LMFDB - Embedded newform 414.3.k.b.35.2

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			35.2
Character	$\chi$	$=$	414.35
Dual form			414.3.k.b.71.2

$q$-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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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	0.940490	−	0.339821i	$-0.110367\pi$
$5$	−0.172109	−	0.586151i	−0.0344219	−	0.117230i	−0.974912	+	0.222591i	$0.928548\pi$
$6$		0			0
$7$	−4.94341	−	5.70500i	−0.706202	−	0.815000i	0.283375	−	0.959009i	$-0.408546\pi$
$7$	−4.94341	−	5.70500i	−0.706202	−	0.815000i	−0.989576	+	0.144009i	$0.954001\pi$
$8$	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	0.185911	+	0.982567i	$0.440476\pi$
$11$	−8.63603	+	13.4379i	−0.785093	+	1.22163i	−0.971004	+	0.239063i	$0.923160\pi$
$12$		0			0
$13$	11.0851	−	12.7929i	0.852701	−	0.984069i	−0.147287	−	0.989094i	$-0.547054\pi$
$13$	11.0851	−	12.7929i	0.852701	−	0.984069i	0.999987	+	0.00502491i	$0.00159949\pi$
$14$	−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	−0.470701	−	0.882293i	$-0.655999\pi$
$17$	−1.90658	+	0.870706i	−0.112152	+	0.0512180i	0.358549	+	0.933511i	$0.383272\pi$
$18$		0			0
$19$	−8.74546	+	19.1499i	−0.460287	+	1.00789i	0.527135	+	0.849782i	$0.323266\pi$
$19$	−8.74546	+	19.1499i	−0.460287	+	1.00789i	−0.987422	+	0.158107i	$0.949461\pi$
$20$	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	−0.849248	−	0.527994i	$-0.822944\pi$
$29$	−29.1843	+	13.3280i	−1.00636	+	0.459587i	−0.157108	+	0.987581i	$0.550217\pi$
$30$		0			0
$31$	7.05976	+	49.1017i	0.227734	+	1.58393i	0.707619	+	0.706594i	$0.249769\pi$
$31$	7.05976	+	49.1017i	0.227734	+	1.58393i	−0.479885	+	0.877331i	$0.659322\pi$
$32$	−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	−0.738141	−	0.674647i	$-0.764296\pi$
$37$	−63.7823	−	18.7282i	−1.72385	−	0.506167i	−0.985705	+	0.168480i	$0.946114\pi$
$38$	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	0.943836	+	0.330415i	$0.107189\pi$
$41$	13.4671	+	45.8648i	0.328466	+	1.11865i	−0.615369	+	0.788239i	$0.710993\pi$
$42$		0			0
$43$	−1.87890	+	13.0680i	−0.0436954	+	0.303908i	0.956240	+	0.292582i	$0.0945144\pi$
$43$	−1.87890	+	13.0680i	−0.0436954	+	0.303908i	−0.999936	+	0.0113261i	$0.996395\pi$
$44$	−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	$0.0508051\pi$
$47$			14.9396i			0.317864i	−0.987290	+	0.158932i	$0.949195\pi$
$48$		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	−0.987436	−	0.158022i	$-0.949488\pi$
$53$	−51.4921	+	44.6182i	−0.971549	+	0.841852i	0.0158867	+	0.999874i	$0.494943\pi$
$54$		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	0.765723	−	0.643170i	$-0.222381\pi$
$59$	14.0463	+	12.1712i	0.238073	+	0.206292i	−0.527650	+	0.849462i	$0.676927\pi$
$60$		0			0
$61$	10.3773	+	72.1756i	0.170119	+	1.18321i	0.878629	+	0.477505i	$0.158459\pi$
$61$	10.3773	+	72.1756i	0.170119	+	1.18321i	−0.708510	+	0.705701i	$0.750632\pi$
$62$	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	0.181041	−	0.983476i	$-0.442053\pi$
$67$	77.1069	−	49.5536i	1.15085	−	0.739605i	0.969808	+	0.243870i	$0.0784171\pi$
$68$		−	4.19198i		−	0.0616468i
$69$		0			0
$70$	6.52169			0.0931670
$71$	48.0839	+	74.8200i	0.677238	+	1.05380i	0.994426	+	0.105441i	$0.0336253\pi$
$71$	48.0839	+	74.8200i	0.677238	+	1.05380i	−0.317187	+	0.948363i	$0.602738\pi$
$72$		0			0
$73$	30.7201	−	67.2676i	0.420823	−	0.921473i	−0.573905	−	0.818922i	$-0.694572\pi$
$73$	30.7201	−	67.2676i	0.420823	−	0.921473i	0.994728	−	0.102551i	$-0.0327006\pi$
$74$	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	−0.999798	−	0.0200812i	$-0.993608\pi$
