LMFDB - Embedded newform 1368.2.e.g.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 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("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (of order $2$, degree $1$, 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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.1
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.g.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41195 - 0.0800606i) q^{2} +(1.98718 + 0.226082i) q^{4} -1.12499i q^{5} +4.22432i q^{7} +(-2.78769 - 0.478311i) q^{8} +O(q^{10})$	\(q+(-1.41195 - 0.0800606i) q^{2} +(1.98718 + 0.226082i) q^{4} -1.12499i q^{5} +4.22432i q^{7} +(-2.78769 - 0.478311i) q^{8} +(-0.0900673 + 1.58842i) q^{10} -2.32868 q^{11} +1.28719 q^{13} +(0.338202 - 5.96451i) q^{14} +(3.89777 + 0.898533i) q^{16} +4.98265 q^{17} +(-2.09531 - 3.82226i) q^{19} +(0.254340 - 2.23556i) q^{20} +(3.28798 + 0.186436i) q^{22} +7.45363i q^{23} +3.73440 q^{25} +(-1.81745 - 0.103054i) q^{26} +(-0.955044 + 8.39448i) q^{28} -3.42120 q^{29} -8.74423 q^{31} +(-5.43151 - 1.58074i) q^{32} +(-7.03522 - 0.398914i) q^{34} +4.75231 q^{35} +5.87915 q^{37} +(2.65245 + 5.56457i) q^{38} +(-0.538095 + 3.13612i) q^{40} +10.8123i q^{41} -10.4688 q^{43} +(-4.62752 - 0.526475i) q^{44} +(0.596742 - 10.5241i) q^{46} -5.81414i q^{47} -10.8449 q^{49} +(-5.27277 - 0.298978i) q^{50} +(2.55789 + 0.291012i) q^{52} -4.80109 q^{53} +2.61975i q^{55} +(2.02054 - 11.7761i) q^{56} +(4.83054 + 0.273903i) q^{58} +3.68157i q^{59} +8.19904i q^{61} +(12.3464 + 0.700069i) q^{62} +(7.54244 + 2.66677i) q^{64} -1.44808i q^{65} +4.42230i q^{67} +(9.90142 + 1.12649i) q^{68} +(-6.71001 - 0.380473i) q^{70} +11.1441 q^{71} +8.02158 q^{73} +(-8.30104 - 0.470688i) q^{74} +(-3.29962 - 8.06923i) q^{76} -9.83711i q^{77} -5.34856 q^{79} +(1.01084 - 4.38495i) q^{80} +(0.865637 - 15.2663i) q^{82} -4.86570 q^{83} -5.60542i q^{85} +(14.7814 + 0.838141i) q^{86} +(6.49165 + 1.11384i) q^{88} -3.70180i q^{89} +5.43752i q^{91} +(-1.68514 + 14.8117i) q^{92} +(-0.465484 + 8.20925i) q^{94} +(-4.30000 + 2.35720i) q^{95} +10.4738i q^{97} +(15.3124 + 0.868247i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4}+O(q^{10}) $ 40 * q - 4 * q^4	$ 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.41195	−	0.0800606i	−0.998396	−	0.0566114i
$2$	−1.41195	−	0.0800606i	−0.998396	−	0.0566114i
$3$		0			0
$3$		0			0
$4$	1.98718	+	0.226082i	0.993590	+	0.113041i
$5$		−	1.12499i		−	0.503111i	−0.967843	−	0.251555i	$-0.919058\pi$
$5$		−	1.12499i		−	0.503111i	0.967843	−	0.251555i	$-0.0809420\pi$
$6$		0			0
$7$			4.22432i			1.59664i	0.602232	+	0.798321i	$0.294278\pi$
$7$			4.22432i			1.59664i	−0.602232	+	0.798321i	$0.705722\pi$
$8$	−2.78769	−	0.478311i	−0.985597	−	0.169108i
$9$		0			0
$10$	−0.0900673	+	1.58842i	−0.0284818	+	0.502304i
$11$	−2.32868			−0.702125			−0.351062	−	0.936352i	$-0.614180\pi$
$11$	−2.32868			−0.702125			−0.351062	+	0.936352i	$0.614180\pi$
$12$		0			0
$13$	1.28719			0.357003			0.178502	−	0.983940i	$-0.442875\pi$
$13$	1.28719			0.357003			0.178502	+	0.983940i	$0.442875\pi$
$14$	0.338202	−	5.96451i	0.0903882	−	1.59408i
$15$		0			0
$16$	3.89777	+	0.898533i	0.974443	+	0.224633i
$17$	4.98265			1.20847			0.604234	−	0.796807i	$-0.293479\pi$
$17$	4.98265			1.20847			0.604234	+	0.796807i	$0.293479\pi$
$18$		0			0
$19$	−2.09531	−	3.82226i	−0.480698	−	0.876886i
$19$	−2.09531	−	3.82226i	−0.480698	−	0.876886i
$20$	0.254340	−	2.23556i	0.0568722	−	0.499886i
$21$		0			0
$22$	3.28798	+	0.186436i	0.700999	+	0.0397483i
$23$			7.45363i			1.55419i	0.629384	+	0.777095i	$0.283307\pi$
$23$			7.45363i			1.55419i	−0.629384	+	0.777095i	$0.716693\pi$
$24$		0			0
$25$	3.73440			0.746880
$26$	−1.81745	−	0.103054i	−0.356431	−	0.0202105i
$27$		0			0
$28$	−0.955044	+	8.39448i	−0.180486	+	1.58641i
$29$	−3.42120			−0.635300			−0.317650	−	0.948208i	$-0.602894\pi$
$29$	−3.42120			−0.635300			−0.317650	+	0.948208i	$0.602894\pi$
$30$		0			0
$31$	−8.74423			−1.57051			−0.785255	−	0.619172i	$-0.787468\pi$
$31$	−8.74423			−1.57051			−0.785255	+	0.619172i	$0.787468\pi$
$32$	−5.43151	−	1.58074i	−0.960164	−	0.279438i
$33$		0			0
$34$	−7.03522	−	0.398914i	−1.20653	−	0.0684131i
$35$	4.75231			0.803288
$36$		0			0
$37$	5.87915			0.966526			0.483263	−	0.875475i	$-0.339452\pi$
$37$	5.87915			0.966526			0.483263	+	0.875475i	$0.339452\pi$
$38$	2.65245	+	5.56457i	0.430285	+	0.902693i
$39$		0			0
$40$	−0.538095	+	3.13612i	−0.0850803	+	0.495864i
$41$			10.8123i			1.68859i	0.535876	+	0.844297i	$0.319981\pi$
$41$			10.8123i			1.68859i	−0.535876	+	0.844297i	$0.680019\pi$
$42$		0			0
$43$	−10.4688			−1.59648			−0.798241	−	0.602339i	$-0.794236\pi$
$43$	−10.4688			−1.59648			−0.798241	+	0.602339i	$0.794236\pi$
$44$	−4.62752	−	0.526475i	−0.697624	−	0.0793691i
$45$		0			0
$46$	0.596742	−	10.5241i	0.0879849	−	1.55170i
$47$		−	5.81414i		−	0.848080i	−0.905644	−	0.424040i	$-0.860612\pi$
$47$		−	5.81414i		−	0.848080i	0.905644	−	0.424040i	$-0.139388\pi$
$48$		0			0
$49$	−10.8449			−1.54927
$50$	−5.27277	−	0.298978i	−0.745682	−	0.0422819i
$51$		0			0
$52$	2.55789	+	0.291012i	0.354715	+	0.0403561i
$53$	−4.80109			−0.659481			−0.329740	−	0.944072i	$-0.606961\pi$
$53$	−4.80109			−0.659481			−0.329740	+	0.944072i	$0.606961\pi$
$54$		0			0
$55$			2.61975i			0.353246i
$56$	2.02054	−	11.7761i	0.270006	−	1.57365i
$57$		0			0
$58$	4.83054	+	0.273903i	0.634281	+	0.0359652i
$59$			3.68157i			0.479299i	0.970859	+	0.239650i	$0.0770325\pi$
$59$			3.68157i			0.479299i	−0.970859	+	0.239650i	$0.922967\pi$
$60$		0			0
$61$			8.19904i			1.04978i	0.851170	+	0.524890i	$0.175894\pi$
$61$			8.19904i			1.04978i	−0.851170	+	0.524890i	$0.824106\pi$
$62$	12.3464	+	0.700069i	1.56799	+	0.0889088i
$63$		0			0
$64$	7.54244	+	2.66677i	0.942805	+	0.333346i
$65$		−	1.44808i		−	0.179612i
$66$		0			0
$67$			4.42230i			0.540270i	0.962822	+	0.270135i	$0.0870684\pi$
$67$			4.42230i			0.540270i	−0.962822	+	0.270135i	$0.912932\pi$
$68$	9.90142	+	1.12649i	1.20072	+	0.136607i
$69$		0			0
$70$	−6.71001	−	0.380473i	−0.801999	−	0.0454752i
$71$	11.1441			1.32256			0.661279	−	0.750140i	$-0.270014\pi$
$71$	11.1441			1.32256			0.661279	+	0.750140i	$0.270014\pi$
$72$		0			0
$73$	8.02158			0.938855			0.469427	−	0.882971i	$-0.344460\pi$
$73$	8.02158			0.938855			0.469427	+	0.882971i	$0.344460\pi$
$74$	−8.30104	−	0.470688i	−0.964976	−	0.0547164i
$75$		0			0
$76$	−3.29962	−	8.06923i	−0.378492	−	0.925605i
$77$		−	9.83711i		−	1.12104i
$78$		0			0
$79$	−5.34856			−0.601760			−0.300880	−	0.953662i	$-0.597280\pi$
$79$	−5.34856			−0.601760			−0.300880	+	0.953662i	$0.597280\pi$
