LMFDB - Embedded newform 414.3.k.b.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, 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:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	414.71
Dual form			414.3.k.b.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-0.172109 + 0.586151i) q^{5} +(-4.94341 + 5.70500i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})$	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-0.172109 + 0.586151i) q^{5} +(-4.94341 + 5.70500i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-0.565759 - 0.652921i) q^{10} +(-8.63603 - 13.4379i) q^{11} +(11.0851 + 12.7929i) q^{13} +(-3.00767 - 10.2432i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(-1.90658 - 0.870706i) q^{17} +(-8.74546 - 19.1499i) q^{19} +(1.20936 - 0.173879i) q^{20} +22.5902 q^{22} +(-15.5903 - 16.9098i) q^{23} +(20.7174 + 13.3143i) q^{25} +(-23.6953 + 3.40687i) q^{26} +(14.4860 + 4.25348i) q^{28} +(-29.1843 - 13.3280i) q^{29} +(7.05976 - 49.1017i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(2.49363 - 1.60256i) q^{34} +(-2.49318 - 3.87947i) q^{35} +(-63.7823 + 18.7282i) q^{37} +(29.4695 + 4.23707i) q^{38} +(-0.717785 + 1.57173i) q^{40} +(13.4671 - 45.8648i) q^{41} +(-1.87890 - 13.0680i) q^{43} +(-17.2721 + 26.8758i) q^{44} +(32.0379 - 5.61903i) q^{46} -14.9396i q^{47} +(-1.13629 - 7.90309i) q^{49} +(-31.6803 + 14.4679i) q^{50} +(14.0638 - 30.7955i) q^{52} +(-51.4921 - 44.6182i) q^{53} +(9.36299 - 2.74922i) q^{55} +(-16.1362 + 13.9821i) q^{56} +(38.1703 - 24.5306i) q^{58} +(14.0463 - 12.1712i) q^{59} +(10.3773 - 72.1756i) q^{61} +(53.0191 + 45.9413i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-9.40641 + 4.29577i) q^{65} +(77.1069 + 49.5536i) q^{67} +4.19198i q^{68} +6.52169 q^{70} +(48.0839 - 74.8200i) q^{71} +(30.7201 + 67.2676i) q^{73} +(26.4856 - 90.2018i) q^{74} +(-27.5727 + 31.8206i) q^{76} +(119.355 + 17.1606i) q^{77} +(-66.1732 - 76.3679i) q^{79} +(-1.32110 - 2.05567i) q^{80} +(44.2692 + 51.0894i) q^{82} +(36.5369 + 124.433i) q^{83} +(0.838506 - 0.967687i) q^{85} +(16.9838 + 7.75623i) q^{86} +(-18.7686 - 41.0976i) q^{88} +(-117.030 + 16.8263i) q^{89} -127.782 q^{91} +(-17.8106 + 42.4121i) q^{92} +(17.7738 + 11.4225i) q^{94} +(12.7299 - 1.83028i) q^{95} +(-104.624 - 30.7203i) q^{97} +(10.2712 + 4.69070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 + 16 * q^7	$ 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	−	1.81926i	−0.207708	−	0.454816i
$5$	−0.172109	+	0.586151i	−0.0344219	+	0.117230i	−0.974912	−	0.222591i	$-0.928548\pi$
$5$	−0.172109	+	0.586151i	−0.0344219	+	0.117230i	0.940490	+	0.339821i	$0.110367\pi$
$6$		0			0
$7$	−4.94341	+	5.70500i	−0.706202	+	0.815000i	−0.989576	−	0.144009i	$-0.954001\pi$
$7$	−4.94341	+	5.70500i	−0.706202	+	0.815000i	0.283375	+	0.959009i	$0.408546\pi$
$8$	2.79964	+	0.402527i	0.349955	+	0.0503159i
$9$		0			0
$10$	−0.565759	−	0.652921i	−0.0565759	−	0.0652921i
$11$	−8.63603	−	13.4379i	−0.785093	−	1.22163i	−0.971004	−	0.239063i	$-0.923160\pi$
$11$	−8.63603	−	13.4379i	−0.785093	−	1.22163i	0.185911	−	0.982567i	$-0.440476\pi$
$12$		0			0
$13$	11.0851	+	12.7929i	0.852701	+	0.984069i	0.999987	−	0.00502491i	$-0.00159949\pi$
$13$	11.0851	+	12.7929i	0.852701	+	0.984069i	−0.147287	+	0.989094i	$0.547054\pi$
$14$	−3.00767	−	10.2432i	−0.214833	−	0.731655i
$15$		0			0
$16$	−2.61944	+	3.02300i	−0.163715	+	0.188937i
$17$	−1.90658	−	0.870706i	−0.112152	−	0.0512180i	0.358549	−	0.933511i	$-0.383272\pi$
$17$	−1.90658	−	0.870706i	−0.112152	−	0.0512180i	−0.470701	+	0.882293i	$0.655999\pi$
$18$		0			0
$19$	−8.74546	−	19.1499i	−0.460287	−	1.00789i	−0.987422	−	0.158107i	$-0.949461\pi$
$19$	−8.74546	−	19.1499i	−0.460287	−	1.00789i	0.527135	−	0.849782i	$-0.323266\pi$
$20$	1.20936	−	0.173879i	0.0604678	−	0.00869396i
$21$		0			0
$22$	22.5902			1.02683
$23$	−15.5903	−	16.9098i	−0.677839	−	0.735210i
$23$	−15.5903	−	16.9098i	−0.677839	−	0.735210i
$24$		0			0
$25$	20.7174	+	13.3143i	0.828695	+	0.532570i
$26$	−23.6953	+	3.40687i	−0.911359	+	0.131034i
$27$		0			0
$28$	14.4860	+	4.25348i	0.517359	+	0.151910i
$29$	−29.1843	−	13.3280i	−1.00636	−	0.459587i	−0.157108	−	0.987581i	$-0.550217\pi$
$29$	−29.1843	−	13.3280i	−1.00636	−	0.459587i	−0.849248	+	0.527994i	$0.822944\pi$
$30$		0			0
$31$	7.05976	−	49.1017i	0.227734	−	1.58393i	−0.479885	−	0.877331i	$-0.659322\pi$
$31$	7.05976	−	49.1017i	0.227734	−	1.58393i	0.707619	−	0.706594i	$-0.249769\pi$
$32$	−1.59372	−	5.42771i	−0.0498038	−	0.169616i
$33$		0			0
$34$	2.49363	−	1.60256i	0.0733420	−	0.0471340i
$35$	−2.49318	−	3.87947i	−0.0712338	−	0.110842i
$36$		0			0
$37$	−63.7823	+	18.7282i	−1.72385	+	0.506167i	−0.985705	−	0.168480i	$-0.946114\pi$
$37$	−63.7823	+	18.7282i	−1.72385	+	0.506167i	−0.738141	+	0.674647i	$0.764296\pi$
$38$	29.4695	+	4.23707i	0.775512	+	0.111502i
$39$		0			0
$40$	−0.717785	+	1.57173i	−0.0179446	+	0.0392933i
$41$	13.4671	−	45.8648i	0.328466	−	1.11865i	−0.615369	−	0.788239i	$-0.710993\pi$
$41$	13.4671	−	45.8648i	0.328466	−	1.11865i	0.943836	−	0.330415i	$-0.107189\pi$
$42$		0			0
$43$	−1.87890	−	13.0680i	−0.0436954	−	0.303908i	−0.999936	−	0.0113261i	$-0.996395\pi$
$43$	−1.87890	−	13.0680i	−0.0436954	−	0.303908i	0.956240	−	0.292582i	$-0.0945144\pi$
$44$	−17.2721	+	26.8758i	−0.392547	+	0.610815i
$45$		0			0
$46$	32.0379	−	5.61903i	0.696476	−	0.122153i
$47$		−	14.9396i		−	0.317864i	−0.987290	−	0.158932i	$-0.949195\pi$
$47$		−	14.9396i		−	0.317864i	0.987290	−	0.158932i	$-0.0508051\pi$
$48$		0			0
$49$	−1.13629	−	7.90309i	−0.0231897	−	0.161288i
$50$	−31.6803	+	14.4679i	−0.633605	+	0.289358i
$51$		0			0
$52$	14.0638	−	30.7955i	0.270458	−	0.592220i
$53$	−51.4921	−	44.6182i	−0.971549	−	0.841852i	0.0158867	−	0.999874i	$-0.494943\pi$
$53$	−51.4921	−	44.6182i	−0.971549	−	0.841852i	−0.987436	+	0.158022i	$0.949488\pi$
$54$		0			0
$55$	9.36299	−	2.74922i	0.170236	−	0.0499858i
$56$	−16.1362	+	13.9821i	−0.288146	+	0.249680i
$57$		0			0
$58$	38.1703	−	24.5306i	0.658109	−	0.422941i
$59$	14.0463	−	12.1712i	0.238073	−	0.206292i	−0.527650	−	0.849462i	$-0.676927\pi$
$59$	14.0463	−	12.1712i	0.238073	−	0.206292i	0.765723	+	0.643170i	$0.222381\pi$
$60$		0			0
$61$	10.3773	−	72.1756i	0.170119	−	1.18321i	−0.708510	−	0.705701i	$-0.750632\pi$
$61$	10.3773	−	72.1756i	0.170119	−	1.18321i	0.878629	−	0.477505i	$-0.158459\pi$
$62$	53.0191	+	45.9413i	0.855147	+	0.740989i
$63$		0			0
$64$	7.67594	+	2.25386i	0.119937	+	0.0352166i
$65$	−9.40641	+	4.29577i	−0.144714	+	0.0660887i
$66$		0			0
$67$	77.1069	+	49.5536i	1.15085	+	0.739605i	0.969808	−	0.243870i	$-0.0784171\pi$
$67$	77.1069	+	49.5536i	1.15085	+	0.739605i	0.181041	+	0.983476i	$0.442053\pi$
$68$			4.19198i			0.0616468i
$69$		0			0
$70$	6.52169			0.0931670
$71$	48.0839	−	74.8200i	0.677238	−	1.05380i	−0.317187	−	0.948363i	$-0.602738\pi$
$71$	48.0839	−	74.8200i	0.677238	−	1.05380i	0.994426	−	0.105441i	$-0.0336253\pi$
$72$		0			0
$73$	30.7201	+	67.2676i	0.420823	+	0.921473i	0.994728	+	0.102551i	$0.0327006\pi$
$73$	30.7201	+	67.2676i	0.420823	+	0.921473i	−0.573905	+	0.818922i	$0.694572\pi$
$74$	26.4856	−	90.2018i	0.357914	−	1.21894i
$75$		0			0
$76$	−27.5727	+	31.8206i	−0.362799	+	0.418692i
$77$	119.355	+	17.1606i	1.55006	+	0.222865i
$78$		0			0
$79$	−66.1732	−	76.3679i	−0.837635	−	0.966683i	0.162163	−	0.986764i	$-0.448153\pi$
$79$	−66.1732	−	76.3679i	−0.837635	−	0.966683i	−0.999798	+	0.0200812i	$0.993608\pi$
$80$	−1.32110	−	2.05567i	−0.0165138	−	0.0256959i
$81$		0			0
$82$	44.2692	+	51.0894i	0.539868	+	0.623041i