$79$	−66.1732	+	76.3679i	−0.837635	+	0.966683i	0.162163	+	0.986764i	$0.448153\pi$
$80$	−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	−0.378838	−	0.925463i	$-0.623676\pi$
$83$	36.5369	−	124.433i	0.440204	−	1.49920i	0.819042	−	0.573734i	$-0.194506\pi$
$84$		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	−0.551087	−	0.834448i	$-0.685787\pi$
$89$	−117.030	−	16.8263i	−1.31494	−	0.189060i	−0.763855	+	0.645388i	$0.776696\pi$
$90$		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	−0.772317	−	0.635238i	$-0.780902\pi$
$97$	−104.624	+	30.7203i	−1.07860	+	0.316704i	−0.306279	+	0.951942i	$0.599084\pi$
$98$	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	−0.994919	−	0.100679i	$-0.967898\pi$
$101$	−10.4544	+	35.6043i	−0.103509	+	0.352518i	0.891410	+	0.453197i	$0.149717\pi$
$102$		0			0
$103$	−23.7275	−	15.2487i	−0.230364	−	0.148046i	0.420367	−	0.907354i	$-0.361901\pi$
$103$	−23.7275	−	15.2487i	−0.230364	−	0.148046i	−0.650731	+	0.759308i	$0.725538\pi$
$104$	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	−0.105589	−	0.994410i	$-0.533673\pi$
$107$	7.83849	−	1.12700i	0.0732569	−	0.0105328i	0.178846	+	0.983877i	$0.442764\pi$
$108$		0			0
$109$	−31.3193	−	68.5797i	−0.287333	−	0.629172i	0.709836	−	0.704367i	$-0.248769\pi$
$109$	−31.3193	−	68.5797i	−0.287333	−	0.629172i	−0.997169	+	0.0751954i	$0.976042\pi$
$110$	−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	0.454822	−	0.890583i	$-0.349703\pi$
$113$	−61.4969	−	95.6911i	−0.544220	−	0.846824i	−0.999042	+	0.0437590i	$0.986067\pi$
$114$		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	−0.242149	−	0.970239i	$-0.577852\pi$
$127$	−155.613	−	100.007i	−1.22530	−	0.787454i	−0.983153	+	0.182786i	$0.941489\pi$
$128$	−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	−0.274762	−	0.961512i	$-0.588599\pi$
$131$	83.5598	−	72.4050i	0.637861	−	0.552710i	0.912623	+	0.408803i	$0.134054\pi$
$132$		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	$-0.954175\pi$
$137$		−	39.3102i		−	0.286936i	0.989655	−	0.143468i	$-0.0458254\pi$
$138$		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	−0.235867	−	0.971785i	$-0.575793\pi$
$149$	111.166	−	172.978i	0.746082	−	1.16093i	0.981950	−	0.189142i	$-0.0605705\pi$
$150$		0			0
$151$	0.0601066	−	0.0693667i	0.000398057	−	0.000459382i	−0.755551	−	0.655090i	$-0.772631\pi$
$151$	0.0601066	−	0.0693667i	0.000398057	−	0.000459382i	0.755949	+	0.654631i	$0.227176\pi$
$152$	−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	0.541906	+	0.840439i	$0.317703\pi$
$157$	−70.3561	+	154.058i	−0.448128	+	0.981264i	−0.990035	+	0.140825i	$0.955025\pi$
$158$	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	−0.414482	−	0.910057i	$-0.636037\pi$
$163$	39.3079	−	25.2616i	0.241153	−	0.154979i	0.655635	+	0.755078i	$0.272401\pi$
$164$	−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	−0.912407	−	0.409283i	$-0.865779\pi$
$167$	−200.499	+	91.5647i	−1.20059	+	0.548292i	−0.288184	+	0.957575i	$0.593051\pi$
$168$		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	−0.940768	−	0.339050i	$-0.889895\pi$
$173$	−41.7879	+	65.0233i	−0.241549	+	0.375857i	0.699220	+	0.714907i	$0.253531\pi$
$174$		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	−0.737500	−	0.675347i	$-0.763994\pi$
$179$	−86.3130	−	293.955i	−0.482196	−	1.64221i	0.255304	−	0.966861i	$-0.417824\pi$
$180$		0			0
$181$	21.7014	−	150.937i	0.119897	−	0.833905i	−0.837769	−	0.546025i	$-0.816140\pi$
$181$	21.7014	−	150.937i	0.119897	−	0.833905i	0.957666	−	0.287880i	$-0.0929505\pi$
$182$	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	−0.250242	−	0.968183i	$-0.580510\pi$
