LMFDB - Embedded newform 2100.2.ce.c.493.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("2100.157");

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.ce (of order $12$, degree $4$, 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.2
Character	$\chi$	$=$	2100.493
Dual form			2100.2.ce.c.1657.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{3} +(-2.36577 + 1.18454i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{3} +(-2.36577 + 1.18454i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-2.25649 + 3.90835i) q^{11} +(4.37238 - 4.37238i) q^{13} +(4.35920 - 1.16804i) q^{17} +(-2.51045 - 4.34823i) q^{19} +(1.75649 + 1.97857i) q^{21} +(-1.44721 + 5.40108i) q^{23} +(0.707107 + 0.707107i) q^{27} +(-3.92124 - 2.26393i) q^{31} +(4.35920 + 1.16804i) q^{33} +(-1.67303 - 0.448288i) q^{37} +(-5.35505 - 3.09174i) q^{39} -2.22509i q^{41} +(7.85281 + 7.85281i) q^{43} +(3.33357 - 12.4411i) q^{47} +(4.19371 - 5.60471i) q^{49} +(-2.25649 - 3.90835i) q^{51} +(11.8489 - 3.17491i) q^{53} +(-3.55031 + 3.55031i) q^{57} +(-1.11255 + 1.92699i) q^{59} +(6.34248 - 3.66183i) q^{61} +(1.45654 - 2.20873i) q^{63} +(-1.29950 - 4.84982i) q^{67} +5.59161 q^{69} +14.3670 q^{71} +(-1.12353 - 4.19308i) q^{73} +(0.708707 - 11.9192i) q^{77} +(-1.58312 + 0.914012i) q^{79} +(0.500000 - 0.866025i) q^{81} +(11.2105 - 11.2105i) q^{83} +(-3.90835 - 6.76946i) q^{89} +(-5.16475 + 15.5233i) q^{91} +(-1.17190 + 4.37357i) q^{93} +(3.53553 + 3.53553i) q^{97} -4.51298i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{11} - 4 q^{21} - 60 q^{31} - 8 q^{51} + 84 q^{61} + 112 q^{71} + 12 q^{81} - 136 q^{91}+O(q^{100}) $ 24 * q - 8 * q^11 - 4 * q^21 - 60 * q^31 - 8 * q^51 + 84 * q^61 + 112 * q^71 + 12 * q^81 - 136 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.36577	+	1.18454i	−0.894176	+	0.447716i
$7$	−2.36577	+	1.18454i	−0.894176	+	0.447716i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	−2.25649	+	3.90835i	−0.680357	+	1.17841i	0.294515	+	0.955647i	$0.404842\pi$
$11$	−2.25649	+	3.90835i	−0.680357	+	1.17841i	−0.974872	+	0.222766i	$0.928492\pi$
$12$		0			0
$13$	4.37238	−	4.37238i	1.21268	−	1.21268i	0.242537	−	0.970142i	$-0.422020\pi$
$13$	4.37238	−	4.37238i	1.21268	−	1.21268i	0.970142	−	0.242537i	$-0.0779797\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.35920	−	1.16804i	1.05726	−	0.283292i	0.312012	−	0.950078i	$-0.398997\pi$
$17$	4.35920	−	1.16804i	1.05726	−	0.283292i	0.745249	+	0.666786i	$0.232330\pi$
$18$		0			0
$19$	−2.51045	−	4.34823i	−0.575937	−	0.997552i	−0.995939	−	0.0900286i	$-0.971304\pi$
$19$	−2.51045	−	4.34823i	−0.575937	−	0.997552i	0.420003	−	0.907523i	$-0.362029\pi$
$20$		0			0
$21$	1.75649	+	1.97857i	0.383297	+	0.431760i
$22$		0			0
$23$	−1.44721	+	5.40108i	−0.301765	+	1.12620i	0.633929	+	0.773391i	$0.281441\pi$
$23$	−1.44721	+	5.40108i	−0.301765	+	1.12620i	−0.935694	+	0.352812i	$0.885226\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−3.92124	−	2.26393i	−0.704275	−	0.406613i	0.104663	−	0.994508i	$-0.466624\pi$
$31$	−3.92124	−	2.26393i	−0.704275	−	0.406613i	−0.808938	+	0.587894i	$0.799957\pi$
$32$		0			0
$33$	4.35920	+	1.16804i	0.758839	+	0.203330i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.67303	−	0.448288i	−0.275045	−	0.0736980i	0.118660	−	0.992935i	$-0.462140\pi$
$37$	−1.67303	−	0.448288i	−0.275045	−	0.0736980i	−0.393705	+	0.919237i	$0.628807\pi$
$38$		0			0
$39$	−5.35505	−	3.09174i	−0.857494	−	0.495074i
$40$		0			0
$41$		−	2.22509i		−	0.347501i	−0.984790	−	0.173751i	$-0.944411\pi$
$41$		−	2.22509i		−	0.347501i	0.984790	−	0.173751i	$-0.0555887\pi$
$42$		0			0
$43$	7.85281	+	7.85281i	1.19754	+	1.19754i	0.974900	+	0.222642i	$0.0714682\pi$
$43$	7.85281	+	7.85281i	1.19754	+	1.19754i	0.222642	+	0.974900i	$0.428532\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.33357	−	12.4411i	0.486251	−	1.81471i	−0.0881077	−	0.996111i	$-0.528082\pi$
$47$	3.33357	−	12.4411i	0.486251	−	1.81471i	0.574359	−	0.818604i	$-0.305251\pi$
$48$		0			0
$49$	4.19371	−	5.60471i	0.599101	−	0.800673i
$50$		0			0
$51$	−2.25649	−	3.90835i	−0.315972	−	0.547279i
$52$		0			0
$53$	11.8489	−	3.17491i	1.62757	−	0.436107i	0.674359	−	0.738404i	$-0.264420\pi$
$53$	11.8489	−	3.17491i	1.62757	−	0.436107i	0.953214	+	0.302297i	$0.0977534\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.55031	+	3.55031i	−0.470250	+	0.470250i
$58$		0			0
$59$	−1.11255	+	1.92699i	−0.144841	+	0.250873i	−0.929314	−	0.369291i	$-0.879601\pi$
$59$	−1.11255	+	1.92699i	−0.144841	+	0.250873i	0.784472	+	0.620164i	$0.212934\pi$
$60$		0			0
$61$	6.34248	−	3.66183i	0.812071	−	0.468849i	−0.0356037	−	0.999366i	$-0.511335\pi$
$61$	6.34248	−	3.66183i	0.812071	−	0.468849i	0.847674	+	0.530517i	$0.178002\pi$
$62$		0			0
$63$	1.45654	−	2.20873i	0.183507	−	0.278274i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.29950	−	4.84982i	−0.158760	−	0.592499i	−0.998754	−	0.0499041i	$-0.984108\pi$
$67$	−1.29950	−	4.84982i	−0.158760	−	0.592499i	0.839994	−	0.542595i	$-0.182558\pi$
$68$		0			0
$69$	5.59161			0.673151
$70$		0			0
$71$	14.3670			1.70504			0.852522	−	0.522692i	$-0.175072\pi$
$71$	14.3670			1.70504			0.852522	+	0.522692i	$0.175072\pi$
$72$		0			0
$73$	−1.12353	−	4.19308i	−0.131500	−	0.490763i	0.868488	−	0.495710i	$-0.165092\pi$
$73$	−1.12353	−	4.19308i	−0.131500	−	0.490763i	−0.999988	+	0.00494658i	$0.998425\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.708707	−	11.9192i	0.0807646	−	1.35831i
$78$		0			0
$79$	−1.58312	+	0.914012i	−0.178114	+	0.102834i	−0.586406	−	0.810017i	$-0.699458\pi$
$79$	−1.58312	+	0.914012i	−0.178114	+	0.102834i	0.408292	+	0.912851i	$0.366125\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	11.2105	−	11.2105i	1.23051	−	1.23051i	0.266738	−	0.963769i	$-0.414054\pi$
$83$	11.2105	−	11.2105i	1.23051	−	1.23051i	0.963769	−	0.266738i	$-0.0859459\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.90835	−	6.76946i	−0.414284	−	0.717562i	0.581069	−	0.813855i	$-0.302635\pi$
$89$	−3.90835	−	6.76946i	−0.414284	−	0.717562i	−0.995353	+	0.0962928i	$0.969301\pi$
$90$		0			0
$91$	−5.16475	+	15.5233i	−0.541413	+	1.62728i
$92$		0			0