$83$	36.5369	+	124.433i	0.440204	+	1.49920i	0.819042	+	0.573734i	$0.194506\pi$
$83$	36.5369	+	124.433i	0.440204	+	1.49920i	−0.378838	+	0.925463i	$0.623676\pi$
$84$		0			0
$85$	0.838506	−	0.967687i	0.00986477	−	0.0113846i
$86$	16.9838	+	7.75623i	0.197486	+	0.0901887i
$87$		0			0
$88$	−18.7686	−	41.0976i	−0.213280	−	0.467018i
$89$	−117.030	+	16.8263i	−1.31494	+	0.189060i	−0.763855	−	0.645388i	$-0.776696\pi$
$89$	−117.030	+	16.8263i	−1.31494	+	0.189060i	−0.551087	+	0.834448i	$0.685787\pi$
$90$		0			0
$91$	−127.782			−1.40419
$92$	−17.8106	+	42.4121i	−0.193593	+	0.461001i
$93$		0			0
$94$	17.7738	+	11.4225i	0.189083	+	0.121516i
$95$	12.7299	−	1.83028i	0.133999	−	0.0192661i
$96$		0			0
$97$	−104.624	−	30.7203i	−1.07860	−	0.316704i	−0.306279	−	0.951942i	$-0.599084\pi$
$97$	−104.624	−	30.7203i	−1.07860	−	0.316704i	−0.772317	+	0.635238i	$0.780902\pi$
$98$	10.2712	+	4.69070i	0.104808	+	0.0478643i
$99$		0			0
$100$	7.00952	−	48.7523i	0.0700952	−	0.487523i
$101$	−10.4544	−	35.6043i	−0.103509	−	0.352518i	0.891410	−	0.453197i	$-0.149717\pi$
$101$	−10.4544	−	35.6043i	−0.103509	−	0.352518i	−0.994919	+	0.100679i	$0.967898\pi$
$102$		0			0
$103$	−23.7275	+	15.2487i	−0.230364	+	0.148046i	−0.650731	−	0.759308i	$-0.725538\pi$
$103$	−23.7275	+	15.2487i	−0.230364	+	0.148046i	0.420367	+	0.907354i	$0.361901\pi$
$104$	25.8848	+	40.2775i	0.248892	+	0.387284i
$105$		0			0
$106$	92.4527	−	27.1466i	0.872195	−	0.256100i
$107$	7.83849	+	1.12700i	0.0732569	+	0.0105328i	0.178846	−	0.983877i	$-0.442764\pi$
$107$	7.83849	+	1.12700i	0.0732569	+	0.0105328i	−0.105589	+	0.994410i	$0.533673\pi$
$108$		0			0
$109$	−31.3193	+	68.5797i	−0.287333	+	0.629172i	−0.997169	−	0.0751954i	$-0.976042\pi$
$109$	−31.3193	+	68.5797i	−0.287333	+	0.629172i	0.709836	+	0.704367i	$0.248769\pi$
$110$	−3.88799	+	13.2413i	−0.0353453	+	0.120375i
$111$		0			0
$112$	−4.29722	−	29.8879i	−0.0383681	−	0.266856i
$113$	−61.4969	+	95.6911i	−0.544220	+	0.846824i	−0.999042	−	0.0437590i	$-0.986067\pi$
$113$	−61.4969	+	95.6911i	−0.544220	+	0.846824i	0.454822	+	0.890583i	$0.349703\pi$
$114$		0			0
$115$	12.5949	−	6.22793i	0.109521	−	0.0541559i
$116$			64.1673i			0.553166i
$117$		0			0
$118$	3.74067	+	26.0170i	0.0317006	+	0.220483i
$119$	14.3924	−	6.57279i	0.120945	−	0.0552335i
$120$		0			0
$121$	−55.7316	+	122.035i	−0.460591	+	1.00855i
$122$	77.9339	+	67.5301i	0.638802	+	0.553526i
$123$		0			0
$124$	−95.1944	+	27.9516i	−0.767697	+	0.225416i
$125$	−22.9119	+	19.8533i	−0.183295	+	0.158826i
$126$		0			0
$127$	−155.613	+	100.007i	−1.22530	+	0.787454i	−0.983153	−	0.182786i	$-0.941489\pi$
$127$	−155.613	+	100.007i	−1.22530	+	0.787454i	−0.242149	+	0.970239i	$0.577852\pi$
$128$	−8.55033	+	7.40890i	−0.0667995	+	0.0578821i
$129$		0			0
$130$	2.08125	−	14.4754i	0.0160096	−	0.111349i
$131$	83.5598	+	72.4050i	0.637861	+	0.552710i	0.912623	−	0.408803i	$-0.134054\pi$
$131$	83.5598	+	72.4050i	0.637861	+	0.552710i	−0.274762	+	0.961512i	$0.588599\pi$
$132$		0			0
$133$	152.482	+	44.7729i	1.14648	+	0.336638i
$134$	−117.909	+	53.8472i	−0.879918	+	0.401845i
$135$		0			0
$136$	−4.98725	−	3.20511i	−0.0366710	−	0.0235670i
$137$			39.3102i			0.286936i	0.989655	+	0.143468i	$0.0458254\pi$
$137$			39.3102i			0.286936i	−0.989655	+	0.143468i	$0.954175\pi$
$138$		0			0
$139$	−54.3308			−0.390869			−0.195435	−	0.980717i	$-0.562612\pi$
$139$	−54.3308			−0.390869			−0.195435	+	0.980717i	$0.562612\pi$
$140$	−4.98637	+	7.75894i	−0.0356169	+	0.0554210i
$141$		0			0
$142$	52.2502	+	114.412i	0.367959	+	0.805719i
$143$	76.1786	−	259.441i	0.532718	−	1.81427i
$144$		0			0
$145$	12.8351	−	14.8125i	0.0885181	−	0.102155i
$146$	−103.517	−	14.8835i	−0.709021	−	0.101942i
$147$		0			0
$148$	87.0637	+	100.477i	0.588268	+	0.678898i
$149$	111.166	+	172.978i	0.746082	+	1.16093i	0.981950	+	0.189142i	$0.0605705\pi$
$149$	111.166	+	172.978i	0.746082	+	1.16093i	−0.235867	+	0.971785i	$0.575793\pi$
$150$		0			0
$151$	0.0601066	+	0.0693667i	0.000398057	+	0.000459382i	0.755949	−	0.654631i	$-0.227176\pi$
$151$	0.0601066	+	0.0693667i	0.000398057	+	0.000459382i	−0.755551	+	0.655090i	$0.772631\pi$
$152$	−16.7758	−	57.1330i	−0.110367	−	0.375875i
$153$		0			0
$154$	−111.673	+	128.877i	−0.725147	+	0.836865i
$155$	27.5659	+	12.5889i	0.177845	+	0.0812190i
$156$		0			0
$157$	−70.3561	−	154.058i	−0.448128	−	0.981264i	−0.990035	−	0.140825i	$-0.955025\pi$
$157$	−70.3561	−	154.058i	−0.448128	−	0.981264i	0.541906	−	0.840439i	$-0.317703\pi$
$158$	141.451	−	20.3375i	0.895257	−	0.128719i
$159$		0			0
$160$	3.45575			0.0215984
$161$	173.540	−	5.35044i	1.07789	−	0.0332325i
$162$		0			0
$163$	39.3079	+	25.2616i	0.241153	+	0.154979i	0.655635	−	0.755078i	$-0.272401\pi$
$163$	39.3079	+	25.2616i	0.241153	+	0.154979i	−0.414482	+	0.910057i	$0.636037\pi$
$164$	−94.6291	+	13.6056i	−0.577007	+	0.0829610i
$165$		0			0
$166$	−175.975	−	51.6710i	−1.06009	−	0.311271i
$167$	−200.499	−	91.5647i	−1.20059	−	0.548292i	−0.288184	−	0.957575i	$-0.593051\pi$
$167$	−200.499	−	91.5647i	−1.20059	−	0.548292i	−0.912407	+	0.409283i	$0.865779\pi$
$168$		0			0
$169$	−16.7274	+	116.341i	−0.0989785	+	0.688411i
$170$	0.510163	+	1.73746i	0.00300096	+	0.0102203i
$171$		0			0
$172$	−22.2132	+	14.2755i	−0.129146	+	0.0829973i
$173$	−41.7879	−	65.0233i	−0.241549	−	0.375857i	0.699220	−	0.714907i	$-0.253531\pi$
$173$	−41.7879	−	65.0233i	−0.241549	−	0.375857i	−0.940768	+	0.339050i	$0.889895\pi$
$174$		0			0
$175$	−178.372	+	52.3749i	−1.01927	+	0.299285i
$176$	63.2444	+	9.09317i	0.359343	+	0.0516657i
$177$		0			0
$178$	69.4603	−	152.097i	0.390227	−	0.854477i
$179$	−86.3130	+	293.955i	−0.482196	+	1.64221i	0.255304	+	0.966861i	$0.417824\pi$
$179$	−86.3130	+	293.955i	−0.482196	+	1.64221i	−0.737500	+	0.675347i	$0.763994\pi$
$180$		0			0
$181$	21.7014	+	150.937i	0.119897	+	0.833905i	0.957666	+	0.287880i	$0.0929505\pi$
$181$	21.7014	+	150.937i	0.119897	+	0.833905i	−0.837769	+	0.546025i	$0.816140\pi$
$182$	97.6996	−	152.023i	0.536811	−	0.835294i
$183$		0			0
$184$	−36.8405	−	53.6169i	−0.200220	−	0.291396i
$185$		−	40.6093i		−	0.219510i
$186$		0			0
$187$	4.76480	+	33.1399i	0.0254802	+	0.177219i
$188$	−27.1791	+	12.4123i	−0.144570	+	0.0660227i
$189$		0			0
$190$	−7.55553	+	16.5443i	−0.0397659	+	0.0870753i
$191$	128.443	+	111.296i	0.672474	+	0.582702i	0.922716	−	0.385481i	$-0.125965\pi$
$191$	128.443	+	111.296i	0.672474	+	0.582702i	−0.250242	+	0.968183i	$0.580510\pi$
$192$		0			0
$193$	201.175	−	59.0704i	1.04236	−	0.306064i	0.284633	−	0.958637i	$-0.408128\pi$
$193$	201.175	−	59.0704i	1.04236	−	0.306064i	0.757727	+	0.652572i	$0.226310\pi$
$194$	116.542	−	100.984i	0.600731	−	0.520536i
$195$		0			0
$196$	−13.4337	+	8.63334i	−0.0685395	+	0.0440477i
$197$	−157.681	+	136.631i	−0.800411	+	0.693560i	−0.955711	−	0.294307i	$-0.904911\pi$
$197$	−157.681	+	136.631i	−0.800411	+	0.693560i	0.155300	+	0.987867i	$0.450366\pi$
$198$		0			0
$199$	23.2484	−	161.696i	0.116826	−	0.812542i	−0.844189	−	0.536046i	$-0.819917\pi$
$199$	23.2484	−	161.696i	0.116826	−	0.812542i	0.961015	−	0.276497i	$-0.0891735\pi$
$200$	52.6418	+	45.6144i	0.263209	+	0.228072i
$201$		0			0
$202$	50.3521	+	14.7847i	0.249268	+	0.0731916i
$203$	220.307	−	100.611i	1.08525	−	0.495619i
$204$		0			0
$205$	24.5659	+	15.7875i	0.119834	+	0.0770123i
$206$		−	39.8878i		−	0.193630i
$207$		0			0
$208$	−67.7097			−0.325527
$209$	−181.809	+	282.900i	−0.869897	+	1.35359i
$210$		0			0
$211$	−75.5340	−	165.396i	−0.357981	−	0.783870i	−0.999854	−	0.0170588i	$-0.994570\pi$
$211$	−75.5340	−	165.396i	−0.357981	−	0.783870i	0.641873	−	0.766811i	$-0.278158\pi$