$191$	128.443	−	111.296i	0.672474	−	0.582702i	0.922716	+	0.385481i	$0.125965\pi$
$192$		0			0
$193$	201.175	+	59.0704i	1.04236	+	0.306064i	0.757727	−	0.652572i	$-0.226310\pi$
$193$	201.175	+	59.0704i	1.04236	+	0.306064i	0.284633	+	0.958637i	$0.408128\pi$
$194$	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	0.155300	−	0.987867i	$-0.450366\pi$
$197$	−157.681	−	136.631i	−0.800411	−	0.693560i	−0.955711	+	0.294307i	$0.904911\pi$
$198$		0			0
$199$	23.2484	+	161.696i	0.116826	+	0.812542i	0.961015	+	0.276497i	$0.0891735\pi$
$199$	23.2484	+	161.696i	0.116826	+	0.812542i	−0.844189	+	0.536046i	$0.819917\pi$
$200$	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	0.641873	+	0.766811i	$0.278158\pi$
$211$	−75.5340	+	165.396i	−0.357981	+	0.783870i	−0.999854	+	0.0170588i	$0.994570\pi$
$212$	−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	0.975842	−	0.218478i	$-0.0701091\pi$
$223$	138.419	+	159.744i	0.620711	+	0.716339i	−0.355131	+	0.934817i	$0.615564\pi$
$224$	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	0.161584	−	0.986859i	$-0.448340\pi$
$227$	8.76052	+	1.25957i	0.0385926	+	0.00554878i	−0.122991	+	0.992408i	$0.539249\pi$
$228$		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	0.526623	−	0.850099i	$-0.323458\pi$
$233$	184.632	+	26.5461i	0.792413	+	0.113932i	0.265790	+	0.964031i	$0.414367\pi$
$234$		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	0.320968	+	0.947090i	$0.395992\pi$
$239$	−110.199	+	375.303i	−0.461083	+	1.57030i	−0.782051	+	0.623215i	$0.785826\pi$
$240$		0			0
$241$	290.864	+	186.927i	1.20690	+	0.775630i	0.980138	−	0.198319i	$-0.0635482\pi$
$241$	290.864	+	186.927i	1.20690	+	0.775630i	0.226766	+	0.973949i	$0.427185\pi$
$242$	−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	0.728513	−	0.685032i	$-0.240212\pi$
$251$	−49.5097	−	77.0387i	−0.197250	−	0.306927i	−0.925762	+	0.378106i	$0.876576\pi$
$252$		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	0.540904	−	0.841085i	$-0.318082\pi$
$257$	66.6840	+	30.4535i	0.259471	+	0.118496i	−0.281433	+	0.959581i	$0.590810\pi$
$258$		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	0.449491	−	0.893285i	$-0.351605\pi$
$263$	−97.5024	−	84.4863i	−0.370732	−	0.321241i	−0.820223	+	0.572044i	$0.806151\pi$
$264$		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	−0.465085	+	0.885266i	$0.653976\pi$
$269$	−378.625	+	328.081i	−1.40753	+	1.21963i	−0.942444	+	0.334365i	$0.891478\pi$
$270$		0			0
$271$	158.019	−	46.3985i	0.583095	−	0.171212i	0.0231356	−	0.999732i	$-0.492635\pi$
$271$	158.019	−	46.3985i	0.583095	−	0.171212i	0.559959	+	0.828520i	$0.310817\pi$
$272$	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	0.887866	−	0.460102i	$-0.152187\pi$
$281$	−30.2930	−	103.169i	−0.107804	−	0.367148i	−0.995670	+	0.0929542i	$0.970369\pi$
$282$		0			0
$283$	186.539	+	215.278i	0.659149	+	0.760699i	0.982638	−	0.185533i	$-0.0594013\pi$
$283$	186.539	+	215.278i	0.659149	+	0.760699i	−0.323489	+	0.946232i	$0.604856\pi$
$284$	−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	−0.746826	−	0.665020i	$-0.768423\pi$
$293$	−214.858	+	98.1225i	−0.733305	+	0.334889i	0.0135214	+	0.999909i	$0.495696\pi$
$294$		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	0.933568	+	0.358400i	$0.116678\pi$
$307$	42.6082	+	296.347i	0.138789	+	0.965299i	−0.794779	+	0.606899i	$0.792413\pi$
$308$	−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	0.309937	−	0.950757i	$-0.399692\pi$
$311$	325.313	−	506.197i	1.04602	−	1.62764i	0.736087	−	0.676887i	$-0.236672\pi$
$312$		0			0
$313$	99.8401	+	29.3157i	0.318978	+	0.0936604i	0.437302	−	0.899315i	$-0.355934\pi$
$313$	99.8401	+	29.3157i	0.318978	+	0.0936604i	−0.118324	+	0.992975i	$0.537752\pi$