$93$	−1.17190	+	4.37357i	−0.121520	+	0.453518i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.53553	+	3.53553i	0.358979	+	0.358979i	0.863437	−	0.504457i	$-0.168307\pi$
$97$	3.53553	+	3.53553i	0.358979	+	0.358979i	−0.504457	+	0.863437i	$0.668307\pi$
$98$		0			0
$99$		−	4.51298i		−	0.453571i
$100$		0			0
$101$	−6.08451	−	3.51290i	−0.605432	−	0.349546i	0.165744	−	0.986169i	$-0.446998\pi$
$101$	−6.08451	−	3.51290i	−0.605432	−	0.349546i	−0.771175	+	0.636623i	$0.780331\pi$
$102$		0			0
$103$	−4.02982	−	1.07979i	−0.397070	−	0.106395i	0.0547581	−	0.998500i	$-0.482561\pi$
$103$	−4.02982	−	1.07979i	−0.397070	−	0.106395i	−0.451828	+	0.892105i	$0.649228\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.78639	−	1.81841i	−0.656065	−	0.175792i	−0.0845956	−	0.996415i	$-0.526960\pi$
$107$	−6.78639	−	1.81841i	−0.656065	−	0.175792i	−0.571470	+	0.820623i	$0.693627\pi$
$108$		0			0
$109$	−11.7125	−	6.76224i	−1.12186	−	0.647705i	−0.179983	−	0.983670i	$-0.557604\pi$
$109$	−11.7125	−	6.76224i	−1.12186	−	0.647705i	−0.941875	+	0.335965i	$0.890938\pi$
$110$		0			0
$111$			1.73205i			0.164399i
$112$		0			0
$113$	−7.34847	−	7.34847i	−0.691286	−	0.691286i	0.271229	−	0.962515i	$-0.412570\pi$
$113$	−7.34847	−	7.34847i	−0.691286	−	0.691286i	−0.962515	+	0.271229i	$0.912570\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.60040	+	5.97278i	−0.147957	+	0.552184i
$118$		0			0
$119$	−8.92925	+	7.92699i	−0.818543	+	0.726666i
$120$		0			0
$121$	−4.68348	−	8.11202i	−0.425771	−	0.737456i
$122$		0			0
$123$	−2.14928	+	0.575897i	−0.193794	+	0.0519269i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	10.7059	−	10.7059i	0.949991	−	0.949991i	−0.0488168	−	0.998808i	$-0.515545\pi$
$127$	10.7059	−	10.7059i	0.949991	−	0.949991i	0.998808	+	0.0488168i	$0.0155451\pi$
$128$		0			0
$129$	5.55278	−	9.61769i	0.488895	−	0.846790i
$130$		0			0
$131$	12.8540	−	7.42125i	1.12306	−	0.648397i	0.180878	−	0.983506i	$-0.442106\pi$
$131$	12.8540	−	7.42125i	1.12306	−	0.648397i	0.942180	+	0.335108i	$0.108773\pi$
$132$		0			0
$133$	11.0898	+	7.31315i	0.961608	+	0.634131i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.295421	+	1.10253i	0.0252395	+	0.0941953i	0.977397	−	0.211414i	$-0.0678067\pi$
$137$	0.295421	+	1.10253i	0.0252395	+	0.0941953i	−0.952157	+	0.305609i	$0.901140\pi$
$138$		0			0
$139$	−20.5766			−1.74529			−0.872644	−	0.488357i	$-0.837596\pi$
$139$	−20.5766			−1.74529			−0.872644	+	0.488357i	$0.837596\pi$
$140$		0			0
$141$	−12.8799			−1.08469
$142$		0			0
$143$	7.22257	+	26.9550i	0.603982	+	2.25409i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.49915	−	2.60020i	−0.536041	−	0.214461i
$148$		0			0
$149$	−16.9212	+	9.76946i	−1.38624	+	0.800346i	−0.992889	−	0.119043i	$-0.962017\pi$
$149$	−16.9212	+	9.76946i	−1.38624	+	0.800346i	−0.393350	+	0.919389i	$0.628684\pi$
$150$		0			0
$151$	5.75649	−	9.97053i	0.468456	−	0.811390i	−0.530894	−	0.847438i	$-0.678144\pi$
$151$	5.75649	−	9.97053i	0.468456	−	0.811390i	0.999350	+	0.0360482i	$0.0114770\pi$
$152$		0			0
$153$	−3.19116	+	3.19116i	−0.257990	+	0.257990i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.75247	+	2.07727i	−0.618715	+	0.165784i	−0.554543	−	0.832155i	$-0.687107\pi$
$157$	−7.75247	+	2.07727i	−0.618715	+	0.165784i	−0.0641713	+	0.997939i	$0.520440\pi$
$158$		0			0
$159$	−6.13345	−	10.6234i	−0.486414	−	0.842494i
$160$		0			0
$161$	−2.97405	−	14.4920i	−0.234388	−	1.14213i
$162$		0			0
$163$	−1.11490	+	4.16087i	−0.0873259	+	0.325905i	−0.995744	−	0.0921571i	$-0.970624\pi$
$163$	−1.11490	+	4.16087i	−0.0873259	+	0.325905i	0.908419	+	0.418062i	$0.137290\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.119519	−	0.119519i	−0.00924866	−	0.00924866i	0.702467	−	0.711716i	$-0.252082\pi$
$167$	−0.119519	−	0.119519i	−0.00924866	−	0.00924866i	−0.711716	+	0.702467i	$0.752082\pi$
$168$		0			0
$169$		−	25.2354i		−	1.94118i
$170$		0			0
$171$	4.34823	+	2.51045i	0.332517	+	0.191979i
$172$		0			0
$173$	14.5140	+	3.88900i	1.10348	+	0.295675i	0.764179	−	0.645004i	$-0.223144\pi$
$173$	14.5140	+	3.88900i	1.10348	+	0.295675i	0.339296	+	0.940679i	$0.389811\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.14928	+	0.575897i	0.161549	+	0.0432871i
$178$		0			0
$179$	17.0676	+	9.85398i	1.27569	+	0.736521i	0.976053	−	0.217532i	$-0.0698007\pi$
$179$	17.0676	+	9.85398i	1.27569	+	0.736521i	0.299638	+	0.954053i	$0.403134\pi$
$180$		0			0
$181$			9.32855i			0.693386i	0.937979	+	0.346693i	$0.112695\pi$
$181$			9.32855i			0.693386i	−0.937979	+	0.346693i	$0.887305\pi$
$182$		0			0
$183$	−5.17861	−	5.17861i	−0.382814	−	0.382814i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−5.27136	+	19.6730i	−0.385480	+	1.43863i
$188$		0			0
$189$	−2.51045	−	0.835250i	−0.182608	−	0.0607555i
$190$		0			0
$191$	7.95294	+	13.7749i	0.575455	+	0.996717i	0.995992	+	0.0894414i	$0.0285082\pi$
$191$	7.95294	+	13.7749i	0.575455	+	0.996717i	−0.420538	+	0.907275i	$0.638158\pi$
$192$		0			0
$193$	−4.37357	+	1.17190i	−0.314817	+	0.0843549i	−0.412768	−	0.910836i	$-0.635438\pi$
$193$	−4.37357	+	1.17190i	−0.314817	+	0.0843549i	0.0979510	+	0.995191i	$0.468771\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.5959	−	17.5959i	1.25365	−	1.25365i	0.299582	−	0.954071i	$-0.403153\pi$
$197$	17.5959	−	17.5959i	1.25365	−	1.25365i	0.954071	−	0.299582i	$-0.0968472\pi$
$198$		0			0
$199$	4.59912	−	7.96592i	0.326023	−	0.564689i	−0.655696	−	0.755025i	$-0.727625\pi$
$199$	4.59912	−	7.96592i	0.326023	−	0.564689i	0.981719	+	0.190336i	$0.0609579\pi$
$200$		0			0
$201$	−4.34823	+	2.51045i	−0.306700	+	0.177073i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.44721	−	5.40108i	−0.100588	−	0.375401i
$208$		0			0
$209$	22.6592			1.56737
$210$		0			0
$211$	3.14602			0.216581			0.108291	−	0.994119i	$-0.465462\pi$
$211$	3.14602			0.216581			0.108291	+	0.994119i	$0.465462\pi$
$212$		0			0
$213$	−3.71844	−	13.8774i	−0.254783	−	0.950865i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	11.9585	+	0.711043i	0.811793	+	0.0482688i
$218$		0			0
$219$	−3.75942	+	2.17050i	−0.254038	+	0.146669i
$220$		0			0
$221$	13.9529	−	24.1672i	0.938576	−	1.62566i
$222$		0			0