$212$	−38.3910	+	130.748i	−0.181090	+	0.616735i
$213$		0			0
$214$	−7.33398	+	8.46386i	−0.0342709	+	0.0395508i
$215$	7.98322	+	1.14781i	0.0371312	+	0.00533867i
$216$		0			0
$217$	245.226	+	283.006i	1.13007	+	1.30417i
$218$	−57.6440	−	89.6958i	−0.264422	−	0.411449i
$219$		0			0
$220$	−12.7806	−	14.7496i	−0.0580937	−	0.0670437i
$221$	−9.99580	−	34.0426i	−0.0452299	−	0.154039i
$222$		0			0
$223$	138.419	−	159.744i	0.620711	−	0.716339i	−0.355131	−	0.934817i	$-0.615564\pi$
$223$	138.419	−	159.744i	0.620711	−	0.716339i	0.975842	+	0.218478i	$0.0701091\pi$
$224$	38.8435	+	17.7392i	0.173409	+	0.0791930i
$225$		0			0
$226$	−66.8254	−	146.327i	−0.295688	−	0.647466i
$227$	8.76052	−	1.25957i	0.0385926	−	0.00554878i	−0.122991	−	0.992408i	$-0.539249\pi$
$227$	8.76052	−	1.25957i	0.0385926	−	0.00554878i	0.161584	+	0.986859i	$0.448340\pi$
$228$		0			0
$229$	87.0830			0.380275			0.190138	−	0.981757i	$-0.439107\pi$
$229$	87.0830			0.380275			0.190138	+	0.981757i	$0.439107\pi$
$230$	−2.22042	+	19.7461i	−0.00965402	+	0.0858527i
$231$		0			0
$232$	−76.3406	−	49.0611i	−0.329054	−	0.211470i
$233$	184.632	−	26.5461i	0.792413	−	0.113932i	0.265790	−	0.964031i	$-0.414367\pi$
$233$	184.632	−	26.5461i	0.792413	−	0.113932i	0.526623	+	0.850099i	$0.323458\pi$
$234$		0			0
$235$	8.75686	+	2.57125i	0.0372632	+	0.0109415i
$236$	−33.8127	−	15.4418i	−0.143274	−	0.0654312i
$237$		0			0
$238$	−3.18444	+	22.1482i	−0.0133800	+	0.0930598i
$239$	−110.199	−	375.303i	−0.461083	−	1.57030i	−0.782051	−	0.623215i	$-0.785826\pi$
$239$	−110.199	−	375.303i	−0.461083	−	1.57030i	0.320968	−	0.947090i	$-0.395992\pi$
$240$		0			0
$241$	290.864	−	186.927i	1.20690	−	0.775630i	0.226766	−	0.973949i	$-0.427185\pi$
$241$	290.864	−	186.927i	1.20690	−	0.775630i	0.980138	+	0.198319i	$0.0635482\pi$
$242$	−102.575	−	159.610i	−0.423865	−	0.659547i
$243$		0			0
$244$	−139.928	+	41.0866i	−0.573476	+	0.168388i
$245$	4.82797	+	0.694157i	0.0197060	+	0.00283329i
$246$		0			0
$247$	148.038	−	324.158i	0.599344	−	1.31238i
$248$	39.5295	−	134.625i	0.159393	−	0.542843i
$249$		0			0
$250$	−6.10167	−	42.4381i	−0.0244067	−	0.169752i
$251$	−49.5097	+	77.0387i	−0.197250	+	0.306927i	−0.925762	−	0.378106i	$-0.876576\pi$
$251$	−49.5097	+	77.0387i	−0.197250	+	0.306927i	0.728513	+	0.685032i	$0.240212\pi$
$252$		0			0
$253$	−92.5947	+	355.535i	−0.365987	+	1.40528i
$254$		−	261.598i		−	1.02991i
$255$		0			0
$256$	−2.27704	−	15.8371i	−0.00889468	−	0.0618638i
$257$	66.6840	−	30.4535i	0.259471	−	0.118496i	−0.281433	−	0.959581i	$-0.590810\pi$
$257$	66.6840	−	30.4535i	0.259471	−	0.118496i	0.540904	+	0.841085i	$0.318082\pi$
$258$		0			0
$259$	208.458	−	456.459i	0.804857	−	1.76239i
$260$	15.6303	+	13.5437i	0.0601164	+	0.0520912i
$261$		0			0
$262$	−150.029	+	44.0526i	−0.572631	+	0.168140i
$263$	−97.5024	+	84.4863i	−0.370732	+	0.321241i	−0.820223	−	0.572044i	$-0.806151\pi$
$263$	−97.5024	+	84.4863i	−0.370732	+	0.321241i	0.449491	+	0.893285i	$0.351605\pi$
$264$		0			0
$265$	35.0152	−	22.5029i	0.132133	−	0.0849167i
$266$	−169.852	+	147.178i	−0.638542	+	0.553300i
$267$		0			0
$268$	26.0883	−	181.448i	0.0973445	−	0.677046i
$269$	−378.625	−	328.081i	−1.40753	−	1.21963i	−0.942444	−	0.334365i	$-0.891478\pi$
$269$	−378.625	−	328.081i	−1.40753	−	1.21963i	−0.465085	−	0.885266i	$-0.653976\pi$
$270$		0			0
$271$	158.019	+	46.3985i	0.583095	+	0.171212i	0.559959	−	0.828520i	$-0.310817\pi$
$271$	158.019	+	46.3985i	0.583095	+	0.171212i	0.0231356	+	0.999732i	$0.492635\pi$
$272$	7.62632	−	3.48283i	0.0280380	−	0.0128045i
$273$		0			0
$274$	−46.7679	−	30.0559i	−0.170686	−	0.109693i
$275$		−	393.381i		−	1.43048i
$276$		0			0
$277$	3.54592			0.0128012			0.00640058	−	0.999980i	$-0.497963\pi$
$277$	3.54592			0.0128012			0.00640058	+	0.999980i	$0.497963\pi$
$278$	41.5403	−	64.6380i	0.149426	−	0.232511i
$279$		0			0
$280$	−5.41842	−	11.8647i	−0.0193515	−	0.0423739i
$281$	−30.2930	+	103.169i	−0.107804	+	0.367148i	−0.995670	−	0.0929542i	$-0.970369\pi$
$281$	−30.2930	+	103.169i	−0.107804	+	0.367148i	0.887866	+	0.460102i	$0.152187\pi$
$282$		0			0
$283$	186.539	−	215.278i	0.659149	−	0.760699i	−0.323489	−	0.946232i	$-0.604856\pi$
$283$	186.539	−	215.278i	0.659149	−	0.760699i	0.982638	+	0.185533i	$0.0594013\pi$
$284$	−176.067	−	25.3146i	−0.619954	−	0.0891360i
$285$		0			0
$286$	250.415	+	288.994i	0.875576	+	1.01047i
$287$	195.085	+	303.559i	0.679740	+	1.05770i
$288$		0			0
$289$	−186.378	−	215.091i	−0.644906	−	0.744261i
$290$	7.80914	+	26.5955i	0.0269281	+	0.0917086i
$291$		0			0
$292$	96.8543	−	111.776i	0.331693	−	0.382794i
$293$	−214.858	−	98.1225i	−0.733305	−	0.334889i	0.0135214	−	0.999909i	$-0.495696\pi$
$293$	−214.858	−	98.1225i	−0.733305	−	0.334889i	−0.746826	+	0.665020i	$0.768423\pi$
$294$		0			0
$295$	4.71666	+	10.3280i	0.0159887	+	0.0350103i
$296$	−186.106	+	26.7580i	−0.628736	+	0.0903986i
$297$		0			0
$298$	−290.790			−0.975805
$299$	43.5055	−	386.892i	0.145503	−	1.29395i
$300$		0			0
$301$	83.8414	+	53.8816i	0.278543	+	0.179009i
$302$	−0.128483	+	0.0184730i	−0.000425440	+	6.11690e-5i
$303$		0			0
$304$	80.7983	+	23.7245i	0.265784	+	0.0780412i
$305$	40.5197	+	18.5047i	0.132852	+	0.0606713i
$306$		0			0
$307$	42.6082	−	296.347i	0.138789	−	0.965299i	−0.794779	−	0.606899i	$-0.792413\pi$
$307$	42.6082	−	296.347i	0.138789	−	0.965299i	0.933568	−	0.358400i	$-0.116678\pi$
$308$	−67.9438	−	231.395i	−0.220597	−	0.751284i
$309$		0			0
$310$	−36.0536	+	23.1703i	−0.116302	+	0.0747428i
$311$	325.313	+	506.197i	1.04602	+	1.62764i	0.736087	+	0.676887i	$0.236672\pi$
$311$	325.313	+	506.197i	1.04602	+	1.62764i	0.309937	+	0.950757i	$0.399692\pi$
$312$		0			0
$313$	99.8401	−	29.3157i	0.318978	−	0.0936604i	−0.118324	−	0.992975i	$-0.537752\pi$
$313$	99.8401	−	29.3157i	0.318978	−	0.0936604i	0.437302	+	0.899315i	$0.355934\pi$
$314$	237.078	+	34.0867i	0.755026	+	0.108556i
$315$		0			0
$316$	−83.9548	+	183.835i	−0.265680	+	0.581757i
$317$	−2.85982	+	9.73965i	−0.00902151	+	0.0307244i	−0.963881	−	0.266334i	$-0.914188\pi$
$317$	−2.85982	+	9.73965i	−0.00902151	+	0.0307244i	0.954859	+	0.297059i	$0.0960057\pi$
$318$		0			0
$319$	72.9355	+	507.278i	0.228638	+	1.59021i
$320$	−2.64220	+	4.11135i	−0.00825689	+	0.0128480i
$321$		0			0
$322$	−126.320	+	210.553i	−0.392298	+	0.653893i
$323$			44.1255i			0.136612i
$324$		0			0
$325$	59.3266	+	412.625i	0.182543	+	1.26962i
$326$	−60.1081	+	27.4505i	−0.184381	+	0.0842039i
$327$		0			0
$328$	56.1649	−	122.984i	0.171234	−	0.374951i
$329$	85.2305	+	73.8526i	0.259059	+	0.224476i
$330$		0			0
$331$	−26.1640	+	7.68244i	−0.0790453	+	0.0232098i	−0.321016	−	0.947074i	$-0.604024\pi$
$331$	−26.1640	+	7.68244i	−0.0790453	+	0.0232098i	0.241971	+	0.970284i	$0.422206\pi$
$332$	196.021	−	169.853i	0.590425	−	0.511606i
$333$		0			0
$334$	262.233	−	168.527i	0.785130	−	0.504572i
$335$	−42.3167	+	36.6676i	−0.126318	+	0.109456i
$336$		0			0
$337$	71.7678	−	499.156i	0.212961	−	1.48118i	−0.550236	−	0.835009i	$-0.685462\pi$
$337$	71.7678	−	499.156i	0.212961	−	1.48118i	0.763197	−	0.646166i	$-0.223629\pi$
$338$	−125.623	−	108.853i	−0.371667	−	0.322051i
$339$		0			0
$340$	−2.45713	−	0.721480i	−0.00722686	−	0.00212200i
$341$	−720.793	+	329.175i	−2.11376	+	0.965323i
$342$		0			0
$343$	−260.468	−	167.393i	−0.759382	−	0.488025i
$344$		−	37.3421i		−	0.108553i
$345$		0			0
$346$	109.309			0.315923
$347$	−45.4176	+	70.6712i	−0.130886	+	0.203663i	−0.900511	−	0.434834i	$-0.856807\pi$
$347$	−45.4176	+	70.6712i	−0.130886	+	0.203663i	0.769624	+	0.638497i	$0.220444\pi$
$348$		0			0