$314$	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	0.954859	−	0.297059i	$-0.0960057\pi$
$317$	−2.85982	−	9.73965i	−0.00902151	−	0.0307244i	−0.963881	+	0.266334i	$0.914188\pi$
$318$		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	0.241971	−	0.970284i	$-0.422206\pi$
$331$	−26.1640	−	7.68244i	−0.0790453	−	0.0232098i	−0.321016	+	0.947074i	$0.604024\pi$
$332$	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	0.763197	+	0.646166i	$0.223629\pi$
$337$	71.7678	+	499.156i	0.212961	+	1.48118i	−0.550236	+	0.835009i	$0.685462\pi$
$338$	−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	0.769624	−	0.638497i	$-0.220444\pi$
$347$	−45.4176	−	70.6712i	−0.130886	−	0.203663i	−0.900511	+	0.434834i	$0.856807\pi$
$348$		0			0
$349$	149.945	−	328.334i	0.429642	−	0.940786i	−0.563742	−	0.825951i	$-0.690639\pi$
$349$	149.945	−	328.334i	0.429642	−	0.940786i	0.993385	−	0.114835i	$-0.0366339\pi$
$350$	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	−0.560439	−	0.828196i	$-0.689367\pi$
$353$	−305.290	+	43.8941i	−0.864846	+	0.124346i	−0.304407	+	0.952542i	$0.598458\pi$
$354$		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	0.426693	+	0.904397i	$0.359679\pi$
$359$	−151.217	+	514.998i	−0.421218	+	1.43454i	−0.847911	+	0.530139i	$0.822140\pi$
$360$		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	−0.0333822	−	0.999443i	$-0.510628\pi$
$373$	178.620	−	52.4476i	0.478874	−	0.140610i	0.512257	+	0.858832i	$0.328810\pi$
$374$	−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	−0.388669	−	0.921377i	$-0.627065\pi$
$379$	−526.144	−	338.132i	−1.38824	−	0.892169i	−0.999573	+	0.0292080i	$0.990701\pi$
$380$	−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	−0.348795	−	0.937199i	$-0.613409\pi$
$383$	−160.638	+	23.0963i	−0.419421	+	0.0603036i	−0.0706264	+	0.997503i	$0.522500\pi$
$384$		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	0.859384	−	0.511331i	$-0.170848\pi$
$389$	14.4939	+	22.5529i	0.0372593	+	0.0579766i	−0.822124	+	0.569308i	$0.807211\pi$
$390$		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	−0.840453	−	0.541884i	$-0.817711\pi$
$397$	−277.742	−	608.170i	−0.699602	−	1.53191i	0.140851	−	0.990031i	$-0.455016\pi$
$398$	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	0.782628	−	0.622490i	$-0.213879\pi$
$401$	111.419	+	96.5453i	0.277853	+	0.240761i	−0.504774	+	0.863251i	$0.668424\pi$
$402$		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	0.557756	−	0.830005i	$-0.311663\pi$
$409$	603.563	−	177.222i	1.47570	−	0.433306i	0.917949	+	0.396699i	$0.129844\pi$
$410$	−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	0.998436	+	0.0559153i	$0.0178077\pi$
$419$	79.0771	+	269.312i	0.188728	+	0.642749i	−0.809707	+	0.586834i	$0.800374\pi$
$420$		0			0
$421$	46.0397	+	53.1326i	0.109358	+	0.126206i	0.807789	−	0.589471i	$-0.200664\pi$
$421$	46.0397	+	53.1326i	0.109358	+	0.126206i	−0.698432	+	0.715677i	$0.746118\pi$
$422$	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	−0.200152	−	0.979765i	$-0.564144\pi$
$431$	176.380	−	80.5499i	0.409234	−	0.186891i	0.609385	+	0.792874i	$0.291416\pi$
$432$		0			0
$433$	24.7713	−	54.2417i	0.0572086	−	0.125269i	−0.878869	−	0.477064i	$-0.841701\pi$
$433$	24.7713	−	54.2417i	0.0572086	−	0.125269i	0.936077	+	0.351794i	$0.114428\pi$
$434$	−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	−0.892489	−	0.451068i	$-0.851043\pi$
$439$	−374.439	+	240.637i	−0.852937	+	0.548149i	0.0395528	+	0.999217i	$0.487407\pi$
$440$	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	−0.770872	−	0.636990i	$-0.780179\pi$