$223$	6.46722	−	6.46722i	0.433077	−	0.433077i	−0.456597	−	0.889674i	$-0.650932\pi$
$223$	6.46722	−	6.46722i	0.433077	−	0.433077i	0.889674	+	0.456597i	$0.150932\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.1505	−	4.05956i	1.00557	−	0.269443i	0.281795	−	0.959475i	$-0.409070\pi$
$227$	15.1505	−	4.05956i	1.00557	−	0.269443i	0.723779	+	0.690032i	$0.242404\pi$
$228$		0			0
$229$	9.21461	+	15.9602i	0.608918	+	1.05468i	0.991419	+	0.130722i	$0.0417296\pi$
$229$	9.21461	+	15.9602i	0.608918	+	1.05468i	−0.382501	+	0.923955i	$0.624937\pi$
$230$		0			0
$231$	−11.6965	+	2.40035i	−0.769570	+	0.157931i
$232$		0			0
$233$	−0.666615	+	2.48784i	−0.0436714	+	0.162984i	−0.984318	−	0.176404i	$-0.943553\pi$
$233$	−0.666615	+	2.48784i	−0.0436714	+	0.162984i	0.940646	+	0.339388i	$0.110220\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.29261	+	1.29261i	0.0839640	+	0.0839640i
$238$		0			0
$239$		−	0.607095i		−	0.0392697i	−0.999807	−	0.0196349i	$-0.993750\pi$
$239$		−	0.607095i		−	0.0392697i	0.999807	−	0.0196349i	$-0.00625037\pi$
$240$		0			0
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$		0			0
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−29.9887	−	8.03545i	−1.90814	−	0.511284i
$248$		0			0
$249$	−13.7299	−	7.92699i	−0.870100	−	0.502352i
$250$		0			0
$251$			28.2508i			1.78318i	0.452848	+	0.891588i	$0.350408\pi$
$251$			28.2508i			1.78318i	−0.452848	+	0.891588i	$0.649592\pi$
$252$		0			0
$253$	−17.8437	−	17.8437i	−1.12182	−	1.12182i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.33861	+	4.99574i	−0.0834999	+	0.311626i	−0.995026	−	0.0996165i	$-0.968238\pi$
$257$	−1.33861	+	4.99574i	−0.0834999	+	0.311626i	0.911526	+	0.411243i	$0.134905\pi$
$258$		0			0
$259$	4.48902	−	0.921238i	0.278934	−	0.0572429i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.4393	+	4.13694i	−0.952027	+	0.255095i	−0.701222	−	0.712943i	$-0.747362\pi$
$263$	−15.4393	+	4.13694i	−0.952027	+	0.255095i	−0.250805	+	0.968038i	$0.580695\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.52724	+	5.52724i	−0.338262	+	0.338262i
$268$		0			0
$269$	−8.75400	+	15.1624i	−0.533741	+	0.924466i	0.465483	+	0.885057i	$0.345881\pi$
$269$	−8.75400	+	15.1624i	−0.533741	+	0.924466i	−0.999223	+	0.0394089i	$0.987453\pi$
$270$		0			0
$271$	−9.38140	+	5.41636i	−0.569880	+	0.329020i	−0.757101	−	0.653298i	$-0.773385\pi$
$271$	−9.38140	+	5.41636i	−0.569880	+	0.329020i	0.187222	+	0.982318i	$0.440052\pi$
$272$		0			0
$273$	16.3311	+	0.971038i	0.988403	+	0.0587699i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.02719	+	11.2976i	0.181887	+	0.678810i	0.995276	+	0.0970897i	$0.0309534\pi$
$277$	3.02719	+	11.2976i	0.181887	+	0.678810i	−0.813389	+	0.581720i	$0.802380\pi$
$278$		0			0
$279$	4.52786			0.271076
$280$		0			0
$281$	25.5389			1.52352			0.761762	−	0.647857i	$-0.224334\pi$
$281$	25.5389			1.52352			0.761762	+	0.647857i	$0.224334\pi$
$282$		0			0
$283$	−4.41038	−	16.4598i	−0.262170	−	0.978431i	−0.963960	−	0.266048i	$-0.914282\pi$
$283$	−4.41038	−	16.4598i	−0.262170	−	0.978431i	0.701790	−	0.712384i	$-0.252384\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.63572	+	5.26406i	0.155582	+	0.310727i
$288$		0			0
$289$	2.91587	−	1.68348i	0.171522	−	0.0990280i
$290$		0			0
$291$	2.50000	−	4.33013i	0.146553	−	0.253837i
$292$		0			0
$293$	0.429281	−	0.429281i	0.0250789	−	0.0250789i	−0.694456	−	0.719535i	$-0.744355\pi$
$293$	0.429281	−	0.429281i	0.0250789	−	0.0250789i	0.719535	+	0.694456i	$0.244355\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.35920	+	1.16804i	−0.252946	+	0.0677768i
$298$		0			0
$299$	17.2878	+	29.9433i	0.999779	+	1.73167i
$300$		0			0
$301$	−27.8799	−	9.27591i	−1.60697	−	0.534655i
$302$		0			0
$303$	−1.81841	+	6.78639i	−0.104465	+	0.389868i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−11.2390	−	11.2390i	−0.641445	−	0.641445i	0.309466	−	0.950911i	$-0.399850\pi$
$307$	−11.2390	−	11.2390i	−0.641445	−	0.641445i	−0.950911	+	0.309466i	$0.899850\pi$
$308$		0			0
$309$			4.17198i			0.237335i
$310$		0			0
$311$	−0.988499	−	0.570710i	−0.0560526	−	0.0323620i	0.471712	−	0.881753i	$-0.343636\pi$
$311$	−0.988499	−	0.570710i	−0.0560526	−	0.0323620i	−0.527764	+	0.849391i	$0.676970\pi$
$312$		0			0
$313$	4.34809	+	1.16507i	0.245769	+	0.0658535i	0.379600	−	0.925151i	$-0.376061\pi$
$313$	4.34809	+	1.16507i	0.245769	+	0.0658535i	−0.133832	+	0.991004i	$0.542728\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.36107	+	2.50829i	0.525770	+	0.140880i	0.511934	−	0.859025i	$-0.328929\pi$
$317$	9.36107	+	2.50829i	0.525770	+	0.140880i	0.0138358	+	0.999904i	$0.495596\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$			7.02579i			0.392141i
$322$		0			0
$323$	−16.0225	−	16.0225i	−0.891514	−	0.891514i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.50039	+	13.0636i	−0.193572	+	0.722421i
$328$		0			0
$329$	6.85054	+	33.3814i	0.377682	+	1.84038i
$330$		0			0
$331$	−1.90251	−	3.29525i	−0.104571	−	0.181123i	0.808992	−	0.587820i	$-0.200014\pi$
$331$	−1.90251	−	3.29525i	−0.104571	−	0.181123i	−0.913563	+	0.406697i	$0.866680\pi$
$332$		0			0
$333$	1.67303	−	0.448288i	0.0916816	−	0.0245660i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−10.8616	+	10.8616i	−0.591667	+	0.591667i	−0.938082	−	0.346415i	$-0.887399\pi$
$337$	−10.8616	+	10.8616i	−0.591667	+	0.591667i	0.346415	+	0.938082i	$0.387399\pi$
$338$		0			0
$339$	−5.19615	+	9.00000i	−0.282216	+	0.488813i
$340$		0			0
$341$	17.6965	−	10.2171i	0.958317	−	0.553284i
$342$		0			0
$343$	−3.28230	+	18.2271i	−0.177227	+	0.984170i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.47033	−	12.9514i	−0.186297	−	0.695270i	−0.994349	−	0.106159i	$-0.966145\pi$
$347$	−3.47033	−	12.9514i	−0.186297	−	0.695270i	0.808052	−	0.589111i	$-0.200522\pi$
$348$		0			0
$349$	35.2766			1.88831			0.944156	−	0.329497i	$-0.106879\pi$
$349$	35.2766			1.88831			0.944156	+	0.329497i	$0.106879\pi$
$350$		0			0
$351$	6.18348			0.330050
$352$		0			0
$353$	1.15461	+	4.30906i	0.0614537	+	0.229348i	0.989821	−	0.142314i	$-0.0454544\pi$
$353$	1.15461	+	4.30906i	0.0614537	+	0.229348i	−0.928368	+	0.371663i	$0.878788\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	9.96794	+	6.57334i	0.527559	+	0.347898i
