LMFDB - Embedded newform 690.2.q.a.11.5

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.5

$q$-expansion

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(0.0741266 - 1.73046i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.49583 + 0.873200i) q^{6} +(1.57600 - 1.36561i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98901 - 0.256547i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(0.0741266 - 1.73046i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.49583 + 0.873200i) q^{6} +(1.57600 - 1.36561i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98901 - 0.256547i) q^{9} +(0.755750 + 0.654861i) q^{10} +(-1.24535 - 0.800337i) q^{11} +(1.54329 + 0.786289i) q^{12} +(2.35898 - 2.72241i) q^{13} +(-2.00088 - 0.587510i) q^{14} +(0.416404 + 1.68125i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.644355 - 1.41094i) q^{17} +(1.40016 + 2.65322i) q^{18} +(-3.96292 - 1.80980i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-2.24632 - 2.82844i) q^{21} +1.48035i q^{22} +(-4.70815 + 0.912857i) q^{23} +(-0.172899 - 1.72340i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-3.56560 - 0.512655i) q^{26} +(-0.665511 + 5.15336i) q^{27} +(0.587510 + 2.00088i) q^{28} +(-3.46045 + 1.58033i) q^{29} +(1.18923 - 1.25925i) q^{30} +(-0.782046 - 5.43925i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-1.47727 + 2.09570i) q^{33} +(-0.838595 + 1.30488i) q^{34} +(-1.12742 + 1.75431i) q^{35} +(1.47504 - 2.61233i) q^{36} +(-0.926782 + 3.15633i) q^{37} +(0.620012 + 4.31228i) q^{38} +(-4.53617 - 4.28393i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(0.215704 + 0.734621i) q^{41} +(-1.16498 + 3.41889i) q^{42} +(-0.970313 - 0.139510i) q^{43} +(1.24535 - 0.800337i) q^{44} +(2.94021 - 0.595947i) q^{45} +(3.31336 + 3.46722i) q^{46} -3.52324i q^{47} +(-1.35634 + 1.07719i) q^{48} +(-0.377323 + 2.62434i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(-2.48935 + 1.01045i) q^{51} +(1.49643 + 3.27673i) q^{52} +(0.0457414 + 0.0527884i) q^{53} +(4.69508 - 2.22625i) q^{54} +(1.42038 + 0.417062i) q^{55} +(1.36561 - 1.57600i) q^{56} +(-3.42556 + 6.72354i) q^{57} +(3.20032 + 2.05672i) q^{58} +(-3.63188 - 3.14705i) q^{59} +(-1.70230 - 0.319643i) q^{60} +(7.47445 - 1.07466i) q^{61} +(-4.15298 + 3.59858i) q^{62} +(-5.06102 + 3.67751i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.49643 + 3.27673i) q^{65} +(2.56169 + 0.109733i) q^{66} +(-2.17671 - 3.38702i) q^{67} +1.55111 q^{68} +(1.23067 + 8.21495i) q^{69} +2.08535 q^{70} +(0.353774 + 0.550483i) q^{71} +(-2.99510 + 0.171445i) q^{72} +(-2.57958 + 5.64850i) q^{73} +(3.15633 - 0.926782i) q^{74} +(-0.873200 - 1.49583i) q^{75} +(3.29251 - 2.85298i) q^{76} +(-3.05562 + 0.439332i) q^{77} +(-1.15144 + 6.13213i) q^{78} +(-2.27327 - 1.96980i) q^{79} +(0.841254 + 0.540641i) q^{80} +(8.86837 + 1.53364i) q^{81} +(0.501384 - 0.578628i) q^{82} +(2.07167 + 0.608297i) q^{83} +(3.50599 - 0.868347i) q^{84} +(1.01576 + 1.17225i) q^{85} +(0.407228 + 0.891704i) q^{86} +(2.47820 + 6.10533i) q^{87} +(-1.34657 - 0.614959i) q^{88} +(1.04365 - 7.25875i) q^{89} +(-2.09094 - 2.15127i) q^{90} -7.51197i q^{91} +(1.12547 - 4.66190i) q^{92} +(-9.47039 + 0.950109i) q^{93} +(-2.96394 + 1.90481i) q^{94} +(4.31228 + 0.620012i) q^{95} +(1.63948 + 0.558652i) q^{96} +(3.51291 + 11.9639i) q^{97} +(2.41173 - 1.10140i) q^{98} +(3.51703 + 2.71171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) $	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$3$	0.0741266	−	1.73046i	0.0427970	−	0.999084i