$80$	1.01084	−	4.38495i	0.113015	−	0.490253i
$81$		0			0
$82$	0.865637	−	15.2663i	0.0955936	−	1.68589i
$83$	−4.86570			−0.534080			−0.267040	−	0.963685i	$-0.586046\pi$
$83$	−4.86570			−0.534080			−0.267040	+	0.963685i	$0.586046\pi$
$84$		0			0
$85$		−	5.60542i		−	0.607993i
$86$	14.7814	+	0.838141i	1.59392	+	0.0903791i
$87$		0			0
$88$	6.49165	+	1.11384i	0.692012	+	0.118735i
$89$		−	3.70180i		−	0.392390i	−0.980565	−	0.196195i	$-0.937141\pi$
$89$		−	3.70180i		−	0.392390i	0.980565	−	0.196195i	$-0.0628586\pi$
$90$		0			0
$91$			5.43752i			0.570007i
$92$	−1.68514	+	14.8117i	−0.175688	+	1.54423i
$93$		0			0
$94$	−0.465484	+	8.20925i	−0.0480110	+	0.846720i
$95$	−4.30000	+	2.35720i	−0.441171	+	0.241844i
$96$		0			0
$97$			10.4738i			1.06346i	0.846915	+	0.531728i	$0.178457\pi$
$97$			10.4738i			1.06346i	−0.846915	+	0.531728i	$0.821543\pi$
$98$	15.3124	+	0.868247i	1.54678	+	0.0877062i
$99$		0			0
$100$	7.42093	+	0.844282i	0.742093	+	0.0844282i
$101$			11.9942i			1.19346i	0.802441	+	0.596732i	$0.203534\pi$
$101$			11.9942i			1.19346i	−0.802441	+	0.596732i	$0.796466\pi$
$102$		0			0
$103$	−10.2940			−1.01429			−0.507147	−	0.861859i	$-0.669300\pi$
$103$	−10.2940			−1.01429			−0.507147	+	0.861859i	$0.669300\pi$
$104$	−3.58830	−	0.615679i	−0.351862	−	0.0603723i
$105$		0			0
$106$	6.77888	+	0.384378i	0.658423	+	0.0373341i
$107$			8.10172i			0.783223i	0.920131	+	0.391611i	$0.128082\pi$
$107$			8.10172i			0.783223i	−0.920131	+	0.391611i	$0.871918\pi$
$108$		0			0
$109$	−4.56924			−0.437654			−0.218827	−	0.975764i	$-0.570223\pi$
$109$	−4.56924			−0.437654			−0.218827	+	0.975764i	$0.570223\pi$
$110$	0.209738	−	3.69894i	0.0199978	−	0.352680i
$111$		0			0
$112$	−3.79569	+	16.4654i	−0.358659	+	1.55584i
$113$			13.6437i			1.28349i	0.766917	+	0.641747i	$0.221790\pi$
$113$			13.6437i			1.28349i	−0.766917	+	0.641747i	$0.778210\pi$
$114$		0			0
$115$	8.38526			0.781929
$116$	−6.79854	−	0.773473i	−0.631228	−	0.0718151i
$117$		0			0
$118$	0.294748	−	5.19817i	0.0271338	−	0.478530i
$119$			21.0483i			1.92949i
$120$		0			0
$121$	−5.57723			−0.507021
$122$	0.656421	−	11.5766i	0.0594295	−	1.04810i
$123$		0			0
$124$	−17.3764	−	1.97692i	−1.56044	−	0.177532i
$125$		−	9.82611i		−	0.878874i
$126$		0			0
$127$	−12.1078			−1.07439			−0.537196	−	0.843457i	$-0.680517\pi$
$127$	−12.1078			−1.07439			−0.537196	+	0.843457i	$0.680517\pi$
$128$	−10.4360	−	4.36918i	−0.922421	−	0.386185i
$129$		0			0
$130$	−0.115934	+	2.04461i	−0.0101681	+	0.179324i
$131$	−13.9009			−1.21452			−0.607262	−	0.794501i	$-0.707732\pi$
$131$	−13.9009			−1.21452			−0.607262	+	0.794501i	$0.707732\pi$
$132$		0			0
$133$	16.1464	−	8.85127i	1.40007	−	0.767502i
$134$	0.354052	−	6.24405i	0.0305855	−	0.539404i
$135$		0			0
$136$	−13.8901	−	2.38325i	−1.19106	−	0.204362i
$137$	−3.60454			−0.307956			−0.153978	−	0.988074i	$-0.549209\pi$
$137$	−3.60454			−0.307956			−0.153978	+	0.988074i	$0.549209\pi$
$138$		0			0
$139$	4.68573			0.397439			0.198719	−	0.980056i	$-0.436322\pi$
$139$	4.68573			0.397439			0.198719	+	0.980056i	$0.436322\pi$
$140$	9.44371	+	1.07441i	0.798139	+	0.0908046i
$141$		0			0
$142$	−15.7348	−	0.892201i	−1.32044	−	0.0748718i
$143$	−2.99747			−0.250661
$144$		0			0
$145$			3.84881i			0.319626i
$146$	−11.3260	−	0.642213i	−0.937349	−	0.0531499i
$147$		0			0
$148$	11.6829	+	1.32917i	0.960331	+	0.109257i
$149$		−	0.386873i		−	0.0316938i	−0.999874	−	0.0158469i	$-0.994956\pi$
$149$		−	0.386873i		−	0.0316938i	0.999874	−	0.0158469i	$-0.00504444\pi$
$150$		0			0
$151$	18.1175			1.47438			0.737191	−	0.675684i	$-0.236152\pi$
$151$	18.1175			1.47438			0.737191	+	0.675684i	$0.236152\pi$
$152$	4.01285	+	11.6575i	0.325485	+	0.945547i
$153$		0			0
$154$	−0.787565	+	13.8895i	−0.0634638	+	1.11924i
$155$			9.83717i			0.790140i
$156$		0			0
$157$		−	1.49314i		−	0.119166i	−0.998223	−	0.0595828i	$-0.981023\pi$
$157$		−	1.49314i		−	0.119166i	0.998223	−	0.0595828i	$-0.0189770\pi$
$158$	7.55188	+	0.428209i	0.600795	+	0.0340665i
$159$		0			0
$160$	−1.77831	+	6.11039i	−0.140588	+	0.483069i
$161$	−31.4865			−2.48148
$162$		0			0
$163$	22.1804			1.73730			0.868652	−	0.495422i	$-0.164987\pi$
$163$	22.1804			1.73730			0.868652	+	0.495422i	$0.164987\pi$
$164$	−2.44447	+	21.4859i	−0.190881	+	1.67777i
$165$		0			0
$166$	6.87010	+	0.389551i	0.533223	+	0.0302350i
$167$	8.16713			0.631991			0.315996	−	0.948761i	$-0.397661\pi$
$167$	8.16713			0.631991			0.315996	+	0.948761i	$0.397661\pi$
$168$		0			0
$169$	−11.3431			−0.872549
$170$	−0.448774	+	7.91455i	−0.0344194	+	0.607018i
$171$		0			0
$172$	−20.8035	−	2.36682i	−1.58625	−	0.180468i
$173$	10.9944			0.835891			0.417945	−	0.908472i	$-0.362750\pi$
$173$	10.9944			0.835891			0.417945	+	0.908472i	$0.362750\pi$
$174$		0			0
$175$			15.7753i			1.19250i
$176$	−9.07669	−	2.09240i	−0.684181	−	0.157721i
$177$		0			0
$178$	−0.296369	+	5.22674i	−0.0222138	+	0.391761i
$179$			18.6590i			1.39464i	0.716760	+	0.697320i	$0.245624\pi$
$179$			18.6590i			1.39464i	−0.716760	+	0.697320i	$0.754376\pi$
$180$		0			0
$181$	3.58898			0.266767			0.133384	−	0.991064i	$-0.457416\pi$
$181$	3.58898			0.266767			0.133384	+	0.991064i	$0.457416\pi$
$182$	0.435331	−	7.67748i	0.0322689	−	0.569092i
$183$		0			0
$184$	3.56515	−	20.7784i	0.262827	−	1.53181i
$185$		−	6.61398i		−	0.486269i
$186$		0			0
$187$	−11.6030			−0.848496
$188$	1.31448	−	11.5537i	0.0958680	−	0.842644i
$189$		0			0
$190$	6.26009	−	2.98398i	0.454154	−	0.216481i
$191$			12.0060i			0.868723i	0.900739	+	0.434361i	$0.143026\pi$
$191$			12.0060i			0.868723i	−0.900739	+	0.434361i	$0.856974\pi$
$192$		0			0
$193$			2.52307i			0.181615i	0.995868	+	0.0908073i	$0.0289447\pi$
$193$			2.52307i			0.181615i	−0.995868	+	0.0908073i	$0.971055\pi$
$194$	0.838540	−	14.7885i	0.0602037	−	1.06175i
$195$		0			0
$196$	−21.5507	−	2.45183i	−1.53934	−	0.175131i
$197$		−	21.5963i		−	1.53868i	−0.638842	−	0.769338i	$-0.720586\pi$
$197$		−	21.5963i		−	1.53868i	0.638842	−	0.769338i	$-0.279414\pi$
$198$		0			0
$199$			15.8511i			1.12366i	0.827254	+	0.561828i	$0.189902\pi$
$199$			15.8511i			1.12366i	−0.827254	+	0.561828i	$0.810098\pi$
$200$	−10.4103	−	1.78620i	−0.736123	−	0.126304i
$201$		0			0
$202$	0.960260	−	16.9351i	0.0675637	−	1.19155i
$203$		−	14.4522i		−	1.01435i
$204$		0			0
$205$	12.1637			0.849549
$206$	14.5345	+	0.824141i	1.01267	+	0.0574207i
$207$		0			0
$208$	5.01719	+	1.15659i	0.347879	+	0.0801948i
$209$	4.87932	+	8.90084i	0.337510	+	0.615684i
$210$		0			0
$211$			24.8228i			1.70887i	0.519557	+	0.854436i	$0.326097\pi$
$211$			24.8228i			1.70887i	−0.519557	+	0.854436i	$0.673903\pi$
$212$	−9.54064	−	1.08544i	−0.655254	−	0.0745485i