$349$	149.945	+	328.334i	0.429642	+	0.940786i	0.993385	+	0.114835i	$0.0366339\pi$
$349$	149.945	+	328.334i	0.429642	+	0.940786i	−0.563742	+	0.825951i	$0.690639\pi$
$350$	74.0693	−	252.257i	0.211626	−	0.720733i
$351$		0			0
$352$	−59.1738	+	68.2902i	−0.168107	+	0.194006i
$353$	−305.290	−	43.8941i	−0.864846	−	0.124346i	−0.304407	−	0.952542i	$-0.598458\pi$
$353$	−305.290	−	43.8941i	−0.864846	−	0.124346i	−0.560439	+	0.828196i	$0.689367\pi$
$354$		0			0
$355$	35.5801	+	41.0617i	0.100226	+	0.115667i
$356$	127.843	+	198.928i	0.359111	+	0.558787i
$357$		0			0
$358$	−283.729	−	327.440i	−0.792538	−	0.914638i
$359$	−151.217	−	514.998i	−0.421218	−	1.43454i	−0.847911	−	0.530139i	$-0.822140\pi$
$359$	−151.217	−	514.998i	−0.421218	−	1.43454i	0.426693	−	0.904397i	$-0.359679\pi$
$360$		0			0
$361$	−53.8301	+	62.1232i	−0.149114	+	0.172086i
$362$	−196.164	−	89.5851i	−0.541889	−	0.247473i
$363$		0			0
$364$	106.165	+	232.469i	0.291662	+	0.638650i
$365$	−44.7161	+	6.42921i	−0.122510	+	0.0176143i
$366$		0			0
$367$	−322.862			−0.879732			−0.439866	−	0.898064i	$-0.644974\pi$
$367$	−322.862			−0.879732			−0.439866	+	0.898064i	$0.644974\pi$
$368$	91.9563	−	2.83512i	0.249881	−	0.00770413i
$369$		0			0
$370$	48.3134	+	31.0491i	0.130577	+	0.0839166i
$371$	509.093	−	73.1966i	1.37222	−	0.197295i
$372$		0			0
$373$	178.620	+	52.4476i	0.478874	+	0.140610i	0.512257	−	0.858832i	$-0.328810\pi$
$373$	178.620	+	52.4476i	0.478874	+	0.140610i	−0.0333822	+	0.999443i	$0.510628\pi$
$374$	−43.0701	−	19.6694i	−0.115161	−	0.0525921i
$375$		0			0
$376$	6.01360	−	41.8255i	0.0159936	−	0.111238i
$377$	−153.007	−	521.095i	−0.405855	−	1.38221i
$378$		0			0
$379$	−526.144	+	338.132i	−1.38824	+	0.892169i	−0.999573	−	0.0292080i	$-0.990701\pi$
$379$	−526.144	+	338.132i	−1.38824	+	0.892169i	−0.388669	+	0.921377i	$0.627065\pi$
$380$	−13.9061	−	21.6384i	−0.0365951	−	0.0569431i
$381$		0			0
$382$	−230.615	+	67.7147i	−0.603704	+	0.177264i
$383$	−160.638	−	23.0963i	−0.419421	−	0.0603036i	−0.0706264	−	0.997503i	$-0.522500\pi$
$383$	−160.638	−	23.0963i	−0.419421	−	0.0603036i	−0.348795	+	0.937199i	$0.613409\pi$
$384$		0			0
$385$	−30.6008	+	67.0064i	−0.0794826	+	0.174043i
$386$	−83.5382	+	284.505i	−0.216420	+	0.737060i
$387$		0			0
$388$	31.0362	+	215.862i	0.0799902	+	0.556344i
$389$	14.4939	−	22.5529i	0.0372593	−	0.0579766i	−0.822124	−	0.569308i	$-0.807211\pi$
$389$	14.4939	−	22.5529i	0.0372593	−	0.0579766i	0.859384	+	0.511331i	$0.170848\pi$
$390$		0			0
$391$	15.0007	+	45.8145i	0.0383649	+	0.117173i
$392$		−	22.5832i		−	0.0576102i
$393$		0			0
$394$	−41.9920	−	292.061i	−0.106579	−	0.741271i
$395$	56.1521	−	25.6438i	0.142157	−	0.0649211i
$396$		0			0
$397$	−277.742	+	608.170i	−0.699602	+	1.53191i	0.140851	+	0.990031i	$0.455016\pi$
$397$	−277.742	+	608.170i	−0.699602	+	1.53191i	−0.840453	+	0.541884i	$0.817711\pi$
$398$	174.596	+	151.289i	0.438684	+	0.380122i
$399$		0			0
$400$	−94.5170	+	27.7527i	−0.236292	+	0.0693817i
$401$	111.419	−	96.5453i	0.277853	−	0.240761i	−0.504774	−	0.863251i	$-0.668424\pi$
$401$	111.419	−	96.5453i	0.277853	−	0.240761i	0.782628	+	0.622490i	$0.213879\pi$
$402$		0			0
$403$	706.411	−	453.983i	1.75288	−	1.12651i
$404$	−56.0878	+	48.6004i	−0.138831	+	0.120298i
$405$		0			0
$406$	−48.7446	+	339.026i	−0.120061	+	0.835040i
$407$	802.493	+	695.364i	1.97173	+	1.70851i
$408$		0			0
$409$	603.563	+	177.222i	1.47570	+	0.433306i	0.917949	−	0.396699i	$-0.129844\pi$
$409$	603.563	+	177.222i	1.47570	+	0.433306i	0.557756	+	0.830005i	$0.311663\pi$
$410$	−37.5652	+	17.1555i	−0.0916225	+	0.0418426i
$411$		0			0
$412$	47.4550	+	30.4975i	0.115182	+	0.0740231i
$413$			140.302i			0.339713i
$414$		0			0
$415$	−79.2250			−0.190904
$416$	51.7696	−	80.5551i	0.124446	−	0.193642i
$417$		0			0
$418$	−197.562	−	432.600i	−0.472636	−	1.03493i
$419$	79.0771	−	269.312i	0.188728	−	0.642749i	−0.809707	−	0.586834i	$-0.800374\pi$
$419$	79.0771	−	269.312i	0.188728	−	0.642749i	0.998436	−	0.0559153i	$-0.0178077\pi$
$420$		0			0
$421$	46.0397	−	53.1326i	0.109358	−	0.126206i	−0.698432	−	0.715677i	$-0.746118\pi$
$421$	46.0397	−	53.1326i	0.109358	−	0.126206i	0.807789	+	0.589471i	$0.200664\pi$
$422$	254.526	+	36.5953i	0.603143	+	0.0867188i
$423$		0			0
$424$	−126.199	−	145.642i	−0.297640	−	0.343494i
$425$	−27.9066	−	43.4235i	−0.0656625	−	0.102173i
$426$		0			0
$427$	360.463	+	415.996i	0.844175	+	0.974230i
$428$	−4.46213	−	15.1966i	−0.0104255	−	0.0355062i
$429$		0			0
$430$	−7.46939	+	8.62013i	−0.0173707	+	0.0200468i
$431$	176.380	+	80.5499i	0.409234	+	0.186891i	0.609385	−	0.792874i	$-0.291416\pi$
$431$	176.380	+	80.5499i	0.409234	+	0.186891i	−0.200152	+	0.979765i	$0.564144\pi$
$432$		0			0
$433$	24.7713	+	54.2417i	0.0572086	+	0.125269i	0.936077	−	0.351794i	$-0.114428\pi$
$433$	24.7713	+	54.2417i	0.0572086	+	0.125269i	−0.878869	+	0.477064i	$0.841701\pi$
$434$	−524.191	+	75.3672i	−1.20781	+	0.173657i
$435$		0			0
$436$	150.786			0.345839
$437$	−187.477	+	446.437i	−0.429009	+	1.02159i
$438$		0			0
$439$	−374.439	−	240.637i	−0.852937	−	0.548149i	0.0395528	−	0.999217i	$-0.487407\pi$
$439$	−374.439	−	240.637i	−0.852937	−	0.548149i	−0.892489	+	0.451068i	$0.851043\pi$
$440$	27.3196	−	3.92797i	0.0620900	−	0.00892720i
$441$		0			0
$442$	48.1435	+	14.1362i	0.108922	+	0.0319823i
$443$	−351.866	−	160.692i	−0.794280	−	0.362736i	−0.0234085	−	0.999726i	$-0.507452\pi$
$443$	−351.866	−	160.692i	−0.794280	−	0.362736i	−0.770872	+	0.636990i	$0.780179\pi$
$444$		0			0
$445$	10.2792	−	71.4931i	0.0230992	−	0.160659i
$446$	84.2166	+	286.815i	0.188826	+	0.643084i
$447$		0			0
$448$	−50.8036	+	32.6495i	−0.113401	+	0.0728784i
$449$	309.258	+	481.215i	0.688771	+	1.07175i	0.992881	+	0.119111i	$0.0380045\pi$
$449$	309.258	+	481.215i	0.688771	+	1.07175i	−0.304110	+	0.952637i	$0.598359\pi$
$450$		0			0
$451$	−732.630	+	215.120i	−1.62446	+	0.476984i
$452$	225.181	+	32.3761i	0.498188	+	0.0716286i
$453$		0			0
$454$	−5.19960	+	11.3855i	−0.0114529	+	0.0250783i
$455$	21.9924	−	74.8993i	0.0483350	−	0.164614i
$456$		0			0
$457$	44.9733	+	312.796i	0.0984099	+	0.684456i	0.977982	+	0.208690i	$0.0669199\pi$
$457$	44.9733	+	312.796i	0.0984099	+	0.684456i	−0.879572	+	0.475766i	$0.842171\pi$
$458$	−66.5820	+	103.604i	−0.145376	+	0.226209i
$459$		0			0
$460$	−21.7945	−	17.7392i	−0.0473794	−	0.0385634i
$461$			97.9527i			0.212479i	0.994341	+	0.106239i	$0.0338810\pi$
$461$			97.9527i			0.212479i	−0.994341	+	0.106239i	$0.966119\pi$
$462$		0			0
$463$	−101.765	−	707.793i	−0.219795	−	1.52871i	−0.738792	−	0.673934i	$-0.764603\pi$
$463$	−101.765	−	707.793i	−0.219795	−	1.52871i	0.518997	−	0.854776i	$-0.326306\pi$
$464$	116.737	−	53.3121i	0.251589	−	0.114897i
$465$		0			0
$466$	−109.584	+	239.956i	−0.235159	+	0.514927i
$467$	8.39491	+	7.27423i	0.0179762	+	0.0155765i	0.663803	−	0.747908i	$-0.268942\pi$
$467$	8.39491	+	7.27423i	0.0179762	+	0.0155765i	−0.645826	+	0.763484i	$0.723487\pi$
$468$		0			0
$469$	−663.874	+	194.931i	−1.41551	+	0.415631i
$470$	−9.75438	+	8.45222i	−0.0207540	+	0.0179834i
$471$		0			0
$472$	44.2238	−	28.4209i	0.0936946	−	0.0602139i
$473$	−159.381	+	138.104i	−0.336958	+	0.291976i
$474$		0			0
$475$	73.7834	−	513.175i	0.155333	−	1.08037i
$476$	−23.9153	−	20.7227i	−0.0502422	−	0.0435351i
$477$		0			0
$478$	530.758	+	155.845i	1.11037	+	0.326035i
$479$	−251.857	+	115.019i	−0.525798	+	0.240124i	−0.660586	−	0.750751i	$-0.729692\pi$
$479$	−251.857	+	115.019i	−0.525798	+	0.240124i	0.134788	+	0.990874i	$0.456965\pi$
$480$		0			0
$481$	−946.621	−	608.356i	−1.96803	−	1.26477i