$3$	0.0741266	−	1.73046i	0.0427970	−	0.999084i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−1.49583	+	0.873200i	−0.610672	+	0.356482i
$7$	1.57600	−	1.36561i	0.595672	−	0.516153i	−0.304027	−	0.952663i	$-0.598331\pi$
$7$	1.57600	−	1.36561i	0.595672	−	0.516153i	0.899699	+	0.436511i	$0.143786\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−2.98901	−	0.256547i	−0.996337	−	0.0855156i
$10$	0.755750	+	0.654861i	0.238989	+	0.207085i
$11$	−1.24535	−	0.800337i	−0.375487	−	0.241311i	0.339262	−	0.940692i	$-0.389823\pi$
$11$	−1.24535	−	0.800337i	−0.375487	−	0.241311i	−0.714749	+	0.699381i	$0.753459\pi$
$12$	1.54329	+	0.786289i	0.445510	+	0.226982i
$13$	2.35898	−	2.72241i	0.654263	−	0.755060i	−0.327566	−	0.944828i	$-0.606228\pi$
$13$	2.35898	−	2.72241i	0.654263	−	0.755060i	0.981829	+	0.189768i	$0.0607737\pi$
$14$	−2.00088	−	0.587510i	−0.534756	−	0.157019i
$15$	0.416404	+	1.68125i	0.107515	+	0.434097i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.644355	−	1.41094i	−0.156279	−	0.342204i	0.815255	−	0.579102i	$-0.196597\pi$
$17$	−0.644355	−	1.41094i	−0.156279	−	0.342204i	−0.971535	+	0.236898i	$0.923869\pi$
$18$	1.40016	+	2.65322i	0.330021	+	0.625369i
$19$	−3.96292	−	1.80980i	−0.909156	−	0.415198i	−0.0947555	−	0.995501i	$-0.530207\pi$
$19$	−3.96292	−	1.80980i	−0.909156	−	0.415198i	−0.814401	+	0.580303i	$0.802934\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	−2.24632	−	2.82844i	−0.490187	−	0.617216i
$22$			1.48035i			0.315611i
$23$	−4.70815	+	0.912857i	−0.981717	+	0.190344i
$23$	−4.70815	+	0.912857i	−0.981717	+	0.190344i
$24$	−0.172899	−	1.72340i	−0.0352928	−	0.351787i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−3.56560	−	0.512655i	−0.699271	−	0.100540i
$27$	−0.665511	+	5.15336i	−0.128078	+	0.991764i
$28$	0.587510	+	2.00088i	0.111029	+	0.378130i
$29$	−3.46045	+	1.58033i	−0.642589	+	0.293461i	−0.709933	−	0.704269i	$-0.751275\pi$
$29$	−3.46045	+	1.58033i	−0.642589	+	0.293461i	0.0673438	+	0.997730i	$0.478548\pi$
$30$	1.18923	−	1.25925i	0.217123	−	0.229907i
$31$	−0.782046	−	5.43925i	−0.140460	−	0.976918i	−0.931133	−	0.364680i	$-0.881178\pi$
$31$	−0.782046	−	5.43925i	−0.140460	−	0.976918i	0.790673	−	0.612238i	$-0.209731\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	−1.47727	+	2.09570i	−0.257159	+	0.364815i
$34$	−0.838595	+	1.30488i	−0.143818	+	0.223785i
$35$	−1.12742	+	1.75431i	−0.190569	+	0.296532i
$36$	1.47504	−	2.61233i	0.245841	−	0.435388i
$37$	−0.926782	+	3.15633i	−0.152362	+	0.518897i	−0.999931	−	0.0117887i	$-0.996247\pi$
$37$	−0.926782	+	3.15633i	−0.152362	+	0.518897i	0.847569	+	0.530686i	$0.178066\pi$
$38$	0.620012	+	4.31228i	0.100579	+	0.699543i
$39$	−4.53617	−	4.28393i	−0.726368	−	0.685978i
$40$	−0.909632	+	0.415415i	−0.143825	+	0.0656829i
$41$	0.215704	+	0.734621i	0.0336873	+	0.114729i	0.974620	−	0.223864i	$-0.0718673\pi$
$41$	0.215704	+	0.734621i	0.0336873	+	0.114729i	−0.940933	+	0.338593i	$0.890049\pi$
$42$	−1.16498	+	3.41889i	−0.179761	+	0.527547i
$43$	−0.970313	−	0.139510i	−0.147971	−	0.0212751i	0.0679310	−	0.997690i	$-0.478360\pi$