$358$		0			0
$359$	10.0129	−	5.78097i	0.528462	−	0.305108i	−0.211928	−	0.977285i	$-0.567974\pi$
$359$	10.0129	−	5.78097i	0.528462	−	0.305108i	0.740390	+	0.672178i	$0.234641\pi$
$360$		0			0
$361$	−3.10471	+	5.37752i	−0.163406	+	0.283028i
$362$		0			0
$363$	−6.62344	+	6.62344i	−0.347640	+	0.347640i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.72055	−	0.728970i	0.142012	−	0.0380519i	−0.187113	−	0.982338i	$-0.559913\pi$
$367$	2.72055	−	0.728970i	0.142012	−	0.0380519i	0.329125	+	0.944286i	$0.393246\pi$
$368$		0			0
$369$	1.11255	+	1.92699i	0.0579169	+	0.100315i
$370$		0			0
$371$	−24.2709	+	21.5467i	−1.26008	+	1.11865i
$372$		0			0
$373$	−6.10306	+	22.7769i	−0.316004	+	1.17934i	0.607046	+	0.794667i	$0.292354\pi$
$373$	−6.10306	+	22.7769i	−0.316004	+	1.17934i	−0.923051	+	0.384678i	$0.874312\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	12.6445i		−	0.649507i	−0.945799	−	0.324753i	$-0.894719\pi$
$379$		−	12.6445i		−	0.649507i	0.945799	−	0.324753i	$-0.105281\pi$
$380$		0			0
$381$	−13.1119	−	7.57018i	−0.671745	−	0.387832i
$382$		0			0
$383$	8.08186	+	2.16553i	0.412964	+	0.110653i	0.459318	−	0.888272i	$-0.348094\pi$
$383$	8.08186	+	2.16553i	0.412964	+	0.110653i	−0.0463547	+	0.998925i	$0.514760\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.7271	−	2.87433i	−0.545291	−	0.146110i
$388$		0			0
$389$	4.77182	+	2.75501i	0.241941	+	0.139685i	0.616069	−	0.787693i	$-0.288724\pi$
$389$	4.77182	+	2.75501i	0.241941	+	0.139685i	−0.374128	+	0.927377i	$0.622058\pi$
$390$		0			0
$391$			25.2348i			1.27618i
$392$		0			0
$393$	−10.4952	−	10.4952i	−0.529414	−	0.529414i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.49612	+	20.5118i	−0.275842	+	1.02946i	0.679432	+	0.733738i	$0.262226\pi$
$397$	−5.49612	+	20.5118i	−0.275842	+	1.02946i	−0.955275	+	0.295720i	$0.904441\pi$
$398$		0			0
$399$	4.19371	−	12.6047i	0.209948	−	0.631025i
$400$		0			0
$401$	−7.26799	−	12.5885i	−0.362946	−	0.628641i	0.625498	−	0.780226i	$-0.284896\pi$
$401$	−7.26799	−	12.5885i	−0.362946	−	0.628641i	−0.988444	+	0.151585i	$0.951562\pi$
$402$		0			0
$403$	−27.0439	+	7.24639i	−1.34715	+	0.360968i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.52724	−	5.52724i	0.273975	−	0.273975i
$408$		0			0
$409$	−9.21461	+	15.9602i	−0.455633	+	0.789179i	−0.998724	−	0.0504942i	$-0.983920\pi$
$409$	−9.21461	+	15.9602i	−0.455633	+	0.789179i	0.543091	+	0.839674i	$0.317254\pi$
$410$		0			0
$411$	0.988499	−	0.570710i	0.0487591	−	0.0281511i
$412$		0			0
$413$	0.349423	−	5.87667i	0.0171940	−	0.289172i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.32563	+	19.8755i	0.260797	+	0.973308i
$418$		0			0
$419$	−9.74904			−0.476272			−0.238136	−	0.971232i	$-0.576536\pi$
$419$	−9.74904			−0.476272			−0.238136	+	0.971232i	$0.576536\pi$
$420$		0			0
$421$	10.6330			0.518223			0.259112	−	0.965847i	$-0.416570\pi$
$421$	10.6330			0.518223			0.259112	+	0.965847i	$0.416570\pi$
$422$		0			0
$423$	3.33357	+	12.4411i	0.162084	+	0.604905i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.6672	+	16.1760i	−0.516223	+	0.782811i
$428$		0			0
$429$	24.1672	−	13.9529i	1.16680	−	0.673654i
$430$		0			0
$431$	−16.2354	+	28.1205i	−0.782031	+	1.35452i	0.148726	+	0.988878i	$0.452483\pi$
$431$	−16.2354	+	28.1205i	−0.782031	+	1.35452i	−0.930757	+	0.365639i	$0.880851\pi$
$432$		0			0
$433$	23.2782	−	23.2782i	1.11868	−	1.11868i	0.126743	−	0.991936i	$-0.459548\pi$
$433$	23.2782	−	23.2782i	1.11868	−	1.11868i	0.991936	−	0.126743i	$-0.0404523\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	27.1183	−	7.26632i	1.29724	−	0.347595i
$438$		0			0
$439$	−6.99947	−	12.1234i	−0.334067	−	0.578620i	0.649239	−	0.760585i	$-0.275088\pi$
$439$	−6.99947	−	12.1234i	−0.334067	−	0.578620i	−0.983305	+	0.181965i	$0.941754\pi$
$440$		0			0
$441$	−0.829500	+	6.95068i	−0.0395000	+	0.330985i
$442$		0			0
$443$	0.204704	−	0.763964i	0.00972576	−	0.0362970i	−0.960892	−	0.276922i	$-0.910686\pi$
$443$	0.204704	−	0.763964i	0.00972576	−	0.0362970i	0.970618	+	0.240625i	$0.0773523\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	13.8161	+	13.8161i	0.653480	+	0.653480i
$448$		0			0
$449$			15.9059i			0.750645i	0.926894	+	0.375322i	$0.122468\pi$
$449$			15.9059i			0.750645i	−0.926894	+	0.375322i	$0.877532\pi$
$450$		0			0
$451$	8.69645	+	5.02090i	0.409500	+	0.236425i
$452$		0			0
$453$	−11.1207	−	2.97978i	−0.522495	−	0.140002i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	35.4090	+	9.48783i	1.65637	+	0.443822i	0.961385	−	0.275207i	$-0.0887464\pi$
$457$	35.4090	+	9.48783i	1.65637	+	0.443822i	0.694980	+	0.719029i	$0.255413\pi$
$458$		0			0
$459$	3.90835	+	2.25649i	0.182426	+	0.105324i
$460$		0			0
$461$		−	14.1415i		−	0.658634i	−0.944219	−	0.329317i	$-0.893181\pi$
$461$		−	14.1415i		−	0.658634i	0.944219	−	0.329317i	$-0.106819\pi$
$462$		0			0
$463$	−16.4119	−	16.4119i	−0.762728	−	0.762728i	0.214087	−	0.976815i	$-0.431322\pi$
$463$	−16.4119	−	16.4119i	−0.762728	−	0.762728i	−0.976815	+	0.214087i	$0.931322\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.22509	−	23.2324i	0.288063	−	1.07507i	−0.658509	−	0.752573i	$-0.728813\pi$
$467$	6.22509	−	23.2324i	0.288063	−	1.07507i	0.946572	−	0.322492i	$-0.104521\pi$
$468$		0			0
$469$	8.81915	+	9.93421i	0.407230	+	0.458719i
$470$		0			0
$471$	4.01298	+	6.95068i	0.184908	+	0.320270i
$472$		0			0
$473$	−48.4113	+	12.9718i	−2.22596	+	0.596443i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−8.67400	+	8.67400i	−0.397155	+	0.397155i
$478$		0			0
$479$	0.146380	−	0.253538i	0.00668829	−	0.0115845i	−0.862662	−	0.505781i	$-0.831204\pi$
$479$	0.146380	−	0.253538i	0.00668829	−	0.0115845i	0.869350	+	0.494197i	$0.164538\pi$
$480$		0			0
$481$	−9.27521	+	5.35505i	−0.422913	+	0.244169i
$482$		0			0
$483$	−13.2284	+	6.62351i	−0.601915	+	0.301380i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	1.08118	+	4.03501i	0.0489928	+	0.182844i	0.986086	−	0.166235i	$-0.0531611\pi$
$487$	1.08118	+	4.03501i	0.0489928	+	0.182844i	−0.937093	+	0.349079i	$0.886494\pi$
$488$		0			0
$489$	4.30765			0.194799