$482$			488.965i			1.01445i
$483$		0			0
$484$	268.317			0.554375
$485$	36.0135	−	56.0380i	0.0742545	−	0.115542i
$486$		0			0
$487$	−106.576	−	233.368i	−0.218841	−	0.479195i	0.768089	−	0.640343i	$-0.221208\pi$
$487$	−106.576	−	233.368i	−0.218841	−	0.479195i	−0.986930	+	0.161148i	$0.948480\pi$
$488$	58.1053	−	197.888i	0.119068	−	0.405509i
$489$		0			0
$490$	−4.51722	+	5.21315i	−0.00921882	+	0.0106391i
$491$	−661.544	−	95.1157i	−1.34734	−	0.193718i	−0.569403	−	0.822059i	$-0.692825\pi$
$491$	−661.544	−	95.1157i	−1.34734	−	0.193718i	−0.777938	+	0.628340i	$0.783734\pi$
$492$		0			0
$493$	44.0375	+	50.8220i	0.0893255	+	0.103087i
$494$	272.468	+	423.968i	0.551554	+	0.858235i
$495$		0			0
$496$	129.942	+	149.961i	0.261979	+	0.302340i
$497$	189.150	+	644.185i	0.380583	+	1.29615i
$498$		0			0
$499$	−595.865	+	687.665i	−1.19412	+	1.37809i	−0.286612	+	0.958047i	$0.592529\pi$
$499$	−595.865	+	687.665i	−1.19412	+	1.37809i	−0.907506	+	0.420039i	$0.862016\pi$
$500$	55.1543	+	25.1881i	0.110309	+	0.0503763i
$501$		0			0
$502$	−53.7996	−	117.805i	−0.107170	−	0.234671i
$503$	507.656	−	72.9899i	1.00926	−	0.145109i	0.382197	−	0.924081i	$-0.375168\pi$
$503$	507.656	−	72.9899i	1.00926	−	0.145109i	0.627059	+	0.778972i	$0.284258\pi$
$504$		0			0
$505$	22.6688			0.0448887
$506$	−352.188	−	381.997i	−0.696024	−	0.754934i
$507$		0			0
$508$	311.227	+	200.013i	0.612651	+	0.393727i
$509$	732.401	−	105.303i	1.43890	−	0.206883i	0.621710	−	0.783248i	$-0.286438\pi$
$509$	732.401	−	105.303i	1.43890	−	0.206883i	0.817192	+	0.576365i	$0.195529\pi$
$510$		0			0
$511$	−535.623	−	157.273i	−1.04819	−	0.307775i
$512$	20.5826	+	9.39977i	0.0402004	+	0.0183589i
$513$		0			0
$514$	−14.7544	+	102.619i	−0.0287050	+	0.199648i
$515$	−4.85434	−	16.5324i	−0.00942590	−	0.0321017i
$516$		0			0
$517$	−200.757	+	129.019i	−0.388312	+	0.249553i
$518$	383.672	+	597.005i	0.740679	+	1.15252i
$519$		0			0
$520$	−28.0637	+	8.24025i	−0.0539687	+	0.0158466i
$521$	833.369	+	119.820i	1.59956	+	0.229982i	0.883627	−	0.468191i	$-0.155094\pi$
$521$	833.369	+	119.820i	1.59956	+	0.229982i	0.715930	+	0.698172i	$0.246003\pi$
$522$		0			0
$523$	−146.409	+	320.591i	−0.279941	+	0.612984i	−0.996412	−	0.0846318i	$-0.973029\pi$
$523$	−146.409	+	320.591i	−0.279941	+	0.612984i	0.716472	+	0.697616i	$0.245756\pi$
$524$	62.2998	−	212.174i	0.118893	−	0.404911i
$525$		0			0
$526$	−25.9659	−	180.597i	−0.0493648	−	0.343339i
$527$	−56.2132	+	87.4694i	−0.106666	+	0.165976i
$528$		0			0
$529$	−42.8849	+	527.259i	−0.0810678	+	0.996709i
$530$			58.8634i			0.111063i
$531$		0			0
$532$	−45.2333	−	314.605i	−0.0850250	−	0.591362i
$533$	736.028	−	336.133i	1.38092	−	0.630643i
$534$		0			0
$535$	−2.00967	+	4.40057i	−0.00375640	+	0.00822536i
$536$	195.925	+	169.770i	0.365531	+	0.316734i
$537$		0			0
$538$	679.811	−	199.611i	1.26359	−	0.371023i
$539$	−96.3881	+	83.5207i	−0.178828	+	0.154955i
$540$		0			0
$541$	618.254	−	397.328i	1.14280	−	0.734432i	0.174606	−	0.984638i	$-0.444135\pi$
$541$	618.254	−	397.328i	1.14280	−	0.734432i	0.968193	+	0.250206i	$0.0804985\pi$
$542$	−176.019	+	152.521i	−0.324758	+	0.281405i
$543$		0			0
$544$	−1.68739	+	11.7360i	−0.00310181	+	0.0215736i
$545$	−34.8077	−	30.1611i	−0.0638674	−	0.0553414i
$546$		0			0
$547$	489.546	+	143.744i	0.894965	+	0.262785i	0.696700	−	0.717363i	$-0.254651\pi$
$547$	489.546	+	143.744i	0.894965	+	0.262785i	0.198265	+	0.980148i	$0.436469\pi$
$548$	71.5157	−	32.6601i	0.130503	−	0.0595988i
$549$		0			0
$550$	468.010	+	300.772i	0.850927	+	0.546858i
$551$			675.436i			1.22584i
$552$		0			0
$553$	762.801			1.37939
$554$	−2.71115	+	4.21863i	−0.00489377	+	0.00761485i
$555$		0			0
$556$	45.1397	+	98.8421i	0.0811865	+	0.177774i
$557$	219.818	−	748.631i	0.394646	−	1.34404i	−0.487523	−	0.873110i	$-0.662100\pi$
$557$	219.818	−	748.631i	0.394646	−	1.34404i	0.882169	−	0.470932i	$-0.156082\pi$
$558$		0			0
$559$	146.350	−	168.897i	0.261807	−	0.302142i
$560$	18.2584	+	2.62516i	0.0326042	+	0.00468778i
$561$		0			0
$562$	−99.5794	−	114.921i	−0.177187	−	0.204485i
$563$	−289.603	−	450.631i	−0.514392	−	0.800410i	0.482766	−	0.875750i	$-0.339632\pi$
$563$	−289.603	−	450.631i	−0.514392	−	0.800410i	−0.997158	+	0.0753397i	$0.975996\pi$
$564$		0			0
$565$	−45.5052	−	52.5158i	−0.0805401	−	0.0929483i
$566$	113.494	+	386.525i	0.200520	+	0.682907i
$567$		0			0
$568$	164.735	−	190.114i	0.290026	−	0.334708i
$569$	428.118	+	195.515i	0.752404	+	0.343611i	0.754425	−	0.656387i	$-0.227916\pi$
$569$	428.118	+	195.515i	0.752404	+	0.343611i	−0.00202080	+	0.999998i	$0.500643\pi$
$570$		0			0
$571$	−404.464	−	885.653i	−0.708344	−	1.55106i	−0.829552	−	0.558430i	$-0.811404\pi$
$571$	−404.464	−	885.653i	−0.708344	−	1.55106i	0.121208	−	0.992627i	$-0.461323\pi$
$572$	−535.282	+	76.9620i	−0.935809	+	0.134549i
$573$		0			0
$574$	−510.306			−0.889035
$575$	−97.8485	−	557.901i	−0.170171	−	0.970262i
$576$		0			0
$577$	−51.7096	−	33.2318i	−0.0896181	−	0.0575940i	0.495064	−	0.868856i	$-0.335144\pi$
$577$	−51.7096	−	33.2318i	−0.0896181	−	0.0575940i	−0.584682	+	0.811262i	$0.698781\pi$
$578$	398.398	−	57.2810i	0.689270	−	0.0991021i
$579$		0			0
$580$	−37.6117	−	11.0438i	−0.0648478	−	0.0190410i
$581$	−890.509	−	406.682i	−1.53272	−	0.699969i
$582$		0			0
$583$	−154.888	+	1077.27i	−0.265674	+	1.84781i
$584$	58.9280	+	200.690i	0.100904	+	0.343648i
$585$		0			0
$586$	281.014	−	180.597i	0.479546	−	0.308186i
$587$	299.356	+	465.806i	0.509975	+	0.793537i	0.996798	−	0.0799637i	$-0.0254804\pi$
$587$	299.356	+	465.806i	0.509975	+	0.793537i	−0.486822	+	0.873501i	$0.661844\pi$
$588$		0			0
$589$	−1002.03	+	294.223i	−1.70124	+	0.499530i
$590$	−15.8937	−	2.28516i	−0.0269384	−	0.00387316i
$591$		0			0
$592$	110.459	−	241.871i	0.186586	−	0.408566i
$593$	−182.114	+	620.224i	−0.307107	+	1.04591i	0.650900	+	0.759164i	$0.274392\pi$
$593$	−182.114	+	620.224i	−0.307107	+	1.04591i	−0.958007	+	0.286746i	$0.907426\pi$
$594$		0			0
$595$	1.37558	+	9.56735i	0.00231189	+	0.0160796i
$596$	222.333	−	345.956i	0.373041	−	0.580463i
$597$		0			0
$598$	427.027	+	347.570i	0.714092	+	0.581221i
$599$		−	354.283i		−	0.591458i	−0.955272	−	0.295729i	$-0.904437\pi$
$599$		−	354.283i		−	0.591458i	0.955272	−	0.295729i	$-0.0955625\pi$
$600$		0			0
$601$	−130.126	−	905.048i	−0.216516	−	1.50590i	−0.750761	−	0.660574i	$-0.770313\pi$
$601$	−130.126	−	905.048i	−0.216516	−	1.50590i	0.534245	−	0.845330i	$-0.320596\pi$
$602$	−128.207	+	58.5502i	−0.212969	+	0.0972595i
$603$		0			0
$604$	0.0762580	−	0.166982i	0.000126255	−	0.000276460i
$605$	−61.9390	−	53.6705i	−0.102379	−	0.0887115i
$606$		0			0
$607$	137.831	−	40.4708i	0.227069	−	0.0666735i	−0.166219	−	0.986089i	$-0.553156\pi$
$607$	137.831	−	40.4708i	0.227069	−	0.0666735i	0.393288	+	0.919415i	$0.371338\pi$
$608$	−90.0022	+	77.9874i	−0.148030	+	0.128269i
$609$		0			0
$610$	−52.9960	+	34.0584i	−0.0868786	+	0.0558335i
$611$	191.121	−	165.607i	0.312800	−	0.271043i
$612$		0			0
$613$	59.5493	−	414.175i	0.0971441	−	0.675652i	−0.881815	−	0.471595i	$-0.843678\pi$
$613$	59.5493	−	414.175i	0.0971441	−	0.675652i	0.978959	−	0.204057i	$-0.0654126\pi$
$614$	319.990	+	277.273i	0.521156	+	0.451584i
$615$		0			0
$616$	327.243	+	96.0871i	0.531238	+	0.155986i
$617$	13.5084	−	6.16907i	0.0218936	−	0.00999849i	−0.404438	−	0.914565i	$-0.632533\pi$
$617$	13.5084	−	6.16907i	0.0218936	−	0.00999849i	0.426332	+	0.904567i	$0.359806\pi$
$618$		0			0
$619$	75.3876	+	48.4487i	0.121789	+	0.0782692i	0.600117	−	0.799912i	$-0.295121\pi$
$619$	75.3876	+	48.4487i	0.121789	+	0.0782692i	−0.478328	+	0.878181i	$0.658757\pi$