$443$	−351.866	+	160.692i	−0.794280	+	0.362736i	−0.0234085	+	0.999726i	$0.507452\pi$
$444$		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	−0.304110	−	0.952637i	$-0.598359\pi$
$449$	309.258	−	481.215i	0.688771	−	1.07175i	0.992881	−	0.119111i	$-0.0380045\pi$
$450$		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	−0.879572	−	0.475766i	$-0.842171\pi$
$457$	44.9733	−	312.796i	0.0984099	−	0.684456i	0.977982	−	0.208690i	$-0.0669199\pi$
$458$	−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	$-0.966119\pi$
$461$		−	97.9527i		−	0.212479i	0.994341	−	0.106239i	$-0.0338810\pi$
$462$		0			0
$463$	−101.765	+	707.793i	−0.219795	+	1.52871i	0.518997	+	0.854776i	$0.326306\pi$
$463$	−101.765	+	707.793i	−0.219795	+	1.52871i	−0.738792	+	0.673934i	$0.764603\pi$
$464$	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	−0.645826	−	0.763484i	$-0.723487\pi$
$467$	8.39491	−	7.27423i	0.0179762	−	0.0155765i	0.663803	+	0.747908i	$0.268942\pi$
$468$		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	0.134788	−	0.990874i	$-0.456965\pi$
$479$	−251.857	−	115.019i	−0.525798	−	0.240124i	−0.660586	+	0.750751i	$0.729692\pi$
$480$		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	−0.986930	−	0.161148i	$-0.948480\pi$
$487$	−106.576	+	233.368i	−0.218841	+	0.479195i	0.768089	+	0.640343i	$0.221208\pi$
$488$	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	−0.777938	−	0.628340i	$-0.783734\pi$
$491$	−661.544	+	95.1157i	−1.34734	+	0.193718i	−0.569403	+	0.822059i	$0.692825\pi$
$492$		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	−0.907506	−	0.420039i	$-0.862016\pi$
$499$	−595.865	−	687.665i	−1.19412	−	1.37809i	−0.286612	−	0.958047i	$-0.592529\pi$
$500$	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	0.627059	−	0.778972i	$-0.284258\pi$
$503$	507.656	+	72.9899i	1.00926	+	0.145109i	0.382197	+	0.924081i	$0.375168\pi$
$504$		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	0.817192	−	0.576365i	$-0.195529\pi$
$509$	732.401	+	105.303i	1.43890	+	0.206883i	0.621710	+	0.783248i	$0.286438\pi$
$510$		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	0.715930	−	0.698172i	$-0.246003\pi$
$521$	833.369	−	119.820i	1.59956	−	0.229982i	0.883627	+	0.468191i	$0.155094\pi$
$522$		0			0
$523$	−146.409	−	320.591i	−0.279941	−	0.612984i	0.716472	−	0.697616i	$-0.245756\pi$
$523$	−146.409	−	320.591i	−0.279941	−	0.612984i	−0.996412	+	0.0846318i	$0.973029\pi$
$524$	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	0.968193	−	0.250206i	$-0.0804985\pi$
$541$	618.254	+	397.328i	1.14280	+	0.734432i	0.174606	+	0.984638i	$0.444135\pi$
$542$	−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	0.198265	−	0.980148i	$-0.436469\pi$
$547$	489.546	−	143.744i	0.894965	−	0.262785i	0.696700	+	0.717363i	$0.254651\pi$
$548$	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	0.882169	+	0.470932i	$0.156082\pi$
$557$	219.818	+	748.631i	0.394646	+	1.34404i	−0.487523	+	0.873110i	$0.662100\pi$
$558$		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	−0.997158	−	0.0753397i	$-0.975996\pi$
$563$	−289.603	+	450.631i	−0.514392	+	0.800410i	0.482766	+	0.875750i	$0.339632\pi$
$564$		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	−0.00202080	−	0.999998i	$-0.500643\pi$
$569$	428.118	−	195.515i	0.752404	−	0.343611i	0.754425	+	0.656387i	$0.227916\pi$
$570$		0			0
$571$	−404.464	+	885.653i	−0.708344	+	1.55106i	0.121208	+	0.992627i	$0.461323\pi$
$571$	−404.464	+	885.653i	−0.708344	+	1.55106i	−0.829552	+	0.558430i	$0.811404\pi$
$572$	−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	−0.584682	−	0.811262i	$-0.698781\pi$
$577$	−51.7096	+	33.2318i	−0.0896181	+	0.0575940i	0.495064	+	0.868856i	$0.335144\pi$