$490$		0			0
$491$	5.28910			0.238694			0.119347	−	0.992853i	$-0.461920\pi$
$491$	5.28910			0.238694			0.119347	+	0.992853i	$0.461920\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−33.9889	+	17.0183i	−1.52461	+	0.763375i
$498$		0			0
$499$	−25.4675	+	14.7037i	−1.14008	+	0.658227i	−0.946451	−	0.322847i	$-0.895360\pi$
$499$	−25.4675	+	14.7037i	−1.14008	+	0.658227i	−0.193632	+	0.981074i	$0.562027\pi$
$500$		0			0
$501$	−0.0845127	+	0.146380i	−0.00377575	+	0.00653979i
$502$		0			0
$503$	25.4558	−	25.4558i	1.13502	−	1.13502i	0.145690	−	0.989330i	$-0.453460\pi$
$503$	25.4558	−	25.4558i	1.13502	−	1.13502i	0.989330	−	0.145690i	$-0.0465401\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−24.3755	+	6.53140i	−1.08255	+	0.290070i
$508$		0			0
$509$	−5.76686	−	9.98850i	−0.255612	−	0.442732i	0.709450	−	0.704756i	$-0.248944\pi$
$509$	−5.76686	−	9.98850i	−0.255612	−	0.442732i	−0.965061	+	0.262024i	$0.915610\pi$
$510$		0			0
$511$	7.62492	+	8.58899i	0.337306	+	0.379954i
$512$		0			0
$513$	1.29950	−	4.84982i	0.0573745	−	0.214125i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	41.1019	+	41.1019i	1.80766	+	1.80766i
$518$		0			0
$519$		−	15.0260i		−	0.659566i
$520$		0			0
$521$	0.684951	+	0.395457i	0.0300083	+	0.0173253i	0.514929	−	0.857233i	$-0.327818\pi$
$521$	0.684951	+	0.395457i	0.0300083	+	0.0173253i	−0.484921	+	0.874558i	$0.661152\pi$
$522$		0			0
$523$	−35.9888	−	9.64318i	−1.57368	−	0.421667i	−0.636719	−	0.771096i	$-0.719709\pi$
$523$	−35.9888	−	9.64318i	−1.57368	−	0.421667i	−0.936963	+	0.349429i	$0.886376\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−19.7378	−	5.28874i	−0.859793	−	0.230381i
$528$		0			0
$529$	−7.15865	−	4.13305i	−0.311246	−	0.179698i
$530$		0			0
$531$		−	2.22509i		−	0.0965609i
$532$		0			0
$533$	−9.72895	−	9.72895i	−0.421408	−	0.421408i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.10079	−	19.0364i	0.220115	−	0.821482i
$538$		0			0
$539$	12.4421	+	29.0375i	0.535921	+	1.25073i
$540$		0			0
$541$	−1.05429	−	1.82608i	−0.0453273	−	0.0785091i	0.842472	−	0.538741i	$-0.181100\pi$
$541$	−1.05429	−	1.82608i	−0.0453273	−	0.0785091i	−0.887799	+	0.460232i	$0.847766\pi$
$542$		0			0
$543$	9.01069	−	2.41441i	0.386686	−	0.103612i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.7426	+	20.7426i	−0.886890	+	0.886890i	−0.994223	−	0.107333i	$-0.965769\pi$
$547$	−20.7426	+	20.7426i	−0.886890	+	0.886890i	0.107333	+	0.994223i	$0.465769\pi$
$548$		0			0
$549$	−3.66183	+	6.34248i	−0.156283	+	0.270690i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	2.66259	−	4.03761i	0.113225	−	0.171697i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.98515	+	11.1407i	0.126485	+	0.472048i	0.999888	−	0.0149497i	$-0.00475882\pi$
$557$	2.98515	+	11.1407i	0.126485	+	0.472048i	−0.873403	+	0.486997i	$0.838092\pi$
$558$		0			0
$559$	68.6709			2.90447
$560$		0			0
$561$	20.3670			0.859893
$562$		0			0
$563$	−1.62353	−	6.05909i	−0.0684236	−	0.255360i	0.923238	−	0.384228i	$-0.125532\pi$
$563$	−1.62353	−	6.05909i	−0.0684236	−	0.255360i	−0.991662	+	0.128868i	$0.958866\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.157038	+	2.64109i	−0.00659496	+	0.110915i
$568$		0			0
$569$	−26.1721	+	15.1105i	−1.09719	+	0.633464i	−0.935482	−	0.353375i	$-0.885034\pi$
$569$	−26.1721	+	15.1105i	−1.09719	+	0.633464i	−0.161709	+	0.986838i	$0.551701\pi$
$570$		0			0
$571$	18.7037	−	32.3957i	0.782725	−	1.35572i	−0.147624	−	0.989043i	$-0.547163\pi$
$571$	18.7037	−	32.3957i	0.782725	−	1.35572i	0.930349	−	0.366675i	$-0.119504\pi$
$572$		0			0
$573$	11.2472	−	11.2472i	0.469857	−	0.469857i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−17.8711	+	4.78853i	−0.743982	+	0.199349i	−0.610847	−	0.791749i	$-0.709171\pi$
$577$	−17.8711	+	4.78853i	−0.743982	+	0.199349i	−0.133135	+	0.991098i	$0.542504\pi$
$578$		0			0
$579$	2.26393	+	3.92124i	0.0940856	+	0.162961i
$580$		0			0
$581$	−13.2420	+	39.8006i	−0.549372	+	1.65121i
$582$		0			0
$583$	−14.3283	+	53.4738i	−0.593416	+	2.21466i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.17461	−	5.17461i	−0.213579	−	0.213579i	0.592207	−	0.805786i	$-0.298257\pi$
$587$	−5.17461	−	5.17461i	−0.213579	−	0.213579i	−0.805786	+	0.592207i	$0.798257\pi$
$588$		0			0
$589$			22.7339i			0.936734i
$590$		0			0
$591$	−21.5504	−	12.4421i	−0.886466	−	0.511802i
$592$		0			0
$593$	−40.0827	−	10.7401i	−1.64600	−	0.441045i	−0.687512	−	0.726173i	$-0.741297\pi$
$593$	−40.0827	−	10.7401i	−1.64600	−	0.441045i	−0.958489	+	0.285128i	$0.907964\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.88483	−	2.38068i	−0.363632	−	0.0974348i
$598$		0			0
$599$	36.2716	+	20.9414i	1.48202	+	0.855644i	0.999792	−	0.0204023i	$-0.00649469\pi$
$599$	36.2716	+	20.9414i	1.48202	+	0.855644i	0.482227	+	0.876046i	$0.339828\pi$
$600$		0			0
$601$			3.49682i			0.142638i	0.997454	+	0.0713191i	$0.0227209\pi$
$601$			3.49682i			0.142638i	−0.997454	+	0.0713191i	$0.977279\pi$
$602$		0			0
$603$	3.55031	+	3.55031i	0.144580	+	0.144580i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	4.54613	−	16.9664i	0.184522	−	0.688644i	−0.810211	−	0.586138i	$-0.800647\pi$
$607$	4.54613	−	16.9664i	0.184522	−	0.688644i	0.994732	−	0.102505i	$-0.0326859\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−39.8214	−	68.9726i	−1.61100	−	2.79033i
$612$		0			0
$613$	35.6025	−	9.53966i	1.43797	−	0.385303i	0.546149	−	0.837688i	$-0.316093\pi$
$613$	35.6025	−	9.53966i	1.43797	−	0.385303i	0.891823	+	0.452385i	$0.149427\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.3023	−	11.3023i	0.455015	−	0.455015i	−0.442000	−	0.897015i	$-0.645731\pi$
$617$	11.3023	−	11.3023i	0.455015	−	0.455015i	0.897015	+	0.442000i	$0.145731\pi$
$618$		0			0
$619$	−22.7956	+	39.4832i	−0.916233	+	1.58696i	−0.111148	+	0.993804i	$0.535453\pi$
$619$	−22.7956	+	39.4832i	−0.916233	+	1.58696i	−0.805086	+	0.593159i	$0.797881\pi$
$620$		0			0
$621$	−4.84248	+	2.79580i	−0.194322	+	0.112192i
$622$		0			0
$623$	17.2650	+	11.3854i	0.691707	+	0.456145i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−5.86463	−	21.8871i	−0.234211	−	0.874087i
$628$		0			0
$629$	−7.81670			−0.311672