$620$		−	60.6090i		−	0.0977564i
$621$		0			0
$622$	−850.958			−1.36810
$623$	482.532	−	750.835i	0.774530	−	1.20519i
$624$		0			0
$625$	248.065	+	543.186i	0.396904	+	0.869098i
$626$	−41.4586	+	141.195i	−0.0662279	+	0.225551i
$627$		0			0
$628$	−221.819	+	255.993i	−0.353215	+	0.407632i
$629$	137.913	+	19.8289i	0.219257	+	0.0315244i
$630$		0			0
$631$	376.084	+	434.024i	0.596013	+	0.687835i	0.970968	−	0.239207i	$-0.0768876\pi$
$631$	376.084	+	434.024i	0.596013	+	0.687835i	−0.374956	+	0.927043i	$0.622342\pi$
$632$	−154.521	−	240.439i	−0.244495	−	0.380442i
$633$		0			0
$634$	−9.40081	−	10.8491i	−0.0148278	−	0.0171122i
$635$	−31.8364	−	108.425i	−0.0501361	−	0.170748i
$636$		0			0
$637$	88.5075	−	102.143i	0.138944	−	0.160350i
$638$	−659.280	−	301.083i	−1.03335	−	0.471917i
$639$		0			0
$640$	−2.87114	−	6.28692i	−0.00448616	−	0.00982332i
$641$	−138.488	+	19.9116i	−0.216050	+	0.0310633i	−0.249490	−	0.968377i	$-0.580263\pi$
$641$	−138.488	+	19.9116i	−0.216050	+	0.0310633i	0.0334397	+	0.999441i	$0.489354\pi$
$642$		0			0
$643$	−705.760			−1.09760			−0.548802	−	0.835952i	$-0.684916\pi$
$643$	−705.760			−1.09760			−0.548802	+	0.835952i	$0.684916\pi$
$644$	−153.916	−	311.270i	−0.239000	−	0.483338i
$645$		0			0
$646$	−52.4967	−	33.7376i	−0.0812642	−	0.0522253i
$647$	−646.467	+	92.9479i	−0.999176	+	0.143660i	−0.622446	−	0.782663i	$-0.713861\pi$
$647$	−646.467	+	92.9479i	−0.999176	+	0.143660i	−0.376731	+	0.926323i	$0.622952\pi$
$648$		0			0
$649$	−284.860	−	83.6425i	−0.438922	−	0.128879i
$650$	−536.265	−	244.904i	−0.825024	−	0.376776i
$651$		0			0
$652$	13.2994	−	92.4995i	0.0203979	−	0.141870i
$653$	−325.570	−	1108.79i	−0.498576	−	1.69799i	−0.696313	−	0.717739i	$-0.745177\pi$
$653$	−325.570	−	1108.79i	−0.498576	−	1.69799i	0.197737	−	0.980255i	$-0.436641\pi$
$654$		0			0
$655$	−56.8216	+	36.5170i	−0.0867506	+	0.0557512i
$656$	103.373	+	160.851i	0.157581	+	0.245200i
$657$		0			0
$658$	−153.029	+	44.9334i	−0.232567	+	0.0682878i
$659$	−239.530	−	34.4391i	−0.363474	−	0.0522597i	−0.0418416	−	0.999124i	$-0.513322\pi$
$659$	−239.530	−	34.4391i	−0.363474	−	0.0522597i	−0.321633	+	0.946865i	$0.604232\pi$
$660$		0			0
$661$	−334.744	+	732.987i	−0.506420	+	1.10891i	0.467909	+	0.883777i	$0.345008\pi$
$661$	−334.744	+	732.987i	−0.506420	+	1.10891i	−0.974329	+	0.225129i	$0.927720\pi$
$662$	10.8646	−	37.0015i	0.0164118	−	0.0558935i
$663$		0			0
$664$	52.2024	+	363.075i	0.0786180	+	0.546800i
$665$	−52.4873	+	81.6719i	−0.0789283	+	0.122815i
$666$		0			0
$667$	229.618	+	701.290i	0.344254	+	1.05141i
$668$			440.835i			0.659932i
$669$		0			0
$670$	−11.2693	−	78.3800i	−0.0168199	−	0.116985i
$671$	−1059.51	+	483.861i	−1.57900	+	0.721105i
$672$		0			0
$673$	481.489	−	1054.31i	0.715437	−	1.56659i	−0.104754	−	0.994498i	$-0.533406\pi$
$673$	481.489	−	1054.31i	0.715437	−	1.56659i	0.820191	−	0.572090i	$-0.193867\pi$
$674$	538.980	+	467.029i	0.799673	+	0.692921i
$675$		0			0
$676$	225.553	−	66.2284i	0.333659	−	0.0979711i
$677$	−863.612	+	748.324i	−1.27565	+	1.10535i	−0.286553	+	0.958064i	$0.592509\pi$
$677$	−863.612	+	748.324i	−1.27565	+	1.10535i	−0.989093	+	0.147289i	$0.952945\pi$
$678$		0			0
$679$	692.458	−	445.016i	1.01982	−	0.655398i
$680$	2.73703	−	2.37165i	0.00402505	−	0.00348772i
$681$		0			0
$682$	159.481	−	1109.22i	0.233844	−	1.62642i
$683$	521.857	+	452.191i	0.764066	+	0.662067i	0.947063	−	0.321047i	$-0.104035\pi$
$683$	521.857	+	452.191i	0.764066	+	0.662067i	−0.182998	+	0.983113i	$0.558580\pi$
$684$		0			0
$685$	−23.0417	−	6.76566i	−0.0336376	−	0.00987688i
$686$	398.298	−	181.897i	0.580609	−	0.265155i
$687$		0			0
$688$	44.4263	+	28.5511i	0.0645732	+	0.0414987i
$689$		−	1153.33i		−	1.67392i
$690$		0			0
$691$	−1178.18			−1.70504			−0.852518	−	0.522697i	$-0.824926\pi$
$691$	−1178.18			−1.70504			−0.852518	+	0.522697i	$0.824926\pi$
$692$	−83.5758	+	130.047i	−0.120774	+	0.187929i
$693$		0			0
$694$	−49.3529	−	108.068i	−0.0711137	−	0.155717i
$695$	9.35084	−	31.8460i	0.0134544	−	0.0458216i
$696$		0			0
$697$	−65.6109	+	75.7191i	−0.0941334	+	0.108636i
$698$	−505.269	−	72.6467i	−0.723881	−	0.104078i
$699$		0			0
$700$	243.481	+	280.992i	0.347830	+	0.401417i
$701$	12.6201	+	19.6373i	0.0180030	+	0.0280133i	0.850138	−	0.526559i	$-0.176518\pi$
$701$	12.6201	+	19.6373i	0.0180030	+	0.0280133i	−0.832135	+	0.554573i	$0.812882\pi$
$702$		0			0
$703$	916.447	+	1057.64i	1.30362	+	1.50446i
$704$	−36.0025	−	122.613i	−0.0511399	−	0.174166i
$705$		0			0
$706$	285.641	−	329.647i	0.404590	−	0.466922i
$707$	254.803	+	116.365i	0.360400	+	0.164589i
$708$		0			0
$709$	−146.903	−	321.672i	−0.207197	−	0.453699i	0.777293	−	0.629139i	$-0.216592\pi$
$709$	−146.903	−	321.672i	−0.207197	−	0.453699i	−0.984490	+	0.175440i	$0.943865\pi$
$710$	−76.0555	+	10.9351i	−0.107120	+	0.0154016i
$711$		0			0
$712$	−334.414			−0.469683
$713$	−940.365	+	646.131i	−1.31888	+	0.906214i
$714$		0			0
$715$	138.960	+	89.3043i	0.194350	+	0.124901i
$716$	606.494	−	87.2006i	0.847058	−	0.121789i
$717$		0			0
$718$	728.318	+	213.853i	1.01437	+	0.297846i
$719$	−283.132	−	129.302i	−0.393786	−	0.179836i	0.208674	−	0.977985i	$-0.433085\pi$
$719$	−283.132	−	129.302i	−0.393786	−	0.179836i	−0.602460	+	0.798149i	$0.705813\pi$
$720$		0			0
$721$	30.3008	−	210.746i	0.0420260	−	0.292297i
$722$	−32.7513	−	111.541i	−0.0453618	−	0.154488i
$723$		0			0
$724$	256.564	−	164.884i	0.354370	−	0.227740i
$725$	−427.170	−	664.690i	−0.589200	−	0.916813i
$726$		0			0
$727$	1218.71	−	357.845i	1.67635	−	0.492221i	0.701052	−	0.713110i	$-0.252714\pi$
$727$	1218.71	−	357.845i	1.67635	−	0.492221i	0.975299	+	0.220888i	$0.0708957\pi$
$728$	−357.743	−	51.4356i	−0.491405	−	0.0706533i
$729$		0			0
$730$	26.5402	−	58.1150i	0.0363565	−	0.0796096i
$731$	−7.79615	+	26.5513i	−0.0106650	+	0.0363218i
$732$		0			0
$733$	13.9279	+	96.8707i	0.0190012	+	0.132157i	0.997114	−	0.0759191i	$-0.0241891\pi$
$733$	13.9279	+	96.8707i	0.0190012	+	0.132157i	−0.978113	+	0.208076i	$0.933280\pi$
$734$	246.854	−	384.112i	0.336313	−	0.523314i
$735$		0			0
$736$	−66.9351	+	111.569i	−0.0909445	+	0.151589i
$737$		−	1464.10i		−	1.98657i
$738$		0			0
$739$	35.9787	+	250.237i	0.0486856	+	0.338616i	0.999577	+	0.0290905i	$0.00926109\pi$
$739$	35.9787	+	250.237i	0.0486856	+	0.338616i	−0.950891	+	0.309525i	$0.899830\pi$
$740$	−73.8791	+	33.7394i	−0.0998366	+	0.0455938i
$741$		0			0
$742$	−302.160	+	661.639i	−0.407224	+	0.891697i
$743$	−468.945	−	406.343i	−0.631150	−	0.546895i	0.279462	−	0.960157i	$-0.409844\pi$
$743$	−468.945	−	406.343i	−0.631150	−	0.546895i	−0.910612	+	0.413262i	$0.864389\pi$
$744$		0			0
$745$	−120.524	+	35.3890i	−0.161777	+	0.0475021i
$746$	−198.967	+	172.406i	−0.266712	+	0.231107i
$747$		0			0
$748$	56.3315	−	36.2021i	0.0753096	−	0.0483985i
$749$	−45.1785	+	39.1474i	−0.0603184	+	0.0522662i
$750$		0			0
$751$	−6.02299	+	41.8908i	−0.00801996	+	0.0557801i	−0.993438	−	0.114368i	$-0.963516\pi$
$751$	−6.02299	+	41.8908i	−0.00801996	+	0.0557801i	0.985418	+	0.170148i	$0.0544247\pi$
$752$	45.1624	+	39.1334i	0.0600564	+	0.0520392i
$753$		0			0
$754$	736.939	+	216.385i	0.977373	+	0.286983i
$755$	−0.0510043	+	0.0232929i	−6.75553e−5	+	3.08515e-5i
$756$		0			0
$757$	−1098.71	−	706.097i	−1.45140	−	0.932757i	−0.999165	−	0.0408573i	$-0.986991\pi$
$757$	−1098.71	−	706.097i	−1.45140	−	0.932757i	−0.452233	−	0.891900i	$-0.649373\pi$
$758$		−	884.489i		−	1.16687i
$759$		0			0
$760$	36.3758			0.0478629
$761$	−421.286	+	655.533i	−0.553595	+	0.861411i	−0.999432	−	0.0337036i	$-0.989270\pi$