$578$	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	−0.486822	−	0.873501i	$-0.661844\pi$
$587$	299.356	−	465.806i	0.509975	−	0.793537i	0.996798	+	0.0799637i	$0.0254804\pi$
$588$		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	−0.958007	−	0.286746i	$-0.907426\pi$
$593$	−182.114	−	620.224i	−0.307107	−	1.04591i	0.650900	−	0.759164i	$-0.274392\pi$
$594$		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	$0.0955625\pi$
$599$			354.283i			0.591458i	−0.955272	+	0.295729i	$0.904437\pi$
$600$		0			0
$601$	−130.126	+	905.048i	−0.216516	+	1.50590i	0.534245	+	0.845330i	$0.320596\pi$
$601$	−130.126	+	905.048i	−0.216516	+	1.50590i	−0.750761	+	0.660574i	$0.770313\pi$
$602$	−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	0.393288	−	0.919415i	$-0.371338\pi$
$607$	137.831	+	40.4708i	0.227069	+	0.0666735i	−0.166219	+	0.986089i	$0.553156\pi$
$608$	−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	0.978959	+	0.204057i	$0.0654126\pi$
$613$	59.5493	+	414.175i	0.0971441	+	0.675652i	−0.881815	+	0.471595i	$0.843678\pi$
$614$	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	0.426332	−	0.904567i	$-0.359806\pi$
$617$	13.5084	+	6.16907i	0.0218936	+	0.00999849i	−0.404438	+	0.914565i	$0.632533\pi$
$618$		0			0
$619$	75.3876	−	48.4487i	0.121789	−	0.0782692i	−0.478328	−	0.878181i	$-0.658757\pi$
$619$	75.3876	−	48.4487i	0.121789	−	0.0782692i	0.600117	+	0.799912i	$0.295121\pi$
$620$			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	−0.374956	−	0.927043i	$-0.622342\pi$
$631$	376.084	−	434.024i	0.596013	−	0.687835i	0.970968	+	0.239207i	$0.0768876\pi$
$632$	−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	0.0334397	−	0.999441i	$-0.489354\pi$
$641$	−138.488	−	19.9116i	−0.216050	−	0.0310633i	−0.249490	+	0.968377i	$0.580263\pi$
$642$		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	−0.376731	−	0.926323i	$-0.622952\pi$
$647$	−646.467	−	92.9479i	−0.999176	−	0.143660i	−0.622446	+	0.782663i	$0.713861\pi$
$648$		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	0.197737	+	0.980255i	$0.436641\pi$
$653$	−325.570	+	1108.79i	−0.498576	+	1.69799i	−0.696313	+	0.717739i	$0.745177\pi$
$654$		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	−0.321633	−	0.946865i	$-0.604232\pi$
$659$	−239.530	+	34.4391i	−0.363474	+	0.0522597i	−0.0418416	+	0.999124i	$0.513322\pi$
$660$		0			0
$661$	−334.744	−	732.987i	−0.506420	−	1.10891i	−0.974329	−	0.225129i	$-0.927720\pi$
$661$	−334.744	−	732.987i	−0.506420	−	1.10891i	0.467909	−	0.883777i	$-0.345008\pi$
$662$	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	0.820191	+	0.572090i	$0.193867\pi$
$673$	481.489	+	1054.31i	0.715437	+	1.56659i	−0.104754	+	0.994498i	$0.533406\pi$
$674$	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	−0.989093	−	0.147289i	$-0.952945\pi$
$677$	−863.612	−	748.324i	−1.27565	−	1.10535i	−0.286553	−	0.958064i	$-0.592509\pi$
$678$		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	−0.182998	−	0.983113i	$-0.558580\pi$
$683$	521.857	−	452.191i	0.764066	−	0.662067i	0.947063	+	0.321047i	$0.104035\pi$
$684$		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	−0.832135	−	0.554573i	$-0.812882\pi$
$701$	12.6201	−	19.6373i	0.0180030	−	0.0280133i	0.850138	+	0.526559i	$0.176518\pi$
$702$		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	−0.984490	−	0.175440i	$-0.943865\pi$
$709$	−146.903	+	321.672i	−0.207197	+	0.453699i	0.777293	+	0.629139i	$0.216592\pi$
$710$	−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	−0.602460	−	0.798149i	$-0.705813\pi$
$719$	−283.132	+	129.302i	−0.393786	+	0.179836i	0.208674	+	0.977985i	$0.433085\pi$