$630$		0			0
$631$	33.9029			1.34965			0.674827	−	0.737976i	$-0.264218\pi$
$631$	33.9029			1.34965			0.674827	+	0.737976i	$0.264218\pi$
$632$		0			0
$633$	−0.814251	−	3.03883i	−0.0323636	−	0.120782i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.16946	−	42.8424i	−0.244443	−	1.69748i
$638$		0			0
$639$	−12.4421	+	7.18348i	−0.492204	+	0.284174i
$640$		0			0
$641$	20.0634	−	34.7508i	0.792457	−	1.37258i	−0.131985	−	0.991252i	$-0.542135\pi$
$641$	20.0634	−	34.7508i	0.792457	−	1.37258i	0.924442	−	0.381324i	$-0.124532\pi$
$642$		0			0
$643$	−18.5960	+	18.5960i	−0.733357	+	0.733357i	−0.971283	−	0.237927i	$-0.923532\pi$
$643$	−18.5960	+	18.5960i	−0.733357	+	0.733357i	0.237927	+	0.971283i	$0.423532\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.2049	+	2.73439i	−0.401196	+	0.107500i	−0.453774	−	0.891117i	$-0.649923\pi$
$647$	−10.2049	+	2.73439i	−0.401196	+	0.107500i	0.0525785	+	0.998617i	$0.483256\pi$
$648$		0			0
$649$	−5.02090	−	8.69645i	−0.197088	−	0.341366i
$650$		0			0
$651$	−2.40826	−	11.7350i	−0.0943872	−	0.459932i
$652$		0			0
$653$	−11.1534	+	41.6249i	−0.436465	+	1.62891i	0.301071	+	0.953602i	$0.402656\pi$
$653$	−11.1534	+	41.6249i	−0.436465	+	1.62891i	−0.737536	+	0.675308i	$0.764011\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.06955	+	3.06955i	0.119755	+	0.119755i
$658$		0			0
$659$		−	10.4611i		−	0.407506i	−0.979022	−	0.203753i	$-0.934686\pi$
$659$		−	10.4611i		−	0.407506i	0.979022	−	0.203753i	$-0.0653139\pi$
$660$		0			0
$661$	−36.7584	−	21.2225i	−1.42974	−	0.825458i	−0.432636	−	0.901569i	$-0.642416\pi$
$661$	−36.7584	−	21.2225i	−1.42974	−	0.825458i	−0.997099	+	0.0761106i	$0.975750\pi$
$662$		0			0
$663$	−26.9550	−	7.22257i	−1.04685	−	0.280502i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−7.92069	−	4.57301i	−0.306232	−	0.176803i
$670$		0			0
$671$			33.0515i			1.27594i
$672$		0			0
$673$	−23.0223	−	23.0223i	−0.887445	−	0.887445i	0.106832	−	0.994277i	$-0.465929\pi$
$673$	−23.0223	−	23.0223i	−0.887445	−	0.887445i	−0.994277	+	0.106832i	$0.965929\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.39579	+	5.20915i	−0.0536444	+	0.200204i	−0.987547	−	0.157324i	$-0.949713\pi$
$677$	−1.39579	+	5.20915i	−0.0536444	+	0.200204i	0.933903	+	0.357527i	$0.116380\pi$
$678$		0			0
$679$	−12.5522	−	4.17625i	−0.481711	−	0.160270i
$680$		0			0
$681$	−7.84248	−	13.5836i	−0.300524	−	0.520523i
$682$		0			0
$683$	−36.9010	+	9.88759i	−1.41198	+	0.378338i	−0.882630	−	0.470068i	$-0.844229\pi$
$683$	−36.9010	+	9.88759i	−1.41198	+	0.378338i	−0.529346	+	0.848406i	$0.677563\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	13.0314	−	13.0314i	0.497180	−	0.497180i
$688$		0			0
$689$	37.9260	−	65.6898i	1.44487	−	2.50258i
$690$		0			0
$691$	−4.58451	+	2.64687i	−0.174403	+	0.100692i	−0.584660	−	0.811278i	$-0.698772\pi$
$691$	−4.58451	+	2.64687i	−0.174403	+	0.100692i	0.410257	+	0.911970i	$0.365439\pi$
$692$		0			0
$693$	5.34582	+	10.6766i	0.203071	+	0.405572i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.59901	−	9.69963i	−0.0984445	−	0.367400i
$698$		0			0
$699$	2.57560			0.0974182
$700$		0			0
$701$	17.8310			0.673467			0.336733	−	0.941600i	$-0.390678\pi$
$701$	17.8310			0.673467			0.336733	+	0.941600i	$0.390678\pi$
$702$		0			0
$703$	2.25081	+	8.40013i	0.0848908	+	0.316817i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	18.5557	+	1.10331i	0.697860	+	0.0414944i
$708$		0			0
$709$	−6.63289	+	3.82950i	−0.249103	+	0.143820i	−0.619354	−	0.785112i	$-0.712605\pi$
$709$	−6.63289	+	3.82950i	−0.249103	+	0.143820i	0.370250	+	0.928932i	$0.379272\pi$
$710$		0			0
$711$	0.914012	−	1.58312i	0.0342781	−	0.0593715i
$712$		0			0
$713$	17.9025	−	17.9025i	0.670455	−	0.670455i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.586409	+	0.157128i	−0.0218998	+	0.00586804i
$718$		0			0
$719$	−6.30870	−	10.9270i	−0.235275	−	0.407508i	0.724078	−	0.689718i	$-0.242266\pi$
$719$	−6.30870	−	10.9270i	−0.235275	−	0.407508i	−0.959353	+	0.282210i	$0.908932\pi$
$720$		0			0
$721$	10.8127	−	2.21898i	0.402685	−	0.0826390i
$722$		0			0
$723$	−2.24144	+	8.36516i	−0.0833600	+	0.311104i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−13.4799	−	13.4799i	−0.499940	−	0.499940i	0.411479	−	0.911419i	$-0.365012\pi$
$727$	−13.4799	−	13.4799i	−0.499940	−	0.499940i	−0.911419	+	0.411479i	$0.865012\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	43.4044	+	25.0595i	1.60537	+	0.926861i
$732$		0			0
$733$	−8.67111	−	2.32342i	−0.320275	−	0.0858174i	0.0951000	−	0.995468i	$-0.469683\pi$
$733$	−8.67111	−	2.32342i	−0.320275	−	0.0858174i	−0.415375	+	0.909650i	$0.636350\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	21.8871	+	5.86463i	0.806222	+	0.216026i
$738$		0			0
$739$	−12.5911	−	7.26946i	−0.463170	−	0.267412i	0.250206	−	0.968193i	$-0.419502\pi$
$739$	−12.5911	−	7.26946i	−0.463170	−	0.267412i	−0.713376	+	0.700781i	$0.752835\pi$
$740$		0			0
$741$			31.0466i			1.14053i
$742$		0			0
$743$	24.4486	+	24.4486i	0.896933	+	0.896933i	0.995164	−	0.0982305i	$-0.0313182\pi$
$743$	24.4486	+	24.4486i	0.896933	+	0.896933i	−0.0982305	+	0.995164i	$0.531318\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.10331	+	15.3138i	−0.150132	+	0.560301i
$748$		0			0
$749$	18.2090	−	3.73686i	0.665343	−	0.136542i
$750$		0			0
$751$	−21.4644	−	37.1775i	−0.783249	−	1.35663i	−0.930040	−	0.367459i	$-0.880228\pi$
$751$	−21.4644	−	37.1775i	−0.783249	−	1.35663i	0.146791	−	0.989168i	$-0.453105\pi$
$752$		0			0
$753$	27.2882	−	7.31185i	0.994437	−	0.266459i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−6.43514	+	6.43514i	−0.233889	+	0.233889i	−0.814314	−	0.580425i	$-0.802887\pi$
$757$	−6.43514	+	6.43514i	−0.233889	+	0.233889i	0.580425	+	0.814314i	$0.302887\pi$
$758$		0			0
$759$	−12.6174	+	21.8540i	−0.457983	+	0.793249i
$760$		0			0
$761$	12.2969	−	7.09961i	0.445762	−	0.257361i	−0.260277	−	0.965534i	$-0.583814\pi$
$761$	12.2969	−	7.09961i	0.445762	−	0.257361i	0.706039	+	0.708173i	$0.250480\pi$
$762$		0			0
$763$	35.7193	+	2.12385i	1.29313	+	0.0768886i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.56104	+	13.2900i	0.128582	+	0.479874i
$768$		0			0