$213$		0			0
$214$	0.648629	−	11.4392i	0.0443394	−	0.781967i
$215$			11.7773i			0.803207i
$216$		0			0
$217$		−	36.9384i		−	2.50754i
$218$	6.45152	+	0.365816i	0.436952	+	0.0247762i
$219$		0			0
$220$	−0.592279	+	5.20591i	−0.0399314	+	0.350982i
$221$	6.41363			0.431427
$222$		0			0
$223$	1.86315			0.124766			0.0623828	−	0.998052i	$-0.480130\pi$
$223$	1.86315			0.124766			0.0623828	+	0.998052i	$0.480130\pi$
$224$	6.67754	−	22.9444i	0.446162	−	1.53304i
$225$		0			0
$226$	1.09232	−	19.2642i	0.0726604	−	1.28143i
$227$		−	6.29554i		−	0.417850i	−0.977932	−	0.208925i	$-0.933004\pi$
$227$		−	6.29554i		−	0.417850i	0.977932	−	0.208925i	$-0.0669964\pi$
$228$		0			0
$229$		−	5.30243i		−	0.350394i	−0.984533	−	0.175197i	$-0.943944\pi$
$229$		−	5.30243i		−	0.350394i	0.984533	−	0.175197i	$-0.0560563\pi$
$230$	−11.8395	−	0.671329i	−0.780675	−	0.0442661i
$231$		0			0
$232$	9.53724	+	1.63640i	0.626150	+	0.107435i
$233$	−19.1977			−1.25768			−0.628840	−	0.777535i	$-0.716470\pi$
$233$	−19.1977			−1.25768			−0.628840	+	0.777535i	$0.716470\pi$
$234$		0			0
$235$	−6.54085			−0.426678
$236$	−0.832338	+	7.31594i	−0.0541806	+	0.476227i
$237$		0			0
$238$	1.68514	−	29.7190i	0.109231	−	1.92640i
$239$		−	16.1562i		−	1.04505i	−0.852622	−	0.522527i	$-0.824989\pi$
$239$		−	16.1562i		−	1.04505i	0.852622	−	0.522527i	$-0.175011\pi$
$240$		0			0
$241$			16.5131i			1.06370i	0.846838	+	0.531851i	$0.178503\pi$
$241$			16.5131i			1.06370i	−0.846838	+	0.531851i	$0.821497\pi$
$242$	7.87474	+	0.446516i	0.506208	+	0.0287032i
$243$		0			0
$244$	−1.85366	+	16.2930i	−0.118668	+	1.04305i
$245$			12.2004i			0.779453i
$246$		0			0
$247$	−2.69707	−	4.91999i	−0.171611	−	0.313051i
$248$	24.3762	+	4.18246i	1.54789	+	0.265587i
$249$		0			0
$250$	−0.786684	+	13.8739i	−0.0497543	+	0.877464i
$251$	28.4139			1.79347			0.896735	−	0.442569i	$-0.145933\pi$
$251$	28.4139			1.79347			0.896735	+	0.442569i	$0.145933\pi$
$252$		0			0
$253$		−	17.3572i		−	1.09124i
$254$	17.0955	+	0.969357i	1.07267	+	0.0608229i
$255$		0			0
$256$	14.3853	+	7.00456i	0.899080	+	0.437785i
$257$		−	3.69915i		−	0.230747i	−0.993322	−	0.115373i	$-0.963194\pi$
$257$		−	3.69915i		−	0.230747i	0.993322	−	0.115373i	$-0.0368064\pi$
$258$		0			0
$259$			24.8354i			1.54320i
$260$	0.327385	−	2.87759i	0.0203036	−	0.178461i
$261$		0			0
$262$	19.6273	+	1.11291i	1.21258	+	0.0687559i
$263$		−	24.3517i		−	1.50159i	−0.660534	−	0.750796i	$-0.729670\pi$
$263$		−	24.3517i		−	1.50159i	0.660534	−	0.750796i	$-0.270330\pi$
$264$		0			0
$265$			5.40118i			0.331792i
$266$	−23.5065	+	11.2048i	−1.44128	+	0.687011i
$267$		0			0
$268$	−0.999805	+	8.78791i	−0.0610728	+	0.536807i
$269$	6.60975			0.403004			0.201502	−	0.979488i	$-0.435418\pi$
$269$	6.60975			0.403004			0.201502	+	0.979488i	$0.435418\pi$
$270$		0			0
$271$		−	2.41559i		−	0.146737i	−0.997305	−	0.0733683i	$-0.976625\pi$
$271$		−	2.41559i		−	0.146737i	0.997305	−	0.0733683i	$-0.0233749\pi$
$272$	19.4212	+	4.47707i	1.17758	+	0.271462i
$273$		0			0
$274$	5.08941	+	0.288581i	0.307462	+	0.0174338i
$275$	−8.69624			−0.524403
$276$		0			0
$277$			0.470041i			0.0282420i	0.999900	+	0.0141210i	$0.00449501\pi$
$277$			0.470041i			0.0282420i	−0.999900	+	0.0141210i	$0.995505\pi$
$278$	−6.61600	−	0.375143i	−0.396801	−	0.0224996i
$279$		0			0
$280$	−13.2480	−	2.27308i	−0.791718	−	0.135843i
$281$		−	11.3088i		−	0.674624i	−0.941393	−	0.337312i	$-0.890482\pi$
$281$		−	11.3088i		−	0.674624i	0.941393	−	0.337312i	$-0.109518\pi$
$282$		0			0
$283$	12.2556			0.728517			0.364258	−	0.931298i	$-0.381322\pi$
$283$	12.2556			0.728517			0.364258	+	0.931298i	$0.381322\pi$
$284$	22.1453	+	2.51948i	1.31408	+	0.149504i
$285$		0			0
$286$	4.23226	+	0.239979i	0.250259	+	0.0141903i
$287$	−45.6745			−2.69608
$288$		0			0
$289$	7.82675			0.460397
$290$	0.308138	−	5.43431i	0.0180945	−	0.319114i
$291$		0			0
$292$	15.9403	+	1.81354i	0.932837	+	0.106129i
$293$	−0.185855			−0.0108577			−0.00542887	−	0.999985i	$-0.501728\pi$
$293$	−0.185855			−0.0108577			−0.00542887	+	0.999985i	$0.501728\pi$
$294$		0			0
$295$	4.14172			0.241140
$296$	−16.3892	−	2.81206i	−0.952605	−	0.163448i
$297$		0			0
$298$	−0.0309733	+	0.546243i	−0.00179423	+	0.0316430i
$299$			9.59427i			0.554851i
$300$		0			0
$301$		−	44.2237i		−	2.54901i
$302$	−25.5809	−	1.45050i	−1.47202	−	0.0834669i
$303$		0			0
$304$	−4.73262	−	16.7810i	−0.271435	−	0.962457i
$305$	9.22384			0.528155
$306$		0			0
$307$		−	34.5057i		−	1.96934i	−0.174414	−	0.984672i	$-0.555803\pi$
$307$		−	34.5057i		−	1.96934i	0.174414	−	0.984672i	$-0.444197\pi$
$308$	2.22400	−	19.5481i	0.126724	−	1.11386i
$309$		0			0
$310$	0.787570	−	13.8895i	0.0447310	−	0.788873i
$311$		−	12.8684i		−	0.729697i	−0.931067	−	0.364849i	$-0.881121\pi$
$311$		−	12.8684i		−	0.729697i	0.931067	−	0.364849i	$-0.118879\pi$
$312$		0			0
$313$	18.0506			1.02028			0.510139	−	0.860092i	$-0.329594\pi$
$313$	18.0506			1.02028			0.510139	+	0.860092i	$0.329594\pi$
$314$	−0.119542	+	2.10823i	−0.00674613	+	0.118974i
$315$		0			0
$316$	−10.6286	−	1.20922i	−0.597903	−	0.0680237i
$317$	−11.6086			−0.652004			−0.326002	−	0.945369i	$-0.605702\pi$
$317$	−11.6086			−0.652004			−0.326002	+	0.945369i	$0.605702\pi$
$318$		0			0
$319$	7.96689			0.446060
$320$	3.00008	−	8.48516i	0.167710	−	0.474335i
$321$		0			0
$322$	44.4572	+	2.52083i	2.47751	+	0.140480i
$323$	−10.4402	−	19.0450i	−0.580908	−	1.05969i
$324$		0			0
$325$	4.80689			0.266639
$326$	−31.3176	−	1.77578i	−1.73452	−	0.0983513i
$327$		0			0
$328$	5.17163	−	30.1413i	0.285555	−	1.66427i
$329$	24.5608			1.35408
$330$		0			0
$331$		−	2.63344i		−	0.144747i	−0.997378	−	0.0723735i	$-0.976943\pi$
$331$		−	2.63344i		−	0.144747i	0.997378	−	0.0723735i	$-0.0230573\pi$
$332$	−9.66902	−	1.10005i	−0.530656	−	0.0603730i
$333$		0			0
$334$	−11.5315	−	0.653865i	−0.630978	−	0.0357779i
$335$	4.97504			0.271816
$336$		0			0
$337$			7.52701i			0.410022i	0.978760	+	0.205011i	$0.0657231\pi$
$337$			7.52701i			0.410022i	−0.978760	+	0.205011i	$0.934277\pi$
$338$	16.0159	+	0.908138i	0.871149	+	0.0493962i
$339$		0			0
$340$	1.26729	−	11.1390i	0.0687283	−	0.604096i
$341$	20.3626			1.10269
$342$		0			0
$343$		−	16.2420i		−	0.876983i
$344$	29.1839	+	5.00736i	1.57349	+	0.269979i
$345$		0			0
$346$	−15.5235	−	0.880221i	−0.834550	−	0.0473210i
$347$	−12.8351			−0.689026			−0.344513	−	0.938782i	$-0.611956\pi$
$347$	−12.8351			−0.689026			−0.344513	+	0.938782i	$0.611956\pi$
$348$		0			0
$349$		−	10.4275i		−	0.558170i	−0.960266	−	0.279085i	$-0.909969\pi$
$349$		−	10.4275i		−	0.558170i	0.960266	−	0.279085i	$-0.0900311\pi$
$350$	1.26298	−	22.2739i	0.0675091	−	1.19059i
$351$		0			0