$43$	−0.970313	−	0.139510i	−0.147971	−	0.0212751i	−0.215902	+	0.976415i	$0.569269\pi$
$44$	1.24535	−	0.800337i	0.187743	−	0.120655i
$45$	2.94021	−	0.595947i	0.438301	−	0.0888385i
$46$	3.31336	+	3.46722i	0.488529	+	0.511214i
$47$		−	3.52324i		−	0.513917i	−0.966422	−	0.256959i	$-0.917280\pi$
$47$		−	3.52324i		−	0.513917i	0.966422	−	0.256959i	$-0.0827204\pi$
$48$	−1.35634	+	1.07719i	−0.195771	+	0.155479i
$49$	−0.377323	+	2.62434i	−0.0539034	+	0.374906i
$50$	−0.909632	−	0.415415i	−0.128641	−	0.0587486i
$51$	−2.48935	+	1.01045i	−0.348578	+	0.141491i
$52$	1.49643	+	3.27673i	0.207518	+	0.454401i
$53$	0.0457414	+	0.0527884i	0.00628307	+	0.00725104i	0.758882	−	0.651228i	$-0.225746\pi$
$53$	0.0457414	+	0.0527884i	0.00628307	+	0.00725104i	−0.752599	+	0.658479i	$0.771200\pi$
$54$	4.69508	−	2.22625i	0.638920	−	0.302955i
$55$	1.42038	+	0.417062i	0.191525	+	0.0562367i
$56$	1.36561	−	1.57600i	0.182488	−	0.210602i
$57$	−3.42556	+	6.72354i	−0.453727	+	0.890554i
$58$	3.20032	+	2.05672i	0.420223	+	0.270061i
$59$	−3.63188	−	3.14705i	−0.472831	−	0.409710i	0.385579	−	0.922675i	$-0.374002\pi$
$59$	−3.63188	−	3.14705i	−0.472831	−	0.409710i	−0.858410	+	0.512964i	$0.828547\pi$
$60$	−1.70230	−	0.319643i	−0.219766	−	0.0412657i
$61$	7.47445	−	1.07466i	0.957005	−	0.137597i	0.353922	−	0.935275i	$-0.384848\pi$
$61$	7.47445	−	1.07466i	0.957005	−	0.137597i	0.603083	+	0.797678i	$0.293939\pi$
$62$	−4.15298	+	3.59858i	−0.527429	+	0.457020i
$63$	−5.06102	+	3.67751i	−0.637629	+	0.463323i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−1.49643	+	3.27673i	−0.185610	+	0.406429i
$66$	2.56169	+	0.109733i	0.315322	+	0.0135072i
$67$	−2.17671	−	3.38702i	−0.265927	−	0.413791i	0.682451	−	0.730931i	$-0.260914\pi$
$67$	−2.17671	−	3.38702i	−0.265927	−	0.413791i	−0.948379	+	0.317140i	$0.897277\pi$
$68$	1.55111			0.188100
$69$	1.23067	+	8.21495i	0.148155	+	0.988964i
$70$	2.08535			0.249247
$71$	0.353774	+	0.550483i	0.0419853	+	0.0653303i	0.861612	−	0.507568i	$-0.169455\pi$
$71$	0.353774	+	0.550483i	0.0419853	+	0.0653303i	−0.819626	+	0.572898i	$0.805819\pi$
$72$	−2.99510	+	0.171445i	−0.352976	+	0.0202050i
$73$	−2.57958	+	5.64850i	−0.301917	+	0.661107i	−0.998405	−	0.0564621i	$-0.982018\pi$
$73$	−2.57958	+	5.64850i	−0.301917	+	0.661107i	0.696487	+	0.717569i	$0.254745\pi$
$74$	3.15633	−	0.926782i	0.366916	−	0.107736i
$75$	−0.873200	−	1.49583i	−0.100828	−	0.172724i
$76$	3.29251	−	2.85298i	0.377677	−	0.327259i
$77$	−3.05562	+	0.439332i	−0.348220	+	0.0500665i
$78$	−1.15144	+	6.13213i	−0.130375	+	0.694328i
$79$	−2.27327	−	1.96980i	−0.255763	−	0.221620i	0.517536	−	0.855661i	$-0.326849\pi$
$79$	−2.27327	−	1.96980i	−0.255763	−	0.221620i	−0.773299	+	0.634042i	$0.781395\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	8.86837	+	1.53364i	0.985374	+	0.170405i
$82$	0.501384	−	0.578628i	0.0553686	−	0.0638988i
$83$	2.07167	+	0.608297i	0.227395	+	0.0667693i	0.393445	−	0.919348i	$-0.371283\pi$
$83$	2.07167	+	0.608297i	0.227395	+	0.0667693i	−0.166050	+	0.986117i	$0.553101\pi$
$84$	3.50599	−	0.868347i	0.382535	−	0.0947444i
$85$	1.01576	+	1.17225i	0.110175	+	0.127149i
$86$	0.407228	+	0.891704i	0.0439125	+	0.0961549i
$87$	2.47820	+	6.10533i	0.265691	+	0.654560i
$88$	−1.34657	−	0.614959i	−0.143545	−	0.0655548i