$769$	−12.7272			−0.458955			−0.229478	−	0.973314i	$-0.573702\pi$
$769$	−12.7272			−0.458955			−0.229478	+	0.973314i	$0.573702\pi$
$770$		0			0
$771$	5.17198			0.186264
$772$		0			0
$773$	6.21166	+	23.1822i	0.223418	+	0.833806i	0.983032	+	0.183433i	$0.0587210\pi$
$773$	6.21166	+	23.1822i	0.223418	+	0.833806i	−0.759614	+	0.650374i	$0.774612\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.05169	−	4.09763i	−0.0736040	−	0.147002i
$778$		0			0
$779$	−9.67521	+	5.58599i	−0.346651	+	0.200139i
$780$		0			0
$781$	−32.4189	+	56.1511i	−1.16004	+	2.00924i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−4.00190	+	1.07231i	−0.142652	+	0.0382236i	−0.329439	−	0.944177i	$-0.606859\pi$
$787$	−4.00190	+	1.07231i	−0.142652	+	0.0382236i	0.186786	+	0.982401i	$0.440193\pi$
$788$		0			0
$789$	7.99196	+	13.8425i	0.284521	+	0.492805i
$790$		0			0
$791$	26.0894	+	8.68017i	0.927631	+	0.308631i
$792$		0			0
$793$	11.7208	−	43.7426i	0.416218	−	1.55335i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.2306	+	13.2306i	0.468652	+	0.468652i	0.901478	−	0.432826i	$-0.142483\pi$
$797$	13.2306	+	13.2306i	0.468652	+	0.468652i	−0.432826	+	0.901478i	$0.642483\pi$
$798$		0			0
$799$		−	58.1268i		−	2.05638i
$800$		0			0
$801$	6.76946	+	3.90835i	0.239187	+	0.138095i
$802$		0			0
$803$	18.9233	+	5.07048i	0.667788	+	0.178933i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	16.9114	+	4.53140i	0.595310	+	0.159513i
$808$		0			0
$809$	−8.68017	−	5.01150i	−0.305179	−	0.176195i	0.339588	−	0.940574i	$-0.389712\pi$
$809$	−8.68017	−	5.01150i	−0.305179	−	0.176195i	−0.644767	+	0.764379i	$0.723046\pi$
$810$		0			0
$811$			31.1243i			1.09292i	0.837485	+	0.546461i	$0.184025\pi$
$811$			31.1243i			1.09292i	−0.837485	+	0.546461i	$0.815975\pi$
$812$		0			0
$813$	7.65988	+	7.65988i	0.268644	+	0.268644i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	14.4317	−	53.8599i	0.504902	−	1.88432i
$818$		0			0
$819$	−3.28885	−	16.0260i	−0.114922	−	0.559992i
$820$		0			0
$821$	−6.74351	−	11.6801i	−0.235350	−	0.407638i	0.724024	−	0.689775i	$-0.242290\pi$
$821$	−6.74351	−	11.6801i	−0.235350	−	0.407638i	−0.959374	+	0.282136i	$0.908957\pi$
$822$		0			0
$823$	36.7944	−	9.85902i	1.28257	−	0.343664i	0.447737	−	0.894165i	$-0.352230\pi$
$823$	36.7944	−	9.85902i	1.28257	−	0.343664i	0.834834	+	0.550502i	$0.185564\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.6503	+	28.6503i	−0.996270	+	0.996270i	−0.999993	−	0.00372312i	$-0.998815\pi$
$827$	−28.6503	+	28.6503i	−0.996270	+	0.996270i	0.00372312	+	0.999993i	$0.498815\pi$
$828$		0			0
$829$	23.8430	−	41.2973i	0.828102	−	1.43431i	−0.0714231	−	0.997446i	$-0.522754\pi$
$829$	23.8430	−	41.2973i	0.828102	−	1.43431i	0.899525	−	0.436869i	$-0.143913\pi$
$830$		0			0
$831$	10.1292	−	5.84809i	0.351378	−	0.202868i
$832$		0			0
$833$	11.7347	−	29.3305i	0.406582	−	1.01624i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.17190	−	4.37357i	−0.0405066	−	0.151173i
$838$		0			0
$839$	−28.8941			−0.997534			−0.498767	−	0.866736i	$-0.666214\pi$
$839$	−28.8941			−0.997534			−0.498767	+	0.866736i	$0.666214\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	−6.60996	−	24.6687i	−0.227659	−	0.849636i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	20.6891	+	13.6434i	0.710885	+	0.468791i
$848$		0			0
$849$	−14.7574	+	8.52020i	−0.506473	+	0.292413i
$850$		0			0
$851$	4.84248	−	8.38741i	0.165998	−	0.287517i
$852$		0			0
$853$	−9.80855	+	9.80855i	−0.335838	+	0.335838i	−0.854798	−	0.518960i	$-0.826319\pi$
$853$	−9.80855	+	9.80855i	−0.335838	+	0.335838i	0.518960	+	0.854798i	$0.326319\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.6280	−	2.84777i	0.363047	−	0.0972781i	−0.0726843	−	0.997355i	$-0.523157\pi$
$857$	10.6280	−	2.84777i	0.363047	−	0.0972781i	0.435731	+	0.900077i	$0.356490\pi$
$858$		0			0
$859$	−3.76197	−	6.51593i	−0.128357	−	0.222321i	0.794683	−	0.607024i	$-0.207637\pi$
$859$	−3.76197	−	6.51593i	−0.128357	−	0.222321i	−0.923040	+	0.384704i	$0.874304\pi$
$860$		0			0
$861$	4.40251	−	3.90835i	0.150037	−	0.133196i
$862$		0			0
$863$	4.21271	−	15.7221i	0.143402	−	0.535185i	−0.856419	−	0.516282i	$-0.827316\pi$
$863$	4.21271	−	15.7221i	0.143402	−	0.535185i	0.999821	−	0.0189036i	$-0.00601755\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.38080	−	2.38080i	−0.0808560	−	0.0808560i
$868$		0			0
$869$		−	8.24983i		−	0.279856i
$870$		0			0
$871$	−26.8872	−	15.5233i	−0.911036	−	0.525987i
$872$		0			0
$873$	−4.82963	−	1.29410i	−0.163458	−	0.0437985i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−26.3233	−	7.05332i	−0.888876	−	0.238174i	−0.214643	−	0.976693i	$-0.568859\pi$
$877$	−26.3233	−	7.05332i	−0.888876	−	0.238174i	−0.674233	+	0.738519i	$0.735526\pi$
$878$		0			0
$879$	−0.525760	−	0.303548i	−0.0177334	−	0.0102384i
$880$		0			0
$881$			15.9839i			0.538512i	0.963069	+	0.269256i	$0.0867777\pi$
$881$			15.9839i			0.538512i	−0.963069	+	0.269256i	$0.913222\pi$
$882$		0			0
$883$	−37.9349	−	37.9349i	−1.27661	−	1.27661i	−0.942552	−	0.334059i	$-0.891581\pi$
$883$	−37.9349	−	37.9349i	−1.27661	−	1.27661i	−0.334059	−	0.942552i	$-0.608419\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.35779	+	34.9237i	−0.314204	+	1.17262i	0.610525	+	0.791997i	$0.290959\pi$
$887$	−9.35779	+	34.9237i	−0.314204	+	1.17262i	−0.924729	+	0.380627i	$0.875708\pi$
$888$		0			0
$889$	−12.6460	+	38.0091i	−0.424133	+	1.27478i
$890$		0			0
$891$	2.25649	+	3.90835i	0.0755952	+	0.130935i
$892$		0			0
$893$	−62.4653	+	16.7375i	−2.09032	+	0.560100i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	24.4486	−	24.4486i	0.816316	−	0.816316i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	47.9433	−	27.6801i	1.59722	−	0.922158i
$902$		0			0
$903$	−1.74399	+	29.3307i	−0.0580363	+	0.976065i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−7.04499	−	26.2923i	−0.233925	−	0.873021i	−0.978630	−	0.205627i	$-0.934077\pi$
$907$	−7.04499	−	26.2923i	−0.233925	−	0.873021i	0.744705	−	0.667394i	$-0.232590\pi$
$908$		0			0
$909$	7.02579			0.233031
$910$		0			0
$911$	−13.1009			−0.434051			−0.217025	−	0.976166i	$-0.569635\pi$
$911$	−13.1009			−0.434051			−0.217025	+	0.976166i	$0.569635\pi$