$352$	12.6483	+	3.68104i	0.674155	+	0.196200i
$353$	9.35287			0.497803			0.248902	−	0.968529i	$-0.419930\pi$
$353$	9.35287			0.497803			0.248902	+	0.968529i	$0.419930\pi$
$354$		0			0
$355$		−	12.5370i		−	0.665393i
$356$	0.836913	−	7.35615i	0.0443563	−	0.389875i
$357$		0			0
$358$	1.49385	−	26.3455i	0.0789525	−	1.39240i
$359$			10.0226i			0.528974i	0.964389	+	0.264487i	$0.0852026\pi$
$359$			10.0226i			0.528974i	−0.964389	+	0.264487i	$0.914797\pi$
$360$		0			0
$361$	−10.2193	+	16.0177i	−0.537860	+	0.843034i
$362$	−5.06745	−	0.287336i	−0.266339	−	0.0151021i
$363$		0			0
$364$	−1.22933	+	10.8053i	−0.0644343	+	0.566353i
$365$		−	9.02419i		−	0.472348i
$366$		0			0
$367$			15.0268i			0.784391i	0.919882	+	0.392195i	$0.128284\pi$
$367$			15.0268i			0.784391i	−0.919882	+	0.392195i	$0.871716\pi$
$368$	−6.69734	+	29.0526i	−0.349123	+	1.51447i
$369$		0			0
$370$	−0.529519	+	9.33858i	−0.0275284	+	0.485490i
$371$		−	20.2813i		−	1.05296i
$372$		0			0
$373$	−11.3317			−0.586732			−0.293366	−	0.956000i	$-0.594775\pi$
$373$	−11.3317			−0.586732			−0.293366	+	0.956000i	$0.594775\pi$
$374$	16.3828	+	0.928944i	0.847135	+	0.0480346i
$375$		0			0
$376$	−2.78097	+	16.2080i	−0.143417	+	0.835865i
$377$	−4.40374			−0.226804
$378$		0			0
$379$		−	30.7294i		−	1.57846i	−0.614097	−	0.789230i	$-0.710480\pi$
$379$		−	30.7294i		−	1.57846i	0.614097	−	0.789230i	$-0.289520\pi$
$380$	−9.07780	+	3.71203i	−0.465681	+	0.190423i
$381$		0			0
$382$	0.961207	−	16.9518i	0.0491796	−	0.867329i
$383$	7.40355			0.378304			0.189152	−	0.981948i	$-0.439426\pi$
$383$	7.40355			0.378304			0.189152	+	0.981948i	$0.439426\pi$
$384$		0			0
$385$	−11.0666			−0.564008
$386$	0.201999	−	3.56244i	0.0102815	−	0.181323i
$387$		0			0
$388$	−2.36795	+	20.8134i	−0.120214	+	1.05664i
$389$		−	5.16670i		−	0.261962i	−0.991385	−	0.130981i	$-0.958187\pi$
$389$		−	5.16670i		−	0.261962i	0.991385	−	0.130981i	$-0.0418127\pi$
$390$		0			0
$391$			37.1388i			1.87819i
$392$	30.2321	+	5.18722i	1.52695	+	0.261994i
$393$		0			0
$394$	−1.72902	+	30.4929i	−0.0871066	+	1.53621i
$395$			6.01707i			0.302752i
$396$		0			0
$397$		−	21.8802i		−	1.09813i	−0.835778	−	0.549067i	$-0.814983\pi$
$397$		−	21.8802i		−	1.09813i	0.835778	−	0.549067i	$-0.185017\pi$
$398$	1.26905	−	22.3809i	0.0636117	−	1.12185i
$399$		0			0
$400$	14.5558	+	3.35548i	0.727792	+	0.167774i
$401$		−	23.6016i		−	1.17861i	−0.807912	−	0.589304i	$-0.799402\pi$
$401$		−	23.6016i		−	1.17861i	0.807912	−	0.589304i	$-0.200598\pi$
$402$		0			0
$403$	−11.2555			−0.560677
$404$	−2.71167	+	23.8346i	−0.134911	+	1.18581i
$405$		0			0
$406$	−1.15705	+	20.4058i	−0.0574236	+	1.01272i
$407$	−13.6907			−0.678622
$408$		0			0
$409$		−	1.05710i		−	0.0522701i	−0.999658	−	0.0261351i	$-0.991680\pi$
$409$		−	1.05710i		−	0.0522701i	0.999658	−	0.0261351i	$-0.00831999\pi$
$410$	−17.1745	−	0.973833i	−0.848187	−	0.0480942i
$411$		0			0
$412$	−20.4560	−	2.32729i	−1.00779	−	0.114657i
$413$	−15.5521			−0.765269
$414$		0			0
$415$			5.47386i			0.268701i
$416$	−6.99140	−	2.03472i	−0.342782	−	0.0997602i
$417$		0			0
$418$	−6.17673	−	12.9581i	−0.302114	−	0.633803i
$419$	6.35336			0.310382			0.155191	−	0.987885i	$-0.450401\pi$
$419$	6.35336			0.310382			0.155191	+	0.987885i	$0.450401\pi$
$420$		0			0
$421$	−13.2293			−0.644759			−0.322379	−	0.946611i	$-0.604483\pi$
$421$	−13.2293			−0.644759			−0.322379	+	0.946611i	$0.604483\pi$
$422$	1.98733	−	35.0484i	0.0967416	−	1.70613i
$423$		0			0
$424$	13.3840	+	2.29642i	0.649983	+	0.111524i
$425$	18.6072			0.902581
$426$		0			0
$427$	−34.6354			−1.67612
$428$	−1.83166	+	16.0996i	−0.0885365	+	0.778203i
$429$		0			0
$430$	0.942900	−	16.6289i	0.0454707	−	0.801919i
$431$	6.35570			0.306143			0.153072	−	0.988215i	$-0.451083\pi$
$431$	6.35570			0.306143			0.153072	+	0.988215i	$0.451083\pi$
$432$		0			0
$433$		−	29.1359i		−	1.40018i	−0.714053	−	0.700092i	$-0.753142\pi$
$433$		−	29.1359i		−	1.40018i	0.714053	−	0.700092i	$-0.246858\pi$
$434$	−2.95731	+	52.1550i	−0.141956	+	2.50352i
$435$		0			0
$436$	−9.07990	−	1.03302i	−0.434849	−	0.0494729i
$437$	28.4897	−	15.6177i	1.36285	−	0.747095i
$438$		0			0
$439$	−31.5987			−1.50812			−0.754062	−	0.656804i	$-0.771908\pi$
$439$	−31.5987			−1.50812			−0.754062	+	0.656804i	$0.771908\pi$
$440$	1.25305	−	7.30304i	0.0597370	−	0.348159i
$441$		0			0
$442$	−9.05570	−	0.513479i	−0.430736	−	0.0244237i
$443$	14.9120			0.708493			0.354246	−	0.935152i	$-0.384737\pi$
$443$	14.9120			0.708493			0.354246	+	0.935152i	$0.384737\pi$
$444$		0			0
$445$	−4.16449			−0.197416
$446$	−2.63066	−	0.149165i	−0.124565	−	0.00706316i
$447$		0			0
$448$	−11.2653	+	31.8617i	−0.532234	+	1.50532i
$449$		−	26.7456i		−	1.26220i	−0.775700	−	0.631101i	$-0.782603\pi$
$449$		−	26.7456i		−	1.26220i	0.775700	−	0.631101i	$-0.217397\pi$
$450$		0			0
$451$		−	25.1784i		−	1.18560i
$452$	−3.08461	+	27.1125i	−0.145088	+	1.27527i
$453$		0			0
$454$	−0.504025	+	8.88897i	−0.0236551	+	0.417180i
$455$	6.11715			0.286776
$456$		0			0
$457$	6.87631			0.321660			0.160830	−	0.986982i	$-0.448583\pi$
$457$	6.87631			0.321660			0.160830	+	0.986982i	$0.448583\pi$
$458$	−0.424515	+	7.48674i	−0.0198363	+	0.349832i
$459$		0			0
$460$	16.6630	+	1.89576i	0.776917	+	0.0883902i
$461$			27.5423i			1.28277i	0.767219	+	0.641386i	$0.221640\pi$
$461$			27.5423i			1.28277i	−0.767219	+	0.641386i	$0.778360\pi$
$462$		0			0
$463$		−	35.5777i		−	1.65343i	−0.562618	−	0.826717i	$-0.690206\pi$
$463$		−	35.5777i		−	1.65343i	0.562618	−	0.826717i	$-0.309794\pi$
$464$	−13.3350	−	3.07406i	−0.619064	−	0.142710i
$465$		0			0
$466$	27.1060	+	1.53698i	1.25566	+	0.0711990i
$467$	−2.56754			−0.118811			−0.0594057	−	0.998234i	$-0.518921\pi$
$467$	−2.56754			−0.118811			−0.0594057	+	0.998234i	$0.518921\pi$
$468$		0			0
$469$	−18.6812			−0.862618
$470$	9.23532	+	0.523664i	0.425994	+	0.0241548i
$471$		0			0
$472$	1.76093	−	10.2631i	0.0810535	−	0.472396i
$473$	24.3786			1.12093
$474$		0			0
$475$	−7.82473	−	14.2738i	−0.359023	−	0.654929i
$476$	−4.75865	+	41.8267i	−0.218112	+	1.91713i
$477$		0			0
$478$	−1.29347	+	22.8116i	−0.0591620	+	1.04338i
$479$		−	9.39110i		−	0.429090i	−0.976714	−	0.214545i	$-0.931173\pi$
$479$		−	9.39110i		−	0.429090i	0.976714	−	0.214545i	$-0.0688269\pi$
$480$		0			0
$481$	7.56760			0.345053
$482$	1.32205	−	23.3156i	0.0602176	−	1.06200i
$483$		0			0
$484$	−11.0830	−	1.26091i	−0.503771	−	0.0573142i
$485$	11.7829			0.535036
$486$		0			0
$487$	39.1049			1.77201			0.886006	−	0.463674i	$-0.153469\pi$
$487$	39.1049			1.77201			0.886006	+	0.463674i	$0.153469\pi$
$488$	3.92169	−	22.8564i	0.177527	−	1.03466i
$489$		0			0
$490$	0.976769	−	17.2262i	0.0441259	−	0.778203i