$89$	1.04365	−	7.25875i	0.110627	−	0.769426i	−0.856686	−	0.515839i	$-0.827480\pi$
$89$	1.04365	−	7.25875i	0.110627	−	0.769426i	0.967312	−	0.253588i	$-0.0816106\pi$
$90$	−2.09094	−	2.15127i	−0.220405	−	0.226764i
$91$		−	7.51197i		−	0.787468i
$92$	1.12547	−	4.66190i	0.117339	−	0.486037i
$93$	−9.47039	+	0.950109i	−0.982034	+	0.0985217i
$94$	−2.96394	+	1.90481i	−0.305707	+	0.196466i
$95$	4.31228	+	0.620012i	0.442430	+	0.0636118i
$96$	1.63948	+	0.558652i	0.167329	+	0.0570172i
$97$	3.51291	+	11.9639i	0.356682	+	1.21475i	0.921123	+	0.389273i	$0.127274\pi$
$97$	3.51291	+	11.9639i	0.356682	+	1.21475i	−0.564441	+	0.825473i	$0.690908\pi$
$98$	2.41173	−	1.10140i	0.243622	−	0.111258i
$99$	3.51703	+	2.71171i	0.353475	+	0.272537i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	4.47753	−	15.2491i	0.445531	−	1.51734i	−0.364641	−	0.931148i	$-0.618808\pi$
$101$	4.47753	−	15.2491i	0.445531	−	1.51734i	0.810172	−	0.586192i	$-0.199374\pi$
$102$	2.19588	+	1.54788i	0.217425	+	0.153263i
$103$	1.59645	−	2.48413i	0.157303	−	0.244769i	−0.753652	−	0.657274i	$-0.771710\pi$
$103$	1.59645	−	2.48413i	0.157303	−	0.244769i	0.910955	+	0.412505i	$0.135346\pi$
$104$	1.94753	−	3.03042i	0.190971	−	0.297157i
$105$	2.95219	+	2.08101i	0.288104	+	0.203085i
$106$	0.0196788	−	0.0670197i	0.00191137	−	0.00650953i
$107$	−1.66777	−	11.5996i	−0.161230	−	1.12138i	−0.896320	−	0.443408i	$-0.853769\pi$
$107$	−1.66777	−	11.5996i	−0.161230	−	1.12138i	0.735090	−	0.677969i	$-0.237140\pi$
$108$	−4.41120	−	2.74615i	−0.424468	−	0.264249i
$109$	−13.3090	+	6.07804i	−1.27477	+	0.582170i	−0.933764	−	0.357889i	$-0.883497\pi$
$109$	−13.3090	+	6.07804i	−1.27477	+	0.582170i	−0.341011	+	0.940059i	$0.610769\pi$
$110$	−0.417062	−	1.42038i	−0.0397653	−	0.135428i
$111$	5.39321	+	1.83773i	0.511901	+	0.174430i
$112$	−2.06412	−	0.296776i	−0.195041	−	0.0280427i
$113$	8.88865	−	5.71239i	0.836174	−	0.537376i	−0.0510602	−	0.998696i	$-0.516260\pi$
$113$	8.88865	−	5.71239i	0.836174	−	0.537376i	0.887234	+	0.461319i	$0.152624\pi$
$114$	7.50820	−	0.753253i	0.703207	−	0.0705486i
$115$	4.26026	−	2.20232i	0.397271	−	0.205367i
$116$		−	3.80423i		−	0.353214i
$117$	−7.74944	+	7.53212i	−0.716436	+	0.696345i
$118$	−0.683918	+	4.75676i	−0.0629598	+	0.437895i
$119$	−2.94230	−	1.34370i	−0.269720	−	0.123177i
$120$	0.651433	+	1.60488i	0.0594674	+	0.146505i
$121$	−3.65921	−	8.01256i	−0.332656	−	0.728414i
$122$	−4.94506	−	5.70690i	−0.447705	−	0.516679i
$123$	1.28722	−	0.318813i	0.116065	−	0.0287464i
$124$	5.27259	+	1.54817i	0.473492	+	0.139030i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	5.82991	+	2.26939i	0.519370	+	0.202174i
$127$	0.315342	+	0.202658i	0.0279820	+	0.0179830i	0.554557	−	0.832146i	$-0.312888\pi$
$127$	0.315342	+	0.202658i	0.0279820	+	0.0179830i	−0.526575	+	0.850129i	$0.676524\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	−0.313343	+	1.66875i	−0.0275883	+	0.146925i
$130$	3.56560	−	0.512655i	0.312724	−	0.0449629i
$131$	11.6342	−	10.0811i	1.01648	−	0.880787i	0.0235808	−	0.999722i	$-0.492493\pi$
$131$	11.6342	−	10.0811i	1.01648	−	0.880787i	0.992902	+	0.118934i	$0.0379478\pi$
$132$	−1.29264	−	2.21436i	−0.112510	−	0.192735i
$133$	−8.71705	+	2.55956i	−0.755864	+	0.221942i
$134$	−1.67253	+	3.66233i	−0.144484	+	0.316377i
$135$	−0.813316	−	5.13211i	−0.0699991	−	0.441701i