$761$	−421.286	+	655.533i	−0.553595	+	0.861411i	0.445837	+	0.895114i	$0.352906\pi$
$762$		0			0
$763$	−236.423	−	517.695i	−0.309860	−	0.678499i
$764$	95.7630	−	326.139i	0.125344	−	0.426883i
$765$		0			0
$766$	150.299	−	173.454i	0.196213	−	0.226442i
$767$	311.410	+	44.7740i	0.406010	+	0.0583755i
$768$		0			0
$769$	561.209	+	647.669i	0.729790	+	0.842223i	0.992448	−	0.122666i	$-0.0391444\pi$
$769$	561.209	+	647.669i	0.729790	+	0.842223i	−0.262658	+	0.964889i	$0.584599\pi$
$770$	−56.3215	−	87.6380i	−0.0731448	−	0.113816i
$771$		0			0
$772$	−274.607	−	316.914i	−0.355709	−	0.410510i
$773$	−282.669	−	962.683i	−0.365678	−	1.24539i	−0.912826	−	0.408350i	$-0.866104\pi$
$773$	−282.669	−	962.683i	−0.365678	−	1.24539i	0.547147	−	0.837036i	$-0.315714\pi$
$774$		0			0
$775$	800.012	−	923.263i	1.03227	−	1.19131i
$776$	−280.543	−	128.120i	−0.361524	−	0.165103i
$777$		0			0
$778$	15.7497	+	34.4871i	0.0202438	+	0.0443278i
$779$	−996.082	+	143.215i	−1.27867	+	0.183845i
$780$		0			0
$781$	−1420.68			−1.81905
$782$	−65.9754	−	17.1825i	−0.0843675	−	0.0219725i
$783$		0			0
$784$	26.8675	+	17.2667i	0.0342698	+	0.0220238i
$785$	102.410	−	14.7244i	0.130459	−	0.0187572i
$786$		0			0
$787$	−256.132	−	75.2071i	−0.325454	−	0.0955618i	0.114924	−	0.993374i	$-0.463337\pi$
$787$	−256.132	−	75.2071i	−0.325454	−	0.0955618i	−0.440378	+	0.897812i	$0.645156\pi$
$788$	379.575	+	173.346i	0.481694	+	0.219982i
$789$		0			0
$790$	−12.4241	+	86.4117i	−0.0157267	+	0.109382i
$791$	−241.913	−	823.880i	−0.305832	−	1.04157i
$792$		0			0
$793$	1038.37	−	667.319i	1.30942	−	0.841512i
$794$	−511.191	−	795.429i	−0.643817	−	1.00180i
$795$		0			0
$796$	−313.483	+	92.0469i	−0.393823	+	0.115637i
$797$	973.342	+	139.945i	1.22126	+	0.175590i	0.722635	−	0.691230i	$-0.242931\pi$
$797$	973.342	+	139.945i	1.22126	+	0.175590i	0.498622	+	0.866820i	$0.333840\pi$
$798$		0			0
$799$	−13.0080	+	28.4836i	−0.0162804	+	0.0356490i
$800$	39.2482	−	133.667i	0.0490603	−	0.167084i
$801$		0			0
$802$	29.6720	+	206.373i	0.0369975	+	0.257324i
$803$	638.637	−	993.738i	0.795314	−	1.23753i
$804$		0			0
$805$	−26.7317	+	102.641i	−0.0332071	+	0.127505i
$806$			1187.53i			1.47337i
$807$		0			0
$808$	−14.9367	−	103.887i	−0.0184861	−	0.128573i
$809$	1039.25	−	474.612i	1.28462	−	0.586665i	0.348155	−	0.937437i	$-0.386808\pi$
$809$	1039.25	−	474.612i	1.28462	−	0.586665i	0.936461	+	0.350772i	$0.114081\pi$
$810$		0			0
$811$	−27.8054	+	60.8852i	−0.0342853	+	0.0750743i	−0.926000	−	0.377524i	$-0.876776\pi$
$811$	−27.8054	+	60.8852i	−0.0342853	+	0.0750743i	0.891715	+	0.452598i	$0.149503\pi$
$812$	−366.075	−	317.205i	−0.450831	−	0.390647i
$813$		0			0
$814$	−1440.86	+	423.073i	−1.77009	+	0.519746i
$815$	−21.5724	+	18.6926i	−0.0264692	+	0.0229357i
$816$		0			0
$817$	−233.820	+	150.267i	−0.286193	+	0.183925i
$818$	−672.316	+	582.565i	−0.821903	+	0.712183i
$819$		0			0
$820$	8.31161	−	57.8085i	0.0101361	−	0.0704982i
$821$	906.710	+	785.669i	1.10440	+	0.956966i	0.999297	−	0.0374960i	$-0.0119381\pi$
$821$	906.710	+	785.669i	1.10440	+	0.956966i	0.105100	+	0.994462i	$0.466484\pi$
$822$		0			0
$823$	941.530	+	276.458i	1.14402	+	0.335915i	0.798204	−	0.602387i	$-0.205784\pi$
$823$	941.530	+	276.458i	1.14402	+	0.335915i	0.345817	+	0.938302i	$0.387602\pi$
$824$	−72.5665	+	33.1400i	−0.0880661	+	0.0402185i
$825$		0			0
$826$	−166.918	−	107.272i	−0.202080	−	0.129869i
$827$		−	691.356i		−	0.835981i	−0.908452	−	0.417990i	$-0.862735\pi$
$827$		−	691.356i		−	0.835981i	0.908452	−	0.417990i	$-0.137265\pi$
$828$		0			0
$829$	1139.74			1.37484			0.687422	−	0.726259i	$-0.258743\pi$
$829$	1139.74			1.37484			0.687422	+	0.726259i	$0.258743\pi$
$830$	60.5740	−	94.2550i	0.0729807	−	0.113560i
$831$		0			0
$832$	56.2553	+	123.182i	0.0676145	+	0.148055i
$833$	−4.71484	+	16.0573i	−0.00566007	+	0.0192764i
$834$		0			0
$835$	88.1784	−	101.763i	0.105603	−	0.121872i
$836$	665.721	+	95.7162i	0.796317	+	0.114493i
$837$		0			0
$838$	259.943	+	299.990i	0.310194	+	0.357983i
$839$	402.682	+	626.586i	0.479955	+	0.746825i	0.993815	−	0.111049i	$-0.0354212\pi$
$839$	402.682	+	626.586i	0.479955	+	0.746825i	−0.513860	+	0.857874i	$0.671785\pi$
$840$		0			0
$841$	123.350	+	142.354i	0.146671	+	0.169267i
$842$	28.0114	+	95.3982i	0.0332677	+	0.113299i
$843$		0			0
$844$	−238.144	+	274.833i	−0.282161	+	0.325631i
$845$	−65.3147	−	29.8282i	−0.0772955	−	0.0352997i
$846$		0			0
$847$	−420.706	−	921.218i	−0.496702	−	1.08762i
$848$	269.761	−	38.7858i	0.318115	−	0.0457380i
$849$		0			0
$850$	72.9983			0.0858803
$851$	1311.08	+	786.570i	1.54063	+	0.924289i
$852$		0			0
$853$	1313.24	+	843.968i	1.53956	+	0.989412i	0.987857	+	0.155368i	$0.0496564\pi$
$853$	1313.24	+	843.968i	1.53956	+	0.989412i	0.551698	+	0.834044i	$0.313980\pi$
$854$	−770.519	+	110.784i	−0.902247	+	0.129724i
$855$		0			0
$856$	21.4913	+	6.31041i	0.0251066	+	0.00737198i
$857$	−642.304	−	293.331i	−0.749480	−	0.342276i	0.00378530	−	0.999993i	$-0.498795\pi$
$857$	−642.304	−	293.331i	−0.749480	−	0.342276i	−0.753265	+	0.657717i	$0.771522\pi$
$858$		0			0
$859$	139.170	−	967.949i	0.162014	−	1.12683i	−0.732816	−	0.680426i	$-0.761795\pi$
$859$	139.170	−	967.949i	0.162014	−	1.12683i	0.894830	−	0.446406i	$-0.147296\pi$
$860$	−4.54452	−	15.4772i	−0.00528433	−	0.0179968i
$861$		0			0
$862$	−230.688	+	148.254i	−0.267619	+	0.171988i
$863$	462.226	+	719.238i	0.535604	+	0.833416i	0.998597	−	0.0529460i	$-0.0168611\pi$
$863$	462.226	+	719.238i	0.535604	+	0.833416i	−0.462994	+	0.886362i	$0.653225\pi$
$864$		0			0
$865$	45.3055	−	13.3029i	0.0523763	−	0.0153791i
$866$	−83.4717	−	12.0014i	−0.0963876	−	0.0138584i
$867$		0			0
$868$	311.121	−	681.260i	0.358435	−	0.784862i
$869$	−454.753	+	1548.75i	−0.523306	+	1.78222i
$870$		0			0
$871$	220.804	+	1535.73i	0.253506	+	1.76318i
$872$	−115.288	+	179.392i	−0.132211	+	0.205724i
$873$		0			0
$874$	−387.790	−	564.381i	−0.443695	−	0.645745i
$875$		−	228.856i		−	0.261549i
$876$		0			0
$877$	−24.0742	−	167.440i	−0.0274506	−	0.190923i	0.971482	−	0.237113i	$-0.0762012\pi$
$877$	−24.0742	−	167.440i	−0.0274506	−	0.190923i	−0.998933	+	0.0461898i	$0.985292\pi$
$878$	572.579	−	261.488i	0.652140	−	0.297822i
$879$		0			0
$880$	−16.2149	+	35.5057i	−0.0184260	+	0.0403474i
$881$	506.218	+	438.641i	0.574595	+	0.497889i	0.892995	−	0.450067i	$-0.148600\pi$
$881$	506.218	+	438.641i	0.574595	+	0.497889i	−0.318400	+	0.947957i	$0.603145\pi$
$882$		0			0
$883$	−377.988	+	110.987i	−0.428072	+	0.125693i	−0.488669	−	0.872469i	$-0.662518\pi$
$883$	−377.988	+	110.987i	−0.428072	+	0.125693i	0.0605974	+	0.998162i	$0.480699\pi$
$884$	−53.6276	+	46.4686i	−0.0606647	+	0.0525663i
$885$		0			0
$886$	460.208	−	295.757i	0.519422	−	0.333812i
$887$	−739.087	+	640.422i	−0.833243	+	0.722009i	−0.962990	−	0.269538i	$-0.913129\pi$
$887$	−739.087	+	640.422i	−0.833243	+	0.722009i	0.129747	+	0.991547i	$0.458584\pi$
$888$		0			0
$889$	198.723	−	1382.15i	0.223535	−	1.55472i
$890$	77.1969	+	66.8915i	0.0867381	+	0.0751590i
$891$		0			0
$892$	−405.618	−	119.100i	−0.454729	−	0.133520i
$893$	−286.092	+	130.654i	−0.320371	+	0.146309i
$894$		0			0
$895$	−157.447	−	101.185i	−0.175918	−	0.113056i
$896$		−	85.4049i		−	0.0953180i
$897$		0			0
$898$	−808.960			−0.900847
$899$	−860.463	+	1338.91i	−0.957134	+	1.48933i
$900$		0			0
$901$	59.3245	+	129.903i	0.0658430	+	0.144176i
$902$	304.225	−	1036.10i	0.337278	−	1.14866i
$903$		0			0
$904$	−210.687	+	243.146i	−0.233061	+	0.268967i
$905$	−92.2067	−	13.2573i	−0.101886	−	0.0146490i
$906$		0			0