$491$	1.82945			0.0825621			0.0412810	−	0.999148i	$-0.486856\pi$
$491$	1.82945			0.0825621			0.0412810	+	0.999148i	$0.486856\pi$
$492$		0			0
$493$	−17.0466			−0.767741
$494$	3.41422	+	7.16268i	0.153613	+	0.322264i
$495$		0			0
$496$	−34.0830	−	7.85699i	−1.53037	−	0.352789i
$497$			47.0761i			2.11165i
$498$		0			0
$499$	1.76796			0.0791448			0.0395724	−	0.999217i	$-0.487400\pi$
$499$	1.76796			0.0791448			0.0395724	+	0.999217i	$0.487400\pi$
$500$	2.22151	−	19.5262i	0.0993490	−	0.873240i
$501$		0			0
$502$	−40.1189	−	2.27483i	−1.79059	−	0.101531i
$503$		−	2.50298i		−	0.111602i	−0.998442	−	0.0558012i	$-0.982229\pi$
$503$		−	2.50298i		−	0.111602i	0.998442	−	0.0558012i	$-0.0177713\pi$
$504$		0			0
$505$	13.4933			0.600444
$506$	−1.38962	+	24.5074i	−0.0617764	+	1.08949i
$507$		0			0
$508$	−24.0604	−	2.73736i	−1.06751	−	0.121451i
$509$	11.9531			0.529810			0.264905	−	0.964275i	$-0.414659\pi$
$509$	11.9531			0.529810			0.264905	+	0.964275i	$0.414659\pi$
$510$		0			0
$511$			33.8857i			1.49902i
$512$	−19.7504	−	11.0418i	−0.872854	−	0.487981i
$513$		0			0
$514$	−0.296156	+	5.22300i	−0.0130629	+	0.230377i
$515$			11.5806i			0.510302i
$516$		0			0
$517$			13.5393i			0.595458i
$518$	1.98834	−	35.0662i	0.0873625	−	1.54072i
$519$		0			0
$520$	−0.692632	+	4.03680i	−0.0303739	+	0.177025i
$521$			10.3275i			0.452458i	0.974074	+	0.226229i	$0.0726397\pi$
$521$			10.3275i			0.452458i	−0.974074	+	0.226229i	$0.927360\pi$
$522$		0			0
$523$			36.4090i			1.59205i	0.605262	+	0.796027i	$0.293069\pi$
$523$			36.4090i			1.59205i	−0.605262	+	0.796027i	$0.706931\pi$
$524$	−27.6235	−	3.14274i	−1.20674	−	0.137291i
$525$		0			0
$526$	−1.94962	+	34.3833i	−0.0850073	+	1.49918i
$527$	−43.5694			−1.89791
$528$		0			0
$529$	−32.5566			−1.41550
$530$	0.432422	−	7.62617i	0.0187832	−	0.331260i
$531$		0			0
$532$	34.0870	−	13.9386i	1.47786	−	0.604317i
$533$			13.9175i			0.602833i
$534$		0			0
$535$	9.11435			0.394048
$536$	2.11524	−	12.3280i	0.0913643	−	0.532489i
$537$		0			0
$538$	−9.33261	−	0.529181i	−0.402357	−	0.0228146i
$539$	25.2543			1.08778
$540$		0			0
$541$			13.4072i			0.576420i	0.957567	+	0.288210i	$0.0930601\pi$
$541$			13.4072i			0.576420i	−0.957567	+	0.288210i	$0.906940\pi$
$542$	−0.193394	+	3.41068i	−0.00830697	+	0.146501i
$543$		0			0
$544$	−27.0633	−	7.87626i	−1.16033	−	0.337692i
$545$			5.14035i			0.220188i
$546$		0			0
$547$			30.6099i			1.30879i	0.756154	+	0.654393i	$0.227076\pi$
$547$			30.6099i			1.30879i	−0.756154	+	0.654393i	$0.772924\pi$
$548$	−7.16287	−	0.814923i	−0.305982	−	0.0348118i
$549$		0			0
$550$	12.2786	+	0.696226i	0.523562	+	0.0296872i
$551$	7.16847	+	13.0767i	0.305387	+	0.557086i
$552$		0			0
$553$		−	22.5940i		−	0.960796i
$554$	0.0376318	−	0.663672i	0.00159882	−	0.0281967i
$555$		0			0
$556$	9.31140	+	1.05936i	0.394891	+	0.0449269i
$557$			23.8741i			1.01158i	0.862658	+	0.505788i	$0.168798\pi$
$557$			23.8741i			1.01158i	−0.862658	+	0.505788i	$0.831202\pi$
$558$		0			0
$559$	−13.4754			−0.569949
$560$	18.5234	+	4.27011i	0.782758	+	0.180445i
$561$		0			0
$562$	−0.905387	+	15.9674i	−0.0381914	+	0.673542i
$563$		−	44.0634i		−	1.85705i	−0.371268	−	0.928526i	$-0.621077\pi$
$563$		−	44.0634i		−	1.85705i	0.371268	−	0.928526i	$-0.378923\pi$
$564$		0			0
$565$	15.3490			0.645739
$566$	−17.3042	−	0.981187i	−0.727349	−	0.0412424i
$567$		0			0
$568$	−31.0662	−	5.33033i	−1.30351	−	0.223656i
$569$		−	18.8026i		−	0.788245i	−0.919058	−	0.394123i	$-0.871049\pi$
$569$		−	18.8026i		−	0.788245i	0.919058	−	0.394123i	$-0.128951\pi$
$570$		0			0
$571$	−6.46411			−0.270515			−0.135257	−	0.990810i	$-0.543186\pi$
$571$	−6.46411			−0.270515			−0.135257	+	0.990810i	$0.543186\pi$
$572$	−5.95651	−	0.677675i	−0.249054	−	0.0283350i
$573$		0			0
$574$	64.4899	+	3.65673i	2.69176	+	0.152629i
$575$			27.8348i			1.16079i
$576$		0			0
$577$	24.0265			1.00024			0.500119	−	0.865957i	$-0.333290\pi$
$577$	24.0265			1.00024			0.500119	+	0.865957i	$0.333290\pi$
$578$	−11.0509	−	0.626615i	−0.459659	−	0.0260637i
$579$		0			0
$580$	−0.870148	+	7.64828i	−0.0361309	+	0.317578i
$581$		−	20.5543i		−	0.852734i
$582$		0			0
$583$	11.1802			0.463038
$584$	−22.3617	−	3.83681i	−0.925333	−	0.158768i
$585$		0			0
$586$	0.262417	+	0.0148796i	0.0108403	+	0.000614672i
$587$	35.2500			1.45492			0.727461	−	0.686149i	$-0.240700\pi$
$587$	35.2500			1.45492			0.727461	+	0.686149i	$0.240700\pi$
$588$		0			0
$589$	18.3219	+	33.4227i	0.754941	+	1.37716i
$590$	−5.84789	−	0.331589i	−0.240754	−	0.0136513i
$591$		0			0
$592$	22.9156	+	5.28261i	0.941825	+	0.217114i
$593$	9.17199			0.376648			0.188324	−	0.982107i	$-0.439694\pi$
$593$	9.17199			0.376648			0.188324	+	0.982107i	$0.439694\pi$
$594$		0			0
$595$	23.6791			0.970748
$596$	0.0874651	−	0.768786i	0.00358271	−	0.0314907i
$597$		0			0
$598$	0.768123	−	13.5466i	0.0314109	−	0.553961i
$599$	13.0181			0.531907			0.265954	−	0.963986i	$-0.414313\pi$
$599$	13.0181			0.531907			0.265954	+	0.963986i	$0.414313\pi$
$600$		0			0
$601$		−	3.79782i		−	0.154916i	−0.996996	−	0.0774581i	$-0.975320\pi$
$601$		−	3.79782i		−	0.154916i	0.996996	−	0.0774581i	$-0.0246804\pi$
$602$	−3.54057	+	62.4414i	−0.144303	+	2.54492i
$603$		0			0
$604$	36.0028	+	4.09605i	1.46493	+	0.166666i
$605$			6.27432i			0.255087i
$606$		0			0
$607$	24.9344			1.01205			0.506027	−	0.862517i	$-0.331113\pi$
$607$	24.9344			1.01205			0.506027	+	0.862517i	$0.331113\pi$
$608$	5.33871	+	24.0728i	0.216513	+	0.976280i
$609$		0			0
$610$	−13.0236	−	0.738466i	−0.527308	−	0.0298996i
$611$		−	7.48393i		−	0.302767i
$612$		0			0
$613$			27.9895i			1.13049i	0.824925	+	0.565243i	$0.191217\pi$
$613$			27.9895i			1.13049i	−0.824925	+	0.565243i	$0.808783\pi$
$614$	−2.76255	+	48.7202i	−0.111487	+	1.96619i
$615$		0			0
$616$	−4.70520	+	27.4228i	−0.189578	+	1.10490i
$617$	0.0883404			0.00355645			0.00177822	−	0.999998i	$-0.499434\pi$
$617$	0.0883404			0.00355645			0.00177822	+	0.999998i	$0.499434\pi$
$618$		0			0
$619$	−7.65317			−0.307607			−0.153804	−	0.988101i	$-0.549152\pi$
$619$	−7.65317			−0.307607			−0.153804	+	0.988101i	$0.549152\pi$
$620$	−2.22401	+	19.5482i	−0.0893184	+	0.785076i
$621$		0			0
$622$	−1.03025	+	18.1694i	−0.0413092	+	0.728527i
$623$	15.6376			0.626507
$624$		0			0
$625$	7.61773			0.304709
$626$	−25.4864	−	1.44514i	−1.01864	−	0.0577594i
$627$		0			0
$628$	0.337573	−	2.96714i	0.0134706	−	0.118402i
$629$	29.2937			1.16802
$630$		0			0
$631$			14.4831i			0.576564i	0.957546	+	0.288282i	$0.0930840\pi$
$631$			14.4831i			0.576564i	−0.957546	+	0.288282i	$0.906916\pi$
$632$	14.9101	+	2.55828i	0.593093	+	0.101763i
$633$		0			0