$136$	−0.838595	−	1.30488i	−0.0719089	−	0.111892i
$137$	5.86299			0.500909			0.250455	−	0.968128i	$-0.419420\pi$
$137$	5.86299			0.500909			0.250455	+	0.968128i	$0.419420\pi$
$138$	6.24551	−	5.47664i	0.531653	−	0.466203i
$139$	−3.49925			−0.296802			−0.148401	−	0.988927i	$-0.547413\pi$
$139$	−3.49925			−0.296802			−0.148401	+	0.988927i	$0.547413\pi$
$140$	−1.12742	−	1.75431i	−0.0952847	−	0.148266i
$141$	−6.09684	−	0.261166i	−0.513446	−	0.0219941i
$142$	0.271831	−	0.595227i	0.0228116	−	0.0499504i
$143$	−5.11659	+	1.50237i	−0.427871	+	0.125634i
$144$	1.76350	+	2.42695i	0.146958	+	0.202245i
$145$	2.87505	−	2.49124i	0.238760	−	0.206886i
$146$	6.14645	−	0.883726i	0.508684	−	0.0731377i
$147$	4.51336	+	0.847478i	0.372256	+	0.0698988i
$148$	−2.48610	−	2.15422i	−0.204356	−	0.177076i
$149$	−19.7702	−	12.7056i	−1.61964	−	1.04088i	−0.956226	−	0.292629i	$-0.905470\pi$
$149$	−19.7702	−	12.7056i	−1.61964	−	1.04088i	−0.663415	−	0.748251i	$-0.730894\pi$
$150$	−0.786289	+	1.54329i	−0.0642002	+	0.126009i
$151$	14.9887	−	17.2979i	1.21976	−	1.40768i	0.334626	−	0.942351i	$-0.391390\pi$
$151$	14.9887	−	17.2979i	1.21976	−	1.40768i	0.885137	−	0.465331i	$-0.154065\pi$
$152$	−4.18015	−	1.22740i	−0.339055	−	0.0995554i
$153$	1.56401	+	4.38263i	0.126443	+	0.354314i
$154$	2.02158	+	2.33303i	0.162904	+	0.188001i
$155$	2.28278	+	4.99859i	0.183357	+	0.401497i
$156$	5.78119	−	2.34663i	0.462866	−	0.187881i
$157$	−14.8467	−	6.78028i	−1.18490	−	0.541125i	−0.277227	−	0.960805i	$-0.589415\pi$
$157$	−14.8467	−	6.78028i	−1.18490	−	0.541125i	−0.907673	+	0.419679i	$0.862143\pi$
$158$	−0.428078	+	2.97735i	−0.0340561	+	0.236865i
$159$	0.0947391	−	0.0752408i	0.00751330	−	0.00596699i
$160$		−	1.00000i		−	0.0790569i
$161$	−6.17344	+	7.86817i	−0.486535	+	0.620099i
$162$	−3.50442	−	8.28970i	−0.275333	−	0.651300i
$163$	2.08704	−	1.34126i	0.163469	−	0.105055i	−0.456348	−	0.889801i	$-0.650843\pi$
$163$	2.08704	−	1.34126i	0.163469	−	0.105055i	0.619818	+	0.784746i	$0.287207\pi$
$164$	−0.757842	−	0.108961i	−0.0591775	−	0.00850844i
$165$	0.827000	−	2.42701i	0.0643818	−	0.188942i
$166$	−0.608297	−	2.07167i	−0.0472130	−	0.160793i
$167$	12.6530	−	5.77845i	0.979122	−	0.447150i	0.139441	−	0.990230i	$-0.455469\pi$
$167$	12.6530	−	5.77845i	0.979122	−	0.447150i	0.839681	+	0.543080i	$0.182742\pi$
$168$	−2.62598	−	2.47997i	−0.202599	−	0.191333i
$169$	0.00337370	+	0.0234646i	0.000259516	+	0.00180497i
$170$	0.436999	−	1.48828i	0.0335163	−	0.114146i
$171$	11.3809	+	6.42620i	0.870320	+	0.491424i
$172$	0.529985	−	0.824673i	0.0404110	−	0.0628807i
$173$	13.3869	−	20.8304i	1.01779	−	1.58371i	0.224861	−	0.974391i	$-0.427807\pi$
$173$	13.3869	−	20.8304i	1.01779	−	1.58371i	0.792927	−	0.609317i	$-0.208556\pi$
$174$	3.79631	−	5.38558i	0.287798	−	0.408280i
$175$	0.587510	−	2.00088i	0.0444116	−	0.151252i
$176$	0.210676	+	1.46528i	0.0158803	+	0.110450i
$177$	−5.71507	+	6.05157i	−0.429571	+	0.454864i
$178$	−6.67069	+	3.04640i	−0.499990	+	0.228338i
$179$	4.08858	+	13.9244i	0.305595	+	1.04076i	0.958918	+	0.283682i	$0.0915561\pi$
$179$	4.08858	+	13.9244i	0.305595	+	1.04076i	−0.653323	+	0.757079i	$0.726626\pi$
$180$	−0.679316	+	2.92208i	−0.0506332	+	0.217799i
$181$	1.12095	+	0.161169i	0.0833197	+	0.0119796i	0.183849	−	0.982955i	$-0.441144\pi$
$181$	1.12095	+	0.161169i	0.0833197	+	0.0119796i	−0.100529	+	0.994934i	$0.532053\pi$
