−	1.28803i	0.950825	−	0.309729i	$-0.100238\pi$
$942$		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	0.671383	−	0.741110i	$-0.265700\pi$
$947$	50.7421	−	29.2959i	1.64890	−	0.951990i	0.977512	−	0.210880i	$-0.0676329\pi$
$948$		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
$957$	−2.38838	−	9.94851i	−0.0772054	−	0.321590i
$958$		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
$963$	−18.8642	−	37.0238i	−0.607891	−	1.19308i
$964$		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
$969$	−63.5552	−	66.9737i	−2.04169	−	2.15151i
$970$		0			0
$971$	12.6200	+	21.8585i	0.404996	+	0.701474i	0.994321	−	0.106422i	$-0.0339395\pi$
$971$	12.6200	+	21.8585i	0.404996	+	0.701474i	−0.589325	+	0.807896i	$0.700606\pi$
$972$		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	$-0.295057\pi$
$977$	6.49450	+	3.74960i	0.207778	+	0.119960i	−0.392501	+	0.919752i	$0.628390\pi$
$978$		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	$-0.698316\pi$
$983$	12.9037	−	22.3498i	0.411563	−	0.712848i	0.995061	+	0.0992666i	$0.0316497\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	23.9091	−	17.4234i	0.761036	−	0.554594i
$988$		0			0
$989$	−8.58074	+	4.95409i	−0.272852	+	0.157531i
$990$		0			0
$991$	−11.4009	+	19.7469i	−0.362161	+	0.627280i	−0.988316	−	0.152418i	$-0.951294\pi$
$991$	−11.4009	+	19.7469i	−0.362161	+	0.627280i	0.626156	+	0.779698i	$0.284627\pi$
$992$		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	0.653421	−	0.756995i	$-0.273333\pi$
$997$	10.2479	+	5.91662i	0.324554	+	0.187381i	−0.328867	+	0.944376i	$0.606667\pi$
$998$		0			0
$999$	7.49005	−	21.1504i	0.236975	−	0.669170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.l.101.2	✓	16
3.2	odd	2	inner	2100.2.bi.l.101.5	yes	16
5.2	odd	4		2100.2.bo.i.1949.11		32
5.3	odd	4		2100.2.bo.i.1949.6		32
5.4	even	2		2100.2.bi.m.101.7	yes	16
7.5	odd	6	inner	2100.2.bi.l.1601.5	yes	16
15.2	even	4		2100.2.bo.i.1949.1		32
15.8	even	4		2100.2.bo.i.1949.16		32
15.14	odd	2		2100.2.bi.m.101.4	yes	16
21.5	even	6	inner	2100.2.bi.l.1601.2	yes	16
35.12	even	12		2100.2.bo.i.1349.16		32
35.19	odd	6		2100.2.bi.m.1601.4	yes	16
35.33	even	12		2100.2.bo.i.1349.1		32
105.47	odd	12		2100.2.bo.i.1349.6		32
105.68	odd	12		2100.2.bo.i.1349.11		32
105.89	even	6		2100.2.bi.m.1601.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.2	✓	16	1.1	even	1	trivial
2100.2.bi.l.101.5	yes	16	3.2	odd	2	inner
2100.2.bi.l.1601.2	yes	16	21.5	even	6	inner
2100.2.bi.l.1601.5	yes	16	7.5	odd	6	inner
2100.2.bi.m.101.4	yes	16	15.14	odd	2
2100.2.bi.m.101.7	yes	16	5.4	even	2
2100.2.bi.m.1601.4	yes	16	35.19	odd	6
2100.2.bi.m.1601.7	yes	16	105.89	even	6
2100.2.bo.i.1349.1		32	35.33	even	12
2100.2.bo.i.1349.6		32	105.47	odd	12
2100.2.bo.i.1349.11		32	105.68	odd	12
2100.2.bo.i.1349.16		32	35.12	even	12
2100.2.bo.i.1949.1		32	15.2	even	4
2100.2.bo.i.1949.6		32	5.3	odd	4
2100.2.bo.i.1949.11		32	5.2	odd	4
2100.2.bo.i.1949.16		32	15.8	even	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)

\(f(q)\)	\(=\)	\(q+(-1.25639 + 1.19226i) q^{3} +(1.60761 - 2.10133i) q^{7} +(0.157032 - 2.99589i) q^{9} +O(q^{10})\)	\(q+(-1.25639 + 1.19226i) q^{3} +(1.60761 - 2.10133i) q^{7} +(0.157032 - 2.99589i) q^{9} +(2.05856 + 1.18851i) q^{11} -0.748179i q^{13} +(3.77242 - 6.53402i) q^{17} +(-6.11872 + 3.53264i) q^{19} +(0.485543 + 4.55678i) q^{21} +(2.83006 - 1.63394i) q^{23} +(3.37458 + 3.95123i) q^{27} +2.48504i q^{29} +(-6.84372 - 3.95123i) q^{31} +(-4.00336 + 0.961106i) q^{33} +(-2.15905 - 3.73959i) q^{37} +(0.892024 + 0.940005i) q^{39} -10.8663 q^{41} -3.03200 q^{43} +(-3.22790 - 5.59088i) q^{47} +(-1.83117 - 6.75624i) q^{49} +(3.05062 + 12.7070i) q^{51} +(0.0935472 + 0.0540095i) q^{53} +(3.47567 - 11.7335i) q^{57} +(6.60248 - 11.4358i) q^{59} +(6.90005 - 3.98375i) q^{61} +(-6.04290 - 5.14620i) q^{63} +(-2.94367 + 5.09859i) q^{67} +(-1.60758 + 5.42703i) q^{69} +13.9589i q^{71} +(-1.35221 - 0.780701i) q^{73} +(5.80681 - 2.41505i) q^{77} +(-1.27644 - 2.21086i) q^{79} +(-8.95068 - 0.940900i) q^{81} +0.901948 q^{83} +(-2.96281 - 3.12218i) q^{87} +(2.43223 + 4.21274i) q^{89} +(-1.57217 - 1.20278i) q^{91} +(13.3093 - 3.19522i) q^{93} -12.9183i q^{97} +(3.88390 - 5.98057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 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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