$634$	16.3907	+	0.929392i	0.650958	+	0.0369109i
$635$			13.6211i			0.540538i
$636$		0			0
$637$	−13.9594			−0.553093
$638$	−11.2488	−	0.637834i	−0.445345	−	0.0252521i
$639$		0			0
$640$	−4.91528	+	11.7404i	−0.194294	+	0.464080i
$641$			29.6113i			1.16958i	0.811185	+	0.584789i	$0.198823\pi$
$641$			29.6113i			1.16958i	−0.811185	+	0.584789i	$0.801177\pi$
$642$		0			0
$643$	11.5108			0.453942			0.226971	−	0.973901i	$-0.427118\pi$
$643$	11.5108			0.453942			0.226971	+	0.973901i	$0.427118\pi$
$644$	−62.5694	−	7.11855i	−2.46558	−	0.280510i
$645$		0			0
$646$	13.2162	+	27.7263i	0.519986	+	1.09088i
$647$			3.37072i			0.132517i	0.997802	+	0.0662584i	$0.0211062\pi$
$647$			3.37072i			0.132517i	−0.997802	+	0.0662584i	$0.978894\pi$
$648$		0			0
$649$		−	8.57321i		−	0.336528i
$650$	−6.78707	−	0.384843i	−0.266211	−	0.0150948i
$651$		0			0
$652$	44.0765	+	5.01460i	1.72617	+	0.196387i
$653$		−	39.0817i		−	1.52939i	−0.644395	−	0.764693i	$-0.722891\pi$
$653$		−	39.0817i		−	1.52939i	0.644395	−	0.764693i	$-0.277109\pi$
$654$		0			0
$655$			15.6383i			0.611040i
$656$	−9.71519	+	42.1438i	−0.379314	+	1.64544i
$657$		0			0
$658$	−34.6785	−	1.96635i	−1.35191	−	0.0766564i
$659$		−	15.6044i		−	0.607863i	−0.952694	−	0.303931i	$-0.901701\pi$
$659$		−	15.6044i		−	0.607863i	0.952694	−	0.303931i	$-0.0982993\pi$
$660$		0			0
$661$	29.8139			1.15963			0.579813	−	0.814750i	$-0.303126\pi$
$661$	29.8139			1.15963			0.579813	+	0.814750i	$0.303126\pi$
$662$	−0.210835	+	3.71827i	−0.00819433	+	0.144515i
$663$		0			0
$664$	13.5641	+	2.32732i	0.526388	+	0.0903174i
$665$	−9.95758	−	18.1646i	−0.386138	−	0.704392i
$666$		0			0
$667$		−	25.5003i		−	0.987377i
$668$	16.2296	+	1.84644i	0.627940	+	0.0714411i
$669$		0			0
$670$	−7.02449	−	0.398305i	−0.271380	−	0.0153879i
$671$		−	19.0930i		−	0.737077i
$672$		0			0
$673$		−	0.891436i		−	0.0343623i	−0.999852	−	0.0171812i	$-0.994531\pi$
$673$		−	0.891436i		−	0.0343623i	0.999852	−	0.0171812i	$-0.00546921\pi$
$674$	0.602617	−	10.6277i	0.0232119	−	0.409365i
$675$		0			0
$676$	−22.5409	−	2.56448i	−0.866956	−	0.0986340i
$677$	−47.7338			−1.83456			−0.917280	−	0.398243i	$-0.869620\pi$
$677$	−47.7338			−1.83456			−0.917280	+	0.398243i	$0.869620\pi$
$678$		0			0
$679$	−44.2448			−1.69796
$680$	−2.68114	+	15.6262i	−0.102817	+	0.599237i
$681$		0			0
$682$	−28.7508	−	1.63024i	−1.10093	−	0.0624251i
$683$			26.3380i			1.00780i	0.863763	+	0.503899i	$0.168101\pi$
$683$			26.3380i			1.00780i	−0.863763	+	0.503899i	$0.831899\pi$
$684$		0			0
$685$			4.05507i			0.154936i
$686$	−1.30034	+	22.9328i	−0.0496472	+	0.875577i
$687$		0			0
$688$	−40.8051	−	9.40659i	−1.55568	−	0.358623i
$689$	−6.17994			−0.235437
$690$		0			0
$691$	44.7608			1.70278			0.851391	−	0.524532i	$-0.175760\pi$
$691$	44.7608			1.70278			0.851391	+	0.524532i	$0.175760\pi$
$692$	21.8479	+	2.48565i	0.830533	+	0.0944902i
$693$		0			0
$694$	18.1225	+	1.02759i	0.687921	+	0.0390067i
$695$		−	5.27140i		−	0.199956i
$696$		0			0
$697$			53.8737i			2.04061i
$698$	−0.834830	+	14.7230i	−0.0315988	+	0.557275i
$699$		0			0
$700$	−3.56652	+	31.3484i	−0.134802	+	1.18486i
$701$			24.2205i			0.914796i	0.889262	+	0.457398i	$0.151218\pi$
$701$			24.2205i			0.914796i	−0.889262	+	0.457398i	$0.848782\pi$
$702$		0			0
$703$	−12.3186	−	22.4716i	−0.464607	−	0.847533i
$704$	−17.5640	−	6.21006i	−0.661967	−	0.234050i
$705$		0			0
$706$	−13.2057	−	0.748797i	−0.497005	−	0.0281813i
$707$	−50.6672			−1.90554
$708$		0			0
$709$		−	43.2777i		−	1.62533i	−0.582734	−	0.812663i	$-0.698017\pi$
$709$		−	43.2777i		−	1.62533i	0.582734	−	0.812663i	$-0.301983\pi$
$710$	−1.00372	+	17.7015i	−0.0376688	+	0.664325i
$711$		0			0
$712$	−1.77061	+	10.3195i	−0.0663565	+	0.386739i
$713$		−	65.1763i		−	2.44087i
$714$		0			0
$715$			3.37212i			0.126110i
$716$	−4.21847	+	37.0788i	−0.157652	+	1.38570i
$717$		0			0
$718$	0.802417	−	14.1514i	0.0299460	−	0.528126i
$719$			9.82129i			0.366272i	0.983088	+	0.183136i	$0.0586249\pi$
$719$			9.82129i			0.366272i	−0.983088	+	0.183136i	$0.941375\pi$
$720$		0			0
$721$		−	43.4850i		−	1.61947i
$722$	15.7115	−	21.7979i	0.584722	−	0.811233i
$723$		0			0
$724$	7.13196	+	0.811406i	0.265057	+	0.0301557i
$725$	−12.7761			−0.474493
$726$		0			0
$727$		−	36.6336i		−	1.35866i	−0.733831	−	0.679332i	$-0.762270\pi$
$727$		−	36.6336i		−	1.35866i	0.733831	−	0.679332i	$-0.237730\pi$
$728$	2.60082	−	15.1581i	0.0963930	−	0.561797i
$729$		0			0
$730$	−0.722482	+	12.7417i	−0.0267403	+	0.471590i
$731$	−52.1625			−1.92930
$732$		0			0
$733$			38.2060i			1.41117i	0.708625	+	0.705585i	$0.249316\pi$
$733$			38.2060i			1.41117i	−0.708625	+	0.705585i	$0.750684\pi$
$734$	1.20305	−	21.2170i	0.0444055	−	0.783133i
$735$		0			0
$736$	11.7822	−	40.4844i	0.434299	−	1.49228i
$737$		−	10.2981i		−	0.379337i
$738$		0			0
$739$	−3.61772			−0.133080			−0.0665400	−	0.997784i	$-0.521196\pi$
$739$	−3.61772			−0.133080			−0.0665400	+	0.997784i	$0.521196\pi$
$740$	1.49530	−	13.1432i	0.0549685	−	0.483152i
$741$		0			0
$742$	−1.62374	+	28.6362i	−0.0596093	+	1.05127i
$743$	28.3907			1.04155			0.520777	−	0.853693i	$-0.325642\pi$
$743$	28.3907			1.04155			0.520777	+	0.853693i	$0.325642\pi$
$744$		0			0
$745$	−0.435228			−0.0159455
$746$	15.9997	+	0.907221i	0.585791	+	0.0332157i
$747$		0			0
$748$	−23.0573	−	2.62324i	−0.843058	−	0.0959151i
$749$	−34.2243			−1.25053
$750$		0			0
$751$	37.8598			1.38153			0.690763	−	0.723082i	$-0.257275\pi$
$751$	37.8598			1.38153			0.690763	+	0.723082i	$0.257275\pi$
$752$	5.22420	−	22.6622i	0.190507	−	0.826406i
$753$		0			0
$754$	6.21785	+	0.352566i	0.226441	+	0.0128397i
$755$		−	20.3820i		−	0.741777i
$756$		0			0
$757$			3.40305i			0.123686i	0.998086	+	0.0618430i	$0.0196978\pi$
$757$			3.40305i			0.123686i	−0.998086	+	0.0618430i	$0.980302\pi$
$758$	−2.46021	+	43.3882i	−0.0893589	+	1.57593i
$759$		0			0
$760$	13.1145	−	4.51442i	0.475715	−	0.163755i
$761$	−5.55454			−0.201352			−0.100676	−	0.994919i	$-0.532101\pi$
$761$	−5.55454			−0.201352			−0.100676	+	0.994919i	$0.532101\pi$
$762$		0			0
$763$		−	19.3019i		−	0.698777i
$764$	−2.71434	+	23.8581i	−0.0982015	+	0.863154i
$765$		0			0
$766$	−10.4534	−	0.592733i	−0.377697	−	0.0214163i
$767$			4.73889i			0.171111i
$768$		0			0
$769$	−47.3789			−1.70853			−0.854263	−	0.519841i	$-0.825991\pi$
$769$	−47.3789			−1.70853			−0.854263	+	0.519841i	$0.825991\pi$
$770$	15.6255	+	0.886002i	0.563104	+	0.0319293i
$771$		0			0
$772$	−0.570422	+	5.01380i	−0.0205299	+	0.180451i
$773$	−48.1155			−1.73059			−0.865296	−	0.501261i	$-0.832870\pi$
$773$	−48.1155			−1.73059			−0.865296	+	0.501261i	$0.832870\pi$
$774$		0			0
$775$	−32.6545			−1.17298
$776$	5.00974	−	29.1978i	0.179839	−	1.04814i