$182$	−6.31947	+	4.06128i	−0.468430	+	0.301042i
$183$	−1.30561	−	13.0139i	−0.0965135	−	0.962017i
$184$	−4.53032	+	1.57361i	−0.333979	+	0.116008i
$185$		−	3.28958i		−	0.241855i
$186$	5.91936	+	7.45333i	0.434029	+	0.546505i
$187$	−0.326781	+	2.27281i	−0.0238966	+	0.166205i
$188$	3.20485	+	1.46361i	0.233738	+	0.106744i
$189$	5.98864	+	9.03052i	0.435610	+	0.656874i
$190$	−1.80980	−	3.96292i	−0.131297	−	0.287500i
$191$	7.44219	+	8.58874i	0.538498	+	0.621459i	0.958164	−	0.286219i	$-0.0923985\pi$
$191$	7.44219	+	8.58874i	0.538498	+	0.621459i	−0.419667	+	0.907678i	$0.637853\pi$
$192$	−0.416404	−	1.68125i	−0.0300514	−	0.121334i
$193$	12.6716	+	3.72073i	0.912125	+	0.267824i	0.703935	−	0.710264i	$-0.251425\pi$
$193$	12.6716	+	3.72073i	0.912125	+	0.267824i	0.208190	+	0.978088i	$0.433243\pi$
$194$	8.16542	−	9.42340i	0.586243	−	0.676560i
$195$	5.55934	+	2.83242i	0.398113	+	0.202834i
$196$	−2.23044	−	1.43342i	−0.159317	−	0.102387i
$197$	19.5857	+	16.9711i	1.39542	+	1.20914i	0.949379	+	0.314132i	$0.101714\pi$
$197$	19.5857	+	16.9711i	1.39542	+	1.20914i	0.446046	+	0.895010i	$0.352832\pi$
$198$	0.379779	−	4.42478i	0.0269897	−	0.314455i
$199$	21.0112	−	3.02095i	1.48944	−	0.214150i	0.650974	−	0.759100i	$-0.274361\pi$
$199$	21.0112	−	3.02095i	1.48944	−	0.214150i	0.838468	+	0.544950i	$0.183451\pi$
$200$	0.755750	−	0.654861i	0.0534396	−	0.0463056i
$201$	−6.02247	+	3.51565i	−0.424793	+	0.247975i
$202$	−15.2491	+	4.47753i	−1.07292	+	0.315038i
$203$	−3.29554	+	7.21624i	−0.231302	+	0.506481i
$204$	0.114979	−	2.68414i	0.00805012	−	0.187928i
$205$	−0.413933	−	0.644093i	−0.0289104	−	0.0449854i
$206$	−2.95289			−0.205738
$207$	14.3069	−	1.52068i	0.994399	−	0.105694i
$208$	−3.60226			−0.249772
$209$	3.48676	+	5.42551i	0.241184	+	0.375290i
$210$	0.154580	−	3.60862i	0.0106670	−	0.249018i
$211$	10.1537	−	22.2336i	0.699012	−	1.53062i	−0.142154	−	0.989845i	$-0.545403\pi$
$211$	10.1537	−	22.2336i	0.699012	−	1.53062i	0.841166	−	0.540777i	$-0.181870\pi$
$212$	−0.0670197	+	0.0196788i	−0.00460293	+	0.00135154i
$213$	0.978815	−	0.571388i	0.0670673	−	0.0391508i
$214$	−8.85655	+	7.67425i	−0.605421	+	0.524601i
$215$	0.970313	−	0.139510i	0.0661748	−	0.00951450i
$216$	0.0746627	+	5.19562i	0.00508015	+	0.353517i
$217$	−8.66041	−	7.50428i	−0.587907	−	0.509424i
$218$	12.3086	+	7.91024i	0.833642	+	0.535749i
$219$	9.58331	+	4.88258i	0.647580	+	0.329934i
$220$	−0.969422	+	1.11877i	−0.0653584	+	0.0754276i
$221$	−5.36118	−	1.57418i	−0.360632	−	0.105891i
$222$	−1.36979	−	5.53061i	−0.0919346	−	0.371190i
$223$	14.3953	+	16.6131i	0.963980	+	1.11249i	0.993603	+	0.112931i	$0.0360240\pi$
$223$	14.3953	+	16.6131i	0.963980	+	1.11249i	−0.0296227	+	0.999561i	$0.509431\pi$
$224$	0.866284	+	1.89690i	0.0578811	+	0.126742i
$225$	−2.65322	+	1.40016i	−0.176881	+	0.0933440i
$226$	−9.61114	−	4.38926i	−0.639323	−	0.291969i
$227$	1.95713	−	13.6121i	0.129899	−	0.903470i	−0.815778	−	0.578365i	$-0.803691\pi$
$227$	1.95713	−	13.6121i	0.129899	−	0.903470i	0.945678	−	0.325105i	$-0.105400\pi$
$228$	−4.69291	−	5.90906i	−0.310796	−	0.391337i
$229$			16.1463i			1.06698i	0.845807	+	0.533489i	$0.179120\pi$
$229$			16.1463i			1.06698i	−0.845807	+	0.533489i	$0.820880\pi$
$230$	−4.15598	−	2.39329i	−0.274037	−	0.157809i