$720$		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	0.975299	−	0.220888i	$-0.0708957\pi$
$727$	1218.71	+	357.845i	1.67635	+	0.492221i	0.701052	+	0.713110i	$0.252714\pi$
$728$	−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	−0.978113	−	0.208076i	$-0.933280\pi$
$733$	13.9279	−	96.8707i	0.0190012	−	0.132157i	0.997114	+	0.0759191i	$0.0241891\pi$
$734$	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	−0.950891	−	0.309525i	$-0.899830\pi$
$739$	35.9787	−	250.237i	0.0486856	−	0.338616i	0.999577	−	0.0290905i	$-0.00926109\pi$
$740$	−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	−0.910612	−	0.413262i	$-0.864389\pi$
$743$	−468.945	+	406.343i	−0.631150	+	0.546895i	0.279462	+	0.960157i	$0.409844\pi$
$744$		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	0.985418	−	0.170148i	$-0.0544247\pi$
$751$	−6.02299	−	41.8908i	−0.00801996	−	0.0557801i	−0.993438	+	0.114368i	$0.963516\pi$
$752$	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	−0.452233	+	0.891900i	$0.649373\pi$
$757$	−1098.71	+	706.097i	−1.45140	+	0.932757i	−0.999165	+	0.0408573i	$0.986991\pi$
$758$			884.489i			1.16687i
$759$		0			0
$760$	36.3758			0.0478629
$761$	−421.286	−	655.533i	−0.553595	−	0.861411i	0.445837	−	0.895114i	$-0.352906\pi$
$761$	−421.286	−	655.533i	−0.553595	−	0.861411i	−0.999432	+	0.0337036i	$0.989270\pi$
$762$		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	−0.262658	−	0.964889i	$-0.584599\pi$
$769$	561.209	−	647.669i	0.729790	−	0.842223i	0.992448	+	0.122666i	$0.0391444\pi$
$770$	−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	0.547147	+	0.837036i	$0.315714\pi$
$773$	−282.669	+	962.683i	−0.365678	+	1.24539i	−0.912826	+	0.408350i	$0.866104\pi$
$774$		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	−0.440378	−	0.897812i	$-0.645156\pi$
$787$	−256.132	+	75.2071i	−0.325454	+	0.0955618i	0.114924	+	0.993374i	$0.463337\pi$
$788$	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	0.498622	−	0.866820i	$-0.333840\pi$
$797$	973.342	−	139.945i	1.22126	−	0.175590i	0.722635	+	0.691230i	$0.242931\pi$
$798$		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	0.936461	−	0.350772i	$-0.114081\pi$
$809$	1039.25	+	474.612i	1.28462	+	0.586665i	0.348155	+	0.937437i	$0.386808\pi$
$810$		0			0
$811$	−27.8054	−	60.8852i	−0.0342853	−	0.0750743i	0.891715	−	0.452598i	$-0.149503\pi$
$811$	−27.8054	−	60.8852i	−0.0342853	−	0.0750743i	−0.926000	+	0.377524i	$0.876776\pi$
$812$	−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	0.105100	−	0.994462i	$-0.466484\pi$
$821$	906.710	−	785.669i	1.10440	−	0.956966i	0.999297	+	0.0374960i	$0.0119381\pi$
$822$		0			0
$823$	941.530	−	276.458i	1.14402	−	0.335915i	0.345817	−	0.938302i	$-0.387602\pi$
$823$	941.530	−	276.458i	1.14402	−	0.335915i	0.798204	+	0.602387i	$0.205784\pi$
$824$	−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	$0.137265\pi$
$827$			691.356i			0.835981i	−0.908452	+	0.417990i	$0.862735\pi$
$828$		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	−0.513860	−	0.857874i	$-0.671785\pi$
$839$	402.682	−	626.586i	0.479955	−	0.746825i	0.993815	+	0.111049i	$0.0354212\pi$
$840$		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	0.551698	−	0.834044i	$-0.313980\pi$
$853$	1313.24	−	843.968i	1.53956	−	0.989412i	0.987857	−	0.155368i	$-0.0496564\pi$
$854$	−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	−0.753265	−	0.657717i	$-0.771522\pi$
$857$	−642.304	+	293.331i	−0.749480	+	0.342276i	0.00378530	+	0.999993i	$0.498795\pi$
$858$		0			0
$859$	139.170	+	967.949i	0.162014	+	1.12683i	0.894830	+	0.446406i	$0.147296\pi$
$859$	139.170	+	967.949i	0.162014	+	1.12683i	−0.732816	+	0.680426i	$0.761795\pi$