$777$		0			0
$778$	−0.413649	+	7.29510i	−0.0148300	+	0.261542i
$779$	41.3273	−	22.6551i	1.48070	−	0.811703i
$780$		0			0
$781$	−25.9510			−0.928600
$782$	2.97336	−	52.4380i	0.106327	−	1.87518i
$783$		0			0
$784$	−42.2708	−	9.74448i	−1.50967	−	0.348017i
$785$	−1.67977			−0.0599534
$786$		0			0
$787$			43.8444i			1.56288i	0.623978	+	0.781442i	$0.285515\pi$
$787$			43.8444i			1.56288i	−0.623978	+	0.781442i	$0.714485\pi$
$788$	4.88256	−	42.9158i	0.173934	−	1.52881i
$789$		0			0
$790$	0.481731	−	8.49578i	0.0171392	−	0.302266i
$791$	−57.6354			−2.04928
$792$		0			0
$793$			10.5538i			0.374775i
$794$	−1.75174	+	30.8936i	−0.0621669	+	1.09637i
$795$		0			0
$796$	−3.58366	+	31.4990i	−0.127019	+	1.11645i
$797$	14.2432			0.504519			0.252259	−	0.967660i	$-0.418826\pi$
$797$	14.2432			0.504519			0.252259	+	0.967660i	$0.418826\pi$
$798$		0			0
$799$		−	28.9698i		−	1.02488i
$800$	−20.2834	−	5.90311i	−0.717127	−	0.208706i
$801$		0			0
$802$	−1.88956	+	33.3242i	−0.0667226	+	1.17672i
$803$	−18.6797			−0.659193
$804$		0			0
$805$			35.4220i			1.24846i
$806$	15.8922	+	0.901124i	0.559778	+	0.0317407i
$807$		0			0
$808$	5.73694	−	33.4360i	0.201825	−	1.17627i
$809$	19.7567			0.694609			0.347304	−	0.937752i	$-0.387097\pi$
$809$	19.7567			0.694609			0.347304	+	0.937752i	$0.387097\pi$
$810$		0			0
$811$		−	6.60741i		−	0.232018i	−0.993248	−	0.116009i	$-0.962990\pi$
$811$		−	6.60741i		−	0.232018i	0.993248	−	0.116009i	$-0.0370101\pi$
$812$	3.26739	−	28.7192i	0.114663	−	1.00785i
$813$		0			0
$814$	19.3305	+	1.09608i	0.677534	+	0.0384177i
$815$		−	24.9527i		−	0.874056i
$816$		0			0
$817$	21.9355	+	40.0146i	0.767425	+	1.39993i
$818$	−0.0846319	+	1.49256i	−0.00295908	+	0.0521863i
$819$		0			0
$820$	24.1715	+	2.75000i	0.844104	+	0.0960341i
$821$			19.6617i			0.686200i	0.939299	+	0.343100i	$0.111477\pi$
$821$			19.6617i			0.686200i	−0.939299	+	0.343100i	$0.888523\pi$
$822$		0			0
$823$			23.9297i			0.834137i	0.908875	+	0.417068i	$0.136942\pi$
$823$			23.9297i			0.834137i	−0.908875	+	0.417068i	$0.863058\pi$
$824$	28.6964	+	4.92372i	0.999686	+	0.171526i
$825$		0			0
$826$	21.9587	+	1.24511i	0.764042	+	0.0433230i
$827$			14.4487i			0.502429i	0.967931	+	0.251215i	$0.0808300\pi$
$827$			14.4487i			0.502429i	−0.967931	+	0.251215i	$0.919170\pi$
$828$		0			0
$829$	−29.3548			−1.01953			−0.509767	−	0.860313i	$-0.670268\pi$
$829$	−29.3548			−1.01953			−0.509767	+	0.860313i	$0.670268\pi$
$830$	0.438241	−	7.72879i	0.0152116	−	0.268270i
$831$		0			0
$832$	9.70858	+	3.43264i	0.336584	+	0.119006i
$833$	−54.0361			−1.87224
$834$		0			0
$835$		−	9.18793i		−	0.317961i
$836$	7.68377	+	18.7907i	0.265749	+	0.649890i
$837$		0			0
$838$	−8.97059	−	0.508654i	−0.309884	−	0.0175711i
$839$	−39.8518			−1.37584			−0.687919	−	0.725788i	$-0.741476\pi$
$839$	−39.8518			−1.37584			−0.687919	+	0.725788i	$0.741476\pi$
$840$		0			0
$841$	−17.2954			−0.596394
$842$	18.6791	+	1.05915i	0.643725	+	0.0365007i
$843$		0			0
$844$	−5.61200	+	49.3274i	−0.193173	+	1.69792i
$845$			12.7609i			0.438988i
$846$		0			0
$847$		−	23.5600i		−	0.809531i
$848$	−18.7136	−	4.31394i	−0.642627	−	0.148141i
$849$		0			0
$850$	−26.2723	−	1.48970i	−0.901134	−	0.0510964i
$851$			43.8210i			1.50216i
$852$		0			0
$853$			6.70405i			0.229542i	0.993392	+	0.114771i	$0.0366135\pi$
$853$			6.70405i			0.229542i	−0.993392	+	0.114771i	$0.963387\pi$
$854$	48.9033	+	2.77293i	1.67344	+	0.0948877i
$855$		0			0
$856$	3.87514	−	22.5851i	0.132450	−	0.771943i
$857$			1.11118i			0.0379573i	0.999820	+	0.0189786i	$0.00604145\pi$
$857$			1.11118i			0.0379573i	−0.999820	+	0.0189786i	$0.993959\pi$
$858$		0			0
$859$	23.5879			0.804809			0.402405	−	0.915462i	$-0.368174\pi$
$859$	23.5879			0.804809			0.402405	+	0.915462i	$0.368174\pi$
$860$	−2.66265	+	23.4037i	−0.0907955	+	0.798058i
$861$		0			0
$862$	−8.97391	−	0.508841i	−0.305652	−	0.0173312i
$863$	44.2702			1.50697			0.753487	−	0.657462i	$-0.228370\pi$
$863$	44.2702			1.50697			0.753487	+	0.657462i	$0.228370\pi$
$864$		0			0
$865$		−	12.3686i		−	0.420546i
$866$	−2.33264	+	41.1383i	−0.0792663	+	1.39794i
$867$		0			0
$868$	8.35113	−	73.4033i	0.283456	−	2.49147i
$869$	12.4551			0.422511
$870$		0			0
$871$			5.69236i			0.192878i
$872$	12.7376	+	2.18552i	0.431350	+	0.0740110i
$873$		0			0
$874$	−41.4763	+	19.7704i	−1.40296	+	0.668744i
$875$	41.5086			1.40325
$876$		0			0
$877$	36.0452			1.21716			0.608581	−	0.793492i	$-0.291739\pi$
$877$	36.0452			1.21716			0.608581	+	0.793492i	$0.291739\pi$
$878$	44.6156	+	2.52981i	1.50570	+	0.0853770i
$879$		0			0
$880$	−2.35393	+	10.2112i	−0.0793509	+	0.344219i
$881$	27.9005			0.939990			0.469995	−	0.882669i	$-0.344256\pi$
$881$	27.9005			0.939990			0.469995	+	0.882669i	$0.344256\pi$
$882$		0			0
$883$	17.0821			0.574859			0.287430	−	0.957802i	$-0.407199\pi$
$883$	17.0821			0.574859			0.287430	+	0.957802i	$0.407199\pi$
$884$	12.7450	+	1.45001i	0.428662	+	0.0487691i
$885$		0			0
$886$	−21.0550	−	1.19387i	−0.707356	−	0.0401088i
$887$	38.8792			1.30544			0.652718	−	0.757601i	$-0.273628\pi$
$887$	38.8792			1.30544			0.652718	+	0.757601i	$0.273628\pi$
$888$		0			0
$889$		−	51.1472i		−	1.71542i
$890$	5.88003	+	0.333412i	0.197099	+	0.0111760i
$891$		0			0
$892$	3.70241	+	0.421225i	0.123966	+	0.0141037i
$893$	−22.2232	+	12.1824i	−0.743670	+	0.407670i
$894$		0			0
$895$	20.9912			0.701658
$896$	18.4568	−	44.0850i	0.616599	−	1.47278i
$897$		0			0
$898$	−2.14127	+	37.7633i	−0.0714551	+	1.26018i
$899$	29.9157			0.997746
$900$		0			0
$901$	−23.9221			−0.796962
$902$	−2.01580	+	35.5505i	−0.0671187	+	1.18370i
$903$		0			0
$904$	6.52594	−	38.0345i	0.217050	−	1.26501i
$905$		−	4.03757i		−	0.134213i
$906$		0			0
$907$		−	35.7708i		−	1.18775i	−0.804558	−	0.593874i	$-0.797598\pi$
$907$		−	35.7708i		−	1.18775i	0.804558	−	0.593874i	$-0.202402\pi$
$908$	1.42331	−	12.5104i	0.0472343	−	0.415172i
$909$		0			0
$910$	−8.63708	−	0.489743i	−0.286316	−	0.0162348i
$911$	27.9479			0.925957			0.462978	−	0.886370i	$-0.346781\pi$
$911$	27.9479			0.925957			0.462978	+	0.886370i	$0.346781\pi$
$912$		0			0
$913$	11.3307			0.374991
$914$	−9.70898	−	0.550522i	−0.321145	−	0.0182096i
$915$		0			0
$916$	1.19879	−	10.5369i	0.0396090	−	0.348148i
$917$		−	58.7217i		−	1.93916i
$918$		0			0
$919$		−	3.56750i		−	0.117681i	−0.998267	−	0.0588406i	$-0.981260\pi$
$919$		−	3.56750i		−	0.117681i	0.998267	−	0.0588406i	$-0.0187404\pi$
$920$	−23.3755	−	4.01076i	−0.770667	−	0.132231i
$921$		0			0
$922$	2.20505	−	38.8882i	0.0726195	−	1.28071i
$923$	14.3446			0.472157
$924$		0			0
$925$	21.9551			0.721879
$926$	−2.84837	+	50.2337i	−0.0936032	+	1.65078i
$927$		0			0