$231$	0.533745	+	5.32020i	0.0351178	+	0.350044i
$232$	−3.20032	+	2.05672i	−0.210111	+	0.135030i
$233$	2.89960	+	0.416899i	0.189959	+	0.0273120i	0.236638	−	0.971598i	$-0.423955\pi$
$233$	2.89960	+	0.416899i	0.189959	+	0.0273120i	−0.0466787	+	0.998910i	$0.514864\pi$
$234$	10.5261	+	2.44708i	0.688112	+	0.159970i
$235$	0.992611	+	3.38052i	0.0647508	+	0.220521i
$236$	4.37139	−	1.99635i	0.284553	−	0.129951i
$237$	−3.57717	+	3.78779i	−0.232362	+	0.246044i
$238$	0.460333	+	3.20168i	0.0298389	+	0.207534i
$239$	2.48675	−	8.46908i	0.160854	−	0.547820i	−0.839138	−	0.543918i	$-0.816940\pi$
$239$	2.48675	−	8.46908i	0.160854	−	0.547820i	0.999992	−	0.00390105i	$-0.00124175\pi$
$240$	0.997919	−	1.41568i	0.0644154	−	0.0913819i
$241$	3.36324	−	5.23330i	0.216645	−	0.337107i	−0.715872	−	0.698231i	$-0.753971\pi$
$241$	3.36324	−	5.23330i	0.216645	−	0.337107i	0.932518	+	0.361125i	$0.117607\pi$
$242$	−4.76227	+	7.41024i	−0.306130	+	0.476348i
$243$	3.31130	−	15.2327i	0.212420	−	0.977179i
$244$	−2.12745	+	7.24543i	−0.136196	+	0.463841i
$245$	−0.377323	−	2.62434i	−0.0241063	−	0.167663i
$246$	−0.964129	−	0.910519i	−0.0614706	−	0.0580526i
$247$	−14.2755	+	6.51939i	−0.908327	+	0.414819i
$248$	−1.54817	−	5.27259i	−0.0983090	−	0.334810i
$249$	1.20620	−	3.53986i	0.0764399	−	0.224329i
$250$	0.989821	+	0.142315i	0.0626018	+	0.00900078i
$251$	−1.56052	+	1.00289i	−0.0984994	+	0.0633017i	−0.588963	−	0.808160i	$-0.700464\pi$
$251$	−1.56052	+	1.00289i	−0.0984994	+	0.0633017i	0.490464	+	0.871462i	$0.336827\pi$
$252$	−1.24276	−	6.13136i	−0.0782862	−	0.386239i
$253$	6.59388	+	2.63128i	0.414554	+	0.165427i
$254$		−	0.374847i		−	0.0235200i
$255$	2.10384	−	1.67085i	0.131747	−	0.104632i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	9.20998	+	4.20606i	0.574503	+	0.262367i	0.681410	−	0.731902i	$-0.261367\pi$
$257$	9.20998	+	4.20606i	0.574503	+	0.262367i	−0.106907	+	0.994269i	$0.534095\pi$
$258$	1.57325	−	0.638594i	0.0979461	−	0.0397571i
$259$	2.84971	+	6.24000i	0.177072	+	0.387735i
$260$	−2.35898	−	2.72241i	−0.146298	−	0.168837i
$261$	10.7487	−	3.83587i	0.665331	−	0.237434i
$262$	−14.7707	−	4.33705i	−0.912534	−	0.267944i
$263$	−15.1467	+	17.4802i	−0.933983	+	1.07787i	0.0628243	+	0.998025i	$0.479989\pi$
$263$	−15.1467	+	17.4802i	−0.933983	+	1.07787i	−0.996807	+	0.0798488i	$0.974556\pi$
$264$	−1.16398	+	2.28461i	−0.0716381	+	0.140608i
$265$	−0.0587608	−	0.0377633i	−0.00360965	−	0.00231978i
$266$	6.86603	+	5.94945i	0.420983	+	0.364784i
$267$	−12.4836	−	2.34407i	−0.763987	−	0.143455i
$268$	3.98518	−	0.572983i	0.243434	−	0.0350005i
$269$	−22.0579	+	19.1133i	−1.34489	+	1.16536i	−0.373568	+	0.927603i	$0.621866\pi$
$269$	−22.0579	+	19.1133i	−1.34489	+	1.16536i	−0.971326	+	0.237753i	$0.923589\pi$
$270$	−3.87769	+	3.45883i	−0.235989	+	0.210498i
$271$	−23.8672	+	7.00804i	−1.44983	+	0.425708i	−0.909485	−	0.415737i	$-0.863524\pi$
$271$	−23.8672	+	7.00804i	−1.44983	+	0.425708i	−0.540343	+	0.841445i	$0.681706\pi$
$272$	−0.644355	+	1.41094i	−0.0390698	+	0.0855509i
$273$	−12.9992	−	0.556837i	−0.786747	−	0.0337013i
$274$	−3.16977	−	4.93226i	−0.191493	−	0.297969i
$275$	−1.48035			−0.0892684
$276$	−7.98382	−	2.29316i	−0.480570	−	0.138032i
$277$	−16.5954			−0.997118			−0.498559	−	0.866856i	$-0.666137\pi$
$277$	−16.5954			−0.997118			−0.498559	+	0.866856i	$0.666137\pi$