$912$		0			0
$913$	18.5181	+	69.1107i	0.612861	+	2.28723i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.6187	+	32.7831i	−0.713913	+	1.08259i
$918$		0			0
$919$	7.08965	−	4.09321i	0.233866	−	0.135023i	−0.378488	−	0.925606i	$-0.623556\pi$
$919$	7.08965	−	4.09321i	0.233866	−	0.135023i	0.612354	+	0.790583i	$0.290223\pi$
$920$		0			0
$921$	−7.94719	+	13.7649i	−0.261869	+	0.453570i
$922$		0			0
$923$	62.8178	−	62.8178i	2.06767	−	2.06767i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.02982	−	1.07979i	0.132357	−	0.0354648i
$928$		0			0
$929$	−14.8136	−	25.6579i	−0.486019	−	0.841810i	0.513852	−	0.857879i	$-0.328218\pi$
$929$	−14.8136	−	25.6579i	−0.486019	−	0.841810i	−0.999871	+	0.0160692i	$0.994885\pi$
$930$		0			0
$931$	−34.8987	−	4.16483i	−1.14376	−	0.136497i
$932$		0			0
$933$	−0.295421	+	1.10253i	−0.00967166	+	0.0360951i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.01202	+	2.01202i	0.0657298	+	0.0657298i	0.739208	−	0.673478i	$-0.235200\pi$
$937$	2.01202	+	2.01202i	0.0657298	+	0.0657298i	−0.673478	+	0.739208i	$0.735200\pi$
$938$		0			0
$939$		−	4.50147i		−	0.146900i
$940$		0			0
$941$	−32.2239	−	18.6045i	−1.05047	−	0.606488i	−0.127688	−	0.991814i	$-0.540756\pi$
$941$	−32.2239	−	18.6045i	−1.05047	−	0.606488i	−0.922780	+	0.385326i	$0.874089\pi$
$942$		0			0
$943$	12.0179	+	3.22019i	0.391357	+	0.104864i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.4618	−	6.55451i	−0.794901	−	0.212993i	−0.161557	−	0.986863i	$-0.551652\pi$
$947$	−24.4618	−	6.55451i	−0.794901	−	0.212993i	−0.633344	+	0.773870i	$0.718318\pi$
$948$		0			0
$949$	−23.2463	−	13.4212i	−0.754606	−	0.435672i
$950$		0			0
$951$		−	9.69129i		−	0.314262i
$952$		0			0
$953$	23.4345	+	23.4345i	0.759118	+	0.759118i	0.976162	−	0.217044i	$-0.0696414\pi$
$953$	23.4345	+	23.4345i	0.759118	+	0.759118i	−0.217044	+	0.976162i	$0.569641\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.00489	−	2.25838i	−0.0647413	−	0.0729270i
$960$		0			0
$961$	−5.24926	−	9.09199i	−0.169331	−	0.293290i
$962$		0			0
$963$	6.78639	−	1.81841i	0.218688	−	0.0585974i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	35.2925	−	35.2925i	1.13493	−	1.13493i	0.145584	−	0.989346i	$-0.453494\pi$
$967$	35.2925	−	35.2925i	1.13493	−	1.13493i	0.989346	−	0.145584i	$-0.0465062\pi$
$968$		0			0
$969$	−11.3296	+	19.6234i	−0.363959	+	0.630396i
$970$		0			0
$971$	−51.5438	+	29.7588i	−1.65412	+	0.955006i	−0.678765	+	0.734355i	$0.737485\pi$
$971$	−51.5438	+	29.7588i	−1.65412	+	0.955006i	−0.975353	+	0.220651i	$0.929182\pi$
$972$		0			0
$973$	48.6795	−	24.3740i	1.56059	−	0.781393i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.45522	+	20.3592i	0.174528	+	0.651348i	0.996632	+	0.0820096i	$0.0261338\pi$
$977$	5.45522	+	20.3592i	0.174528	+	0.651348i	−0.822103	+	0.569338i	$0.807200\pi$
$978$		0			0
$979$	35.2766			1.12744
$980$		0			0
$981$	13.5245			0.431803
$982$		0			0
$983$	9.45773	+	35.2967i	0.301655	+	1.12579i	0.935787	+	0.352566i	$0.114691\pi$
$983$	9.45773	+	35.2967i	0.301655	+	1.12579i	−0.634132	+	0.773225i	$0.718642\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	30.4709	−	15.2569i	0.969900	−	0.485631i
$988$		0			0
$989$	−53.7784	+	31.0490i	−1.71005	+	0.987299i
$990$		0			0
$991$	14.0903	−	24.4051i	0.447592	−	0.775252i	−0.550637	−	0.834745i	$-0.685615\pi$
$991$	14.0903	−	24.4051i	0.447592	−	0.775252i	0.998229	+	0.0594929i	$0.0189484\pi$
$992$		0			0
$993$	−2.69056	+	2.69056i	−0.0853823	+	0.0853823i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−25.0890	+	6.72258i	−0.794577	+	0.212906i	−0.633202	−	0.773987i	$-0.718260\pi$
$997$	−25.0890	+	6.72258i	−0.794577	+	0.212906i	−0.161375	+	0.986893i	$0.551593\pi$
$998$		0			0
$999$	−0.866025	−	1.50000i	−0.0273998	−	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.c.493.2	yes	24
5.2	odd	4	inner	2100.2.ce.c.157.3	✓	24
5.3	odd	4	inner	2100.2.ce.c.157.4	yes	24
5.4	even	2	inner	2100.2.ce.c.493.4	yes	24
7.5	odd	6	inner	2100.2.ce.c.1993.3	yes	24
35.12	even	12	inner	2100.2.ce.c.1657.2	yes	24
35.19	odd	6	inner	2100.2.ce.c.1993.4	yes	24
35.33	even	12	inner	2100.2.ce.c.1657.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.c.157.3	✓	24	5.2	odd	4	inner
2100.2.ce.c.157.4	yes	24	5.3	odd	4	inner
2100.2.ce.c.493.2	yes	24	1.1	even	1	trivial
2100.2.ce.c.493.4	yes	24	5.4	even	2	inner
2100.2.ce.c.1657.2	yes	24	35.12	even	12	inner
2100.2.ce.c.1657.4	yes	24	35.33	even	12	inner
2100.2.ce.c.1993.3	yes	24	7.5	odd	6	inner
2100.2.ce.c.1993.4	yes	24	35.19	odd	6	inner

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.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{3} +(-2.36577 + 1.18454i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{3} +(-2.36577 + 1.18454i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-2.25649 + 3.90835i) q^{11} +(4.37238 - 4.37238i) q^{13} +(4.35920 - 1.16804i) q^{17} +(-2.51045 - 4.34823i) q^{19} +(1.75649 + 1.97857i) q^{21} +(-1.44721 + 5.40108i) q^{23} +(0.707107 + 0.707107i) q^{27} +(-3.92124 - 2.26393i) q^{31} +(4.35920 + 1.16804i) q^{33} +(-1.67303 - 0.448288i) q^{37} +(-5.35505 - 3.09174i) q^{39} -2.22509i q^{41} +(7.85281 + 7.85281i) q^{43} +(3.33357 - 12.4411i) q^{47} +(4.19371 - 5.60471i) q^{49} +(-2.25649 - 3.90835i) q^{51} +(11.8489 - 3.17491i) q^{53} +(-3.55031 + 3.55031i) q^{57} +(-1.11255 + 1.92699i) q^{59} +(6.34248 - 3.66183i) q^{61} +(1.45654 - 2.20873i) q^{63} +(-1.29950 - 4.84982i) q^{67} +5.59161 q^{69} +14.3670 q^{71} +(-1.12353 - 4.19308i) q^{73} +(0.708707 - 11.9192i) q^{77} +(-1.58312 + 0.914012i) q^{79} +(0.500000 - 0.866025i) q^{81} +(11.2105 - 11.2105i) q^{83} +(-3.90835 - 6.76946i) q^{89} +(-5.16475 + 15.5233i) q^{91} +(-1.17190 + 4.37357i) q^{93} +(3.53553 + 3.53553i) q^{97} -4.51298i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{11} - 4 q^{21} - 60 q^{31} - 8 q^{51} + 84 q^{61} + 112 q^{71} + 12 q^{81} - 136 q^{91}+O(q^{100}) \) 24 * q - 8 * q^11 - 4 * q^21 - 60 * q^31 - 8 * q^51 + 84 * q^61 + 112 * q^71 + 12 * q^81 - 136 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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