$860$	−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	−0.462994	−	0.886362i	$-0.653225\pi$
$863$	462.226	−	719.238i	0.535604	−	0.833416i	0.998597	+	0.0529460i	$0.0168611\pi$
$864$		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	−0.998933	−	0.0461898i	$-0.985292\pi$
$877$	−24.0742	+	167.440i	−0.0274506	+	0.190923i	0.971482	+	0.237113i	$0.0762012\pi$
$878$	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	−0.318400	−	0.947957i	$-0.603145\pi$
$881$	506.218	−	438.641i	0.574595	−	0.497889i	0.892995	+	0.450067i	$0.148600\pi$
$882$		0			0
$883$	−377.988	−	110.987i	−0.428072	−	0.125693i	0.0605974	−	0.998162i	$-0.480699\pi$
$883$	−377.988	−	110.987i	−0.428072	−	0.125693i	−0.488669	+	0.872469i	$0.662518\pi$
$884$	−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	0.129747	−	0.991547i	$-0.458584\pi$
$887$	−739.087	−	640.422i	−0.833243	−	0.722009i	−0.962990	+	0.269538i	$0.913129\pi$
$888$		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	−0.122632	−	0.992452i	$-0.539134\pi$
$907$	795.594	−	918.164i	0.877171	−	1.01231i	0.999803	−	0.0198567i	$-0.00632099\pi$
$908$	−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	0.792092	+	0.610402i	$0.208992\pi$
$911$	−186.087	+	633.753i	−0.204266	+	0.695668i	−0.996358	+	0.0852656i	$0.972826\pi$
$912$		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	−0.903594	−	0.428390i	$-0.859081\pi$
$929$	81.9030	−	278.936i	0.0881625	−	0.300254i	0.991757	+	0.128136i	$0.0408993\pi$
$930$		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	0.939790	−	0.341752i	$-0.111020\pi$
$937$	61.9165	+	135.578i	0.0660795	+	0.144694i	−0.873711	+	0.486446i	$0.838293\pi$
$938$	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	0.997744	−	0.0671367i	$-0.0213864\pi$
$941$	491.387	+	764.613i	0.522196	+	0.812553i	−0.475547	+	0.879690i	$0.657750\pi$
$942$		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	−0.0631113	−	0.998006i	$-0.520102\pi$
$947$	−813.173	−	371.364i	−0.858683	−	0.392148i	−0.795572	+	0.605859i	$0.792830\pi$
$948$		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	0.896118	−	0.443815i	$-0.146375\pi$
$953$	556.887	+	482.545i	0.584352	+	0.506344i	−0.311767	+	0.950159i	$0.600921\pi$
$954$		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	−0.935069	−	0.354465i	$-0.884663\pi$
$971$	−330.215	−	1124.61i	−0.340077	−	1.15820i	0.594992	−	0.803731i	$-0.297155\pi$
$972$		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	−0.182767	−	0.983156i	$-0.558505\pi$
$977$	769.356	−	1197.14i	0.787468	−	1.22532i	0.970234	−	0.242167i	$-0.0778583\pi$
$978$		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	−0.325722	−	0.945466i	$-0.605607\pi$
$983$	172.528	−	78.7908i	0.175511	−	0.0801534i	0.501233	+	0.865312i	$0.332880\pi$
$984$		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	−0.0105803	−	0.999944i	$-0.503368\pi$
$991$	886.554	−	569.754i	0.894606	−	0.574928i	0.905186	+	0.425016i	$0.139731\pi$
$992$	−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	−0.785581	−	0.618759i	$-0.787636\pi$
$997$	−205.528	−	1429.48i	−0.206146	−	1.43378i	0.579434	−	0.815019i	$-0.303274\pi$
$998$	−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.35.2	✓	80
3.2	odd	2	inner	414.3.k.b.35.7	yes	80
23.2	even	11	inner	414.3.k.b.71.7	yes	80
69.2	odd	22	inner	414.3.k.b.71.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.b.35.2	✓	80	1.1	even	1	trivial
414.3.k.b.35.7	yes	80	3.2	odd	2	inner
414.3.k.b.71.2	yes	80	69.2	odd	22	inner
414.3.k.b.71.7	yes	80	23.2	even	11	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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