$907$	795.594	+	918.164i	0.877171	+	1.01231i	0.999803	+	0.0198567i	$0.00632099\pi$
$907$	795.594	+	918.164i	0.877171	+	1.01231i	−0.122632	+	0.992452i	$0.539134\pi$
$908$	−9.57000	−	14.8912i	−0.0105396	−	0.0164000i
$909$		0			0
$910$	72.2937	+	83.4313i	0.0794436	+	0.0916828i
$911$	−186.087	−	633.753i	−0.204266	−	0.695668i	−0.996358	−	0.0852656i	$-0.972826\pi$
$911$	−186.087	−	633.753i	−0.204266	−	0.695668i	0.792092	−	0.610402i	$-0.208992\pi$
$912$		0			0
$913$	1356.59	−	1565.59i	1.48586	−	1.71478i
$914$	−406.523	−	185.653i	−0.444774	−	0.203121i
$915$		0			0
$916$	−72.3512	−	158.427i	−0.0789860	−	0.172955i
$917$	−826.141	+	118.781i	−0.900917	+	0.129532i
$918$		0			0
$919$	−23.4505			−0.0255174			−0.0127587	−	0.999919i	$-0.504061\pi$
$919$	−23.4505			−0.0255174			−0.0127587	+	0.999919i	$0.504061\pi$
$920$	37.7682	−	12.3661i	0.0410524	−	0.0134414i
$921$		0			0
$922$	−116.536	−	74.8928i	−0.126394	−	0.0812287i
$923$	1490.18	−	214.256i	1.61450	−	0.232130i
$924$		0			0
$925$	−1570.75	−	461.215i	−1.69811	−	0.498611i
$926$	919.877	+	420.094i	0.993388	+	0.453665i
$927$		0			0
$928$	−25.8291	+	179.645i	−0.0278331	+	0.193583i
$929$	81.9030	+	278.936i	0.0881625	+	0.300254i	0.991757	−	0.128136i	$-0.0408993\pi$
$929$	81.9030	+	278.936i	0.0881625	+	0.300254i	−0.903594	+	0.428390i	$0.859081\pi$
$930$		0			0
$931$	−141.406	+	90.8760i	−0.151886	+	0.0976112i
$932$	−201.692	−	313.839i	−0.216408	−	0.336738i
$933$		0			0
$934$	−15.0728	+	4.42578i	−0.0161379	+	0.00473852i
$935$	−20.2451	−	2.91080i	−0.0216525	−	0.00311316i
$936$		0			0
$937$	61.9165	−	135.578i	0.0660795	−	0.144694i	−0.873711	−	0.486446i	$-0.838293\pi$
$937$	61.9165	−	135.578i	0.0660795	−	0.144694i	0.939790	+	0.341752i	$0.111020\pi$
$938$	275.674	−	938.860i	0.293896	−	1.00092i
$939$		0			0
$940$	−2.59769	−	18.0673i	−0.00276350	−	0.0192205i
$941$	491.387	−	764.613i	0.522196	−	0.812553i	−0.475547	−	0.879690i	$-0.657750\pi$
$941$	491.387	−	764.613i	0.522196	−	0.812553i	0.997744	+	0.0671367i	$0.0213864\pi$
$942$		0			0
$943$	−985.523	+	487.320i	−1.04509	+	0.516776i
$944$			74.3438i			0.0787540i
$945$		0			0
$946$	−42.4448	−	295.210i	−0.0448676	−	0.312061i
$947$	−813.173	+	371.364i	−0.858683	+	0.392148i	−0.795572	−	0.605859i	$-0.792830\pi$
$947$	−813.173	+	371.364i	−0.858683	+	0.392148i	−0.0631113	+	0.998006i	$0.520102\pi$
$948$		0			0
$949$	−520.012	+	1138.67i	−0.547958	+	1.19986i
$950$	554.117	+	480.145i	0.583281	+	0.505416i
$951$		0			0
$952$	42.9392	−	12.6081i	0.0451042	−	0.0132438i
$953$	556.887	−	482.545i	0.584352	−	0.506344i	−0.311767	−	0.950159i	$-0.600921\pi$
$953$	556.887	−	482.545i	0.584352	−	0.506344i	0.896118	+	0.443815i	$0.146375\pi$
$954$		0			0
$955$	−87.3424	+	56.1316i	−0.0914580	+	0.0587765i
$956$	−591.218	+	512.294i	−0.618429	+	0.535872i
$957$		0			0
$958$	55.7255	−	387.579i	0.0581686	−	0.404571i
$959$	−224.265	−	194.327i	−0.233853	−	0.202635i
$960$		0			0
$961$	−1439.06	−	422.547i	−1.49746	−	0.439695i
$962$	1447.54	−	661.069i	1.50472	−	0.687181i
$963$		0			0
$964$	−581.728	−	373.854i	−0.603452	−	0.387815i
$965$			128.086i			0.132731i
$966$		0			0
$967$	178.388			0.184476			0.0922380	−	0.995737i	$-0.470598\pi$
$967$	178.388			0.184476			0.0922380	+	0.995737i	$0.470598\pi$
$968$	−205.151	+	319.221i	−0.211932	+	0.329773i
$969$		0			0
$970$	39.1339	+	85.6913i	0.0403442	+	0.0883415i
$971$	−330.215	+	1124.61i	−0.340077	+	1.15820i	0.594992	+	0.803731i	$0.297155\pi$
$971$	−330.215	+	1124.61i	−0.340077	+	1.15820i	−0.935069	+	0.354465i	$0.884663\pi$
$972$		0			0
$973$	268.580	−	309.957i	0.276032	−	0.318558i
$974$	359.127	+	51.6346i	0.368713	+	0.0530130i
$975$		0			0
$976$	191.004	+	220.430i	0.195701	+	0.225851i
$977$	769.356	+	1197.14i	0.787468	+	1.22532i	0.970234	+	0.242167i	$0.0778583\pi$
$977$	769.356	+	1197.14i	0.787468	+	1.22532i	−0.182767	+	0.983156i	$0.558505\pi$
$978$		0			0
$979$	1236.78	+	1427.32i	1.26331	+	1.45794i
$980$	−2.74837	−	9.36008i	−0.00280446	−	0.00955110i
$981$		0			0
$982$	618.965	−	714.324i	0.630311	−	0.727417i
$983$	172.528	+	78.7908i	0.175511	+	0.0801534i	0.501233	−	0.865312i	$-0.332880\pi$
$983$	172.528	+	78.7908i	0.175511	+	0.0801534i	−0.325722	+	0.945466i	$0.605607\pi$
$984$		0			0
$985$	−52.9482	−	115.940i	−0.0537545	−	0.117706i
$986$	−94.1337	+	13.5344i	−0.0954703	+	0.0137266i
$987$		0			0
$988$	−712.724			−0.721380
$989$	−191.686	+	235.507i	−0.193818	+	0.238126i
$990$		0			0
$991$	886.554	+	569.754i	0.894606	+	0.574928i	0.905186	−	0.425016i	$-0.139731\pi$
$991$	886.554	+	569.754i	0.894606	+	0.574928i	−0.0105803	+	0.999944i	$0.503368\pi$
$992$	−277.761	+	39.9360i	−0.280001	+	0.0402581i
$993$		0			0
$994$	−911.015	−	267.498i	−0.916514	−	0.269113i
$995$	90.7769	+	41.4564i	0.0912331	+	0.0416647i
$996$		0			0
$997$	−205.528	+	1429.48i	−0.206146	+	1.43378i	0.579434	+	0.815019i	$0.303274\pi$
$997$	−205.528	+	1429.48i	−0.206146	+	1.43378i	−0.785581	+	0.618759i	$0.787636\pi$
$998$	−362.536	−	1234.68i	−0.363262	−	1.23716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.b.71.2	yes	80
3.2	odd	2	inner	414.3.k.b.71.7	yes	80
23.12	even	11	inner	414.3.k.b.35.7	yes	80
69.35	odd	22	inner	414.3.k.b.35.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.b.35.2	✓	80	69.35	odd	22	inner
414.3.k.b.35.7	yes	80	23.12	even	11	inner
414.3.k.b.71.2	yes	80	1.1	even	1	trivial
414.3.k.b.71.7	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-0.172109 + 0.586151i) q^{5} +(-4.94341 + 5.70500i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-0.172109 + 0.586151i) q^{5} +(-4.94341 + 5.70500i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-0.565759 - 0.652921i) q^{10} +(-8.63603 - 13.4379i) q^{11} +(11.0851 + 12.7929i) q^{13} +(-3.00767 - 10.2432i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(-1.90658 - 0.870706i) q^{17} +(-8.74546 - 19.1499i) q^{19} +(1.20936 - 0.173879i) q^{20} +22.5902 q^{22} +(-15.5903 - 16.9098i) q^{23} +(20.7174 + 13.3143i) q^{25} +(-23.6953 + 3.40687i) q^{26} +(14.4860 + 4.25348i) q^{28} +(-29.1843 - 13.3280i) q^{29} +(7.05976 - 49.1017i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(2.49363 - 1.60256i) q^{34} +(-2.49318 - 3.87947i) q^{35} +(-63.7823 + 18.7282i) q^{37} +(29.4695 + 4.23707i) q^{38} +(-0.717785 + 1.57173i) q^{40} +(13.4671 - 45.8648i) q^{41} +(-1.87890 - 13.0680i) q^{43} +(-17.2721 + 26.8758i) q^{44} +(32.0379 - 5.61903i) q^{46} -14.9396i q^{47} +(-1.13629 - 7.90309i) q^{49} +(-31.6803 + 14.4679i) q^{50} +(14.0638 - 30.7955i) q^{52} +(-51.4921 - 44.6182i) q^{53} +(9.36299 - 2.74922i) q^{55} +(-16.1362 + 13.9821i) q^{56} +(38.1703 - 24.5306i) q^{58} +(14.0463 - 12.1712i) q^{59} +(10.3773 - 72.1756i) q^{61} +(53.0191 + 45.9413i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-9.40641 + 4.29577i) q^{65} +(77.1069 + 49.5536i) q^{67} +4.19198i q^{68} +6.52169 q^{70} +(48.0839 - 74.8200i) q^{71} +(30.7201 + 67.2676i) q^{73} +(26.4856 - 90.2018i) q^{74} +(-27.5727 + 31.8206i) q^{76} +(119.355 + 17.1606i) q^{77} +(-66.1732 - 76.3679i) q^{79} +(-1.32110 - 2.05567i) q^{80} +(44.2692 + 51.0894i) q^{82} +(36.5369 + 124.433i) q^{83} +(0.838506 - 0.967687i) q^{85} +(16.9838 + 7.75623i) q^{86} +(-18.7686 - 41.0976i) q^{88} +(-117.030 + 16.8263i) q^{89} -127.782 q^{91} +(-17.8106 + 42.4121i) q^{92} +(17.7738 + 11.4225i) q^{94} +(12.7299 - 1.83028i) q^{95} +(-104.624 - 30.7203i) q^{97} +(10.2712 + 4.69070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 + 16 * q^7	\( 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

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