$928$	18.5823	+	5.40802i	0.609992	+	0.177527i
$929$	−42.5738			−1.39680			−0.698401	−	0.715707i	$-0.746105\pi$
$929$	−42.5738			−1.39680			−0.698401	+	0.715707i	$0.746105\pi$
$930$		0			0
$931$	22.7234	+	41.4519i	0.744729	+	1.35853i
$932$	−38.1492	−	4.34025i	−1.24962	−	0.142170i
$933$		0			0
$934$	3.62522	+	0.205558i	0.118621	+	0.00672608i
$935$			13.0533i			0.426887i
$936$		0			0
$937$	12.8739			0.420572			0.210286	−	0.977640i	$-0.432561\pi$
$937$	12.8739			0.420572			0.210286	+	0.977640i	$0.432561\pi$
$938$	26.3769	+	1.49563i	0.861235	+	0.0488340i
$939$		0			0
$940$	−12.9978	−	1.47877i	−0.423943	−	0.0482322i
$941$	−22.1148			−0.720921			−0.360461	−	0.932774i	$-0.617380\pi$
$941$	−22.1148			−0.720921			−0.360461	+	0.932774i	$0.617380\pi$
$942$		0			0
$943$	−80.5907			−2.62439
$944$	−3.30801	+	14.3499i	−0.107667	+	0.467050i
$945$		0			0
$946$	−34.4213	−	1.95177i	−1.11913	−	0.0634574i
$947$	−49.8108			−1.61863			−0.809317	−	0.587372i	$-0.800163\pi$
$947$	−49.8108			−1.61863			−0.809317	+	0.587372i	$0.800163\pi$
$948$		0			0
$949$	10.3253			0.335174
$950$	9.90532	+	20.7803i	0.321371	+	0.674203i
$951$		0			0
$952$	10.0676	−	58.6761i	0.326294	−	1.90170i
$953$		−	35.3570i		−	1.14533i	−0.819790	−	0.572664i	$-0.805910\pi$
$953$		−	35.3570i		−	1.14533i	0.819790	−	0.572664i	$-0.194090\pi$
$954$		0			0
$955$	13.5066			0.437063
$956$	3.65262	−	32.1052i	0.118134	−	1.03836i
$957$		0			0
$958$	−0.751857	+	13.2597i	−0.0242914	+	0.428402i
$959$		−	15.2267i		−	0.491696i
$960$		0			0
$961$	45.4616			1.46650
$962$	−10.6850	−	0.605867i	−0.344500	−	0.0195339i
$963$		0			0
$964$	−3.73332	+	32.8145i	−0.120242	+	1.05688i
$965$	2.83843			0.0913723
$966$		0			0
$967$		−	20.9613i		−	0.674071i	−0.941492	−	0.337036i	$-0.890576\pi$
$967$		−	20.9613i		−	0.674071i	0.941492	−	0.337036i	$-0.109424\pi$
$968$	15.5476	+	2.66765i	0.499718	+	0.0857415i
$969$		0			0
$970$	−16.6369	−	0.943349i	−0.534178	−	0.0302891i
$971$		−	35.3669i		−	1.13498i	−0.823381	−	0.567489i	$-0.807915\pi$
$971$		−	35.3669i		−	1.13498i	0.823381	−	0.567489i	$-0.192085\pi$
$972$		0			0
$973$			19.7940i			0.634567i
$974$	−55.2140	−	3.13076i	−1.76917	−	0.100316i
$975$		0			0
$976$	−7.36712	+	31.9580i	−0.235816	+	1.02295i
$977$			34.3090i			1.09764i	0.835939	+	0.548822i	$0.184923\pi$
$977$			34.3090i			1.09764i	−0.835939	+	0.548822i	$0.815077\pi$
$978$		0			0
$979$			8.62033i			0.275507i
$980$	−2.75829	+	24.2443i	−0.0881103	+	0.774457i
$981$		0			0
$982$	−2.58309	−	0.146467i	−0.0824297	−	0.00467396i
$983$	31.0387			0.989981			0.494991	−	0.868898i	$-0.335171\pi$
$983$	31.0387			0.989981			0.494991	+	0.868898i	$0.335171\pi$
$984$		0			0
$985$	−24.2957			−0.774124
$986$	24.0689	+	1.36476i	0.766509	+	0.0434629i
$987$		0			0
$988$	−4.24725	−	10.3867i	−0.135123	−	0.330444i
$989$		−	78.0308i		−	2.48123i
$990$		0			0
$991$	−48.0040			−1.52490			−0.762448	−	0.647049i	$-0.776003\pi$
$991$	−48.0040			−1.52490			−0.762448	+	0.647049i	$0.776003\pi$
$992$	47.4944	+	13.8223i	1.50795	+	0.438860i
$993$		0			0
$994$	3.76894	−	66.4689i	0.119544	−	2.10826i
$995$	17.8323			0.565323
$996$		0			0
$997$		−	29.1790i		−	0.924107i	−0.886852	−	0.462053i	$-0.847113\pi$
$997$		−	29.1790i		−	0.924107i	0.886852	−	0.462053i	$-0.152887\pi$
$998$	−2.49627	−	0.141544i	−0.0790179	−	0.00448050i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.g.379.1		40
3.2	odd	2		456.2.e.a.379.40	yes	40
4.3	odd	2		5472.2.e.g.5167.11		40
8.3	odd	2	inner	1368.2.e.g.379.39		40
8.5	even	2		5472.2.e.g.5167.10		40
12.11	even	2		1824.2.e.a.1519.32		40
19.18	odd	2	inner	1368.2.e.g.379.40		40
24.5	odd	2		1824.2.e.a.1519.30		40
24.11	even	2		456.2.e.a.379.2	yes	40
57.56	even	2		456.2.e.a.379.1	✓	40
76.75	even	2		5472.2.e.g.5167.9		40
152.37	odd	2		5472.2.e.g.5167.12		40
152.75	even	2	inner	1368.2.e.g.379.2		40
228.227	odd	2		1824.2.e.a.1519.29		40
456.227	odd	2		456.2.e.a.379.39	yes	40
456.341	even	2		1824.2.e.a.1519.31		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.1	✓	40	57.56	even	2
456.2.e.a.379.2	yes	40	24.11	even	2
456.2.e.a.379.39	yes	40	456.227	odd	2
456.2.e.a.379.40	yes	40	3.2	odd	2
1368.2.e.g.379.1		40	1.1	even	1	trivial
1368.2.e.g.379.2		40	152.75	even	2	inner
1368.2.e.g.379.39		40	8.3	odd	2	inner
1368.2.e.g.379.40		40	19.18	odd	2	inner
1824.2.e.a.1519.29		40	228.227	odd	2
1824.2.e.a.1519.30		40	24.5	odd	2
1824.2.e.a.1519.31		40	456.341	even	2
1824.2.e.a.1519.32		40	12.11	even	2
5472.2.e.g.5167.9		40	76.75	even	2
5472.2.e.g.5167.10		40	8.5	even	2
5472.2.e.g.5167.11		40	4.3	odd	2
5472.2.e.g.5167.12		40	152.37	odd	2

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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41195 - 0.0800606i) q^{2} +(1.98718 + 0.226082i) q^{4} -1.12499i q^{5} +4.22432i q^{7} +(-2.78769 - 0.478311i) q^{8} +O(q^{10})\)	\(q+(-1.41195 - 0.0800606i) q^{2} +(1.98718 + 0.226082i) q^{4} -1.12499i q^{5} +4.22432i q^{7} +(-2.78769 - 0.478311i) q^{8} +(-0.0900673 + 1.58842i) q^{10} -2.32868 q^{11} +1.28719 q^{13} +(0.338202 - 5.96451i) q^{14} +(3.89777 + 0.898533i) q^{16} +4.98265 q^{17} +(-2.09531 - 3.82226i) q^{19} +(0.254340 - 2.23556i) q^{20} +(3.28798 + 0.186436i) q^{22} +7.45363i q^{23} +3.73440 q^{25} +(-1.81745 - 0.103054i) q^{26} +(-0.955044 + 8.39448i) q^{28} -3.42120 q^{29} -8.74423 q^{31} +(-5.43151 - 1.58074i) q^{32} +(-7.03522 - 0.398914i) q^{34} +4.75231 q^{35} +5.87915 q^{37} +(2.65245 + 5.56457i) q^{38} +(-0.538095 + 3.13612i) q^{40} +10.8123i q^{41} -10.4688 q^{43} +(-4.62752 - 0.526475i) q^{44} +(0.596742 - 10.5241i) q^{46} -5.81414i q^{47} -10.8449 q^{49} +(-5.27277 - 0.298978i) q^{50} +(2.55789 + 0.291012i) q^{52} -4.80109 q^{53} +2.61975i q^{55} +(2.02054 - 11.7761i) q^{56} +(4.83054 + 0.273903i) q^{58} +3.68157i q^{59} +8.19904i q^{61} +(12.3464 + 0.700069i) q^{62} +(7.54244 + 2.66677i) q^{64} -1.44808i q^{65} +4.42230i q^{67} +(9.90142 + 1.12649i) q^{68} +(-6.71001 - 0.380473i) q^{70} +11.1441 q^{71} +8.02158 q^{73} +(-8.30104 - 0.470688i) q^{74} +(-3.29962 - 8.06923i) q^{76} -9.83711i q^{77} -5.34856 q^{79} +(1.01084 - 4.38495i) q^{80} +(0.865637 - 15.2663i) q^{82} -4.86570 q^{83} -5.60542i q^{85} +(14.7814 + 0.838141i) q^{86} +(6.49165 + 1.11384i) q^{88} -3.70180i q^{89} +5.43752i q^{91} +(-1.68514 + 14.8117i) q^{92} +(-0.465484 + 8.20925i) q^{94} +(-4.30000 + 2.35720i) q^{95} +10.4738i q^{97} +(15.3124 + 0.868247i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4}+O(q^{10}) \) 40 * q - 4 * q^4	\( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Introduction

L-functions

Modular forms

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