$278$	1.89184	+	2.94375i	0.113465	+	0.176555i
$279$	0.942121	+	16.4586i	0.0564033	+	0.985351i
$280$	−0.866284	+	1.89690i	−0.0517704	+	0.113361i
$281$	−26.5272	+	7.78909i	−1.58248	+	0.464658i	−0.950603	−	0.310410i	$-0.899534\pi$
$281$	−26.5272	+	7.78909i	−1.58248	+	0.464658i	−0.631877	+	0.775068i	$0.717715\pi$
$282$	3.07649	+	5.27018i	0.183202	+	0.313835i
$283$	6.33515	−	5.48944i	0.376585	−	0.326313i	−0.445917	−	0.895074i	$-0.647123\pi$
$283$	6.33515	−	5.48944i	0.376585	−	0.326313i	0.822503	+	0.568761i	$0.192577\pi$
$284$	−0.647700	+	0.0931252i	−0.0384339	+	0.00552596i
$285$	1.39256	−	7.41628i	0.0824883	−	0.439302i
$286$	4.03011	+	3.49211i	0.238306	+	0.206493i
$287$	1.34316	+	0.863194i	0.0792840	+	0.0509528i
$288$	1.08826	−	2.79566i	0.0641261	−	0.164736i
$289$	9.55707	−	11.0294i	0.562181	−	0.648791i
$290$	−3.65013	−	1.07178i	−0.214343	−	0.0629368i
$291$	20.9634	−	5.19212i	1.22890	−	0.304367i
$292$	−4.06646	−	4.69294i	−0.237972	−	0.274634i
$293$	−5.81051	−	12.7232i	−0.339454	−	0.743300i	0.660518	−	0.750810i	$-0.270337\pi$
$293$	−5.81051	−	12.7232i	−0.339454	−	0.743300i	−0.999972	+	0.00751020i	$0.997609\pi$
$294$	−1.72716	−	4.25506i	−0.100730	−	0.248160i
$295$	4.37139	+	1.99635i	0.254512	+	0.116232i
$296$	−0.468156	+	3.25610i	−0.0272110	+	0.189257i
$297$	4.95321	−	5.88509i	0.287415	−	0.341488i
$298$			23.5009i			1.36137i
$299$	−8.62127	+	14.9709i	−0.498581	+	0.865791i
$300$	1.72340	−	0.172899i	0.0995005	−	0.00998230i
$301$	−1.71973	+	1.10520i	−0.0991236	+	0.0637028i
$302$	−22.6554	−	3.25736i	−1.30367	−	0.187440i
$303$	−26.0561	−	8.87857i	−1.49688	−	0.510061i
$304$	1.22740	+	4.18015i	0.0703963	+	0.239748i
$305$	−6.86892	+	3.13693i	−0.393313	+	0.179620i
$306$	2.84133	−	3.68516i	0.162428	−	0.210666i
$307$	−3.85172	−	26.7893i	−0.219829	−	1.52895i	−0.738666	−	0.674072i	$-0.764544\pi$
$307$	−3.85172	−	26.7893i	−0.219829	−	1.52895i	0.518836	−	0.854874i	$-0.326365\pi$
$308$	0.869719	−	2.96199i	0.0495569	−	0.168775i
$309$	−4.18036	−	2.94675i	−0.237812	−	0.167635i
$310$	2.97092	−	4.62284i	0.168737	−	0.262560i
$311$	−1.06993	+	1.66485i	−0.0606704	+	0.0944050i	−0.870263	−	0.492587i	$-0.836051\pi$
$311$	−1.06993	+	1.66485i	−0.0606704	+	0.0944050i	0.809593	+	0.586992i	$0.199688\pi$
$312$	−5.09966	−	3.59476i	−0.288711	−	0.203513i
$313$	−1.67277	+	5.69694i	−0.0945507	+	0.322010i	−0.993163	−	0.116733i	$-0.962758\pi$
$313$	−1.67277	+	5.69694i	−0.0945507	+	0.322010i	0.898613	+	0.438743i	$0.144576\pi$
$314$	2.32282	+	16.1556i	0.131084	+	0.911712i
$315$	3.81994	−	4.95440i	0.215229	−	0.279149i
$316$	2.73614	−	1.24955i	0.153920	−	0.0702929i
$317$	3.95398	+	13.4660i	0.222078	+	0.756327i	0.992866	+	0.119236i	$0.0380444\pi$
$317$	3.95398	+	13.4660i	0.222078	+	0.756327i	−0.770788	+	0.637091i	$0.780137\pi$
$318$	−0.114516	−	0.0390213i	−0.00642176	−	0.00218821i
$319$	5.57426	+	0.801458i	0.312099	+	0.0448730i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	−20.1963	+	2.02618i	−1.12725	+	0.113090i
$322$	9.95674	+	0.939573i	0.554867	+	0.0523604i
$323$			6.75761i			0.376003i
$324$	−5.07910	+	7.42985i	−0.282172	+	0.412770i
$325$	0.512655	−	3.56560i	0.0284370	−	0.197784i
$326$	−2.25667	−	1.03059i	−0.124986	−	0.0570790i
$327$	9.53127	+	23.4814i	0.527080	+	1.29852i
$328$	0.318056	+	0.696446i	0.0175617	+	0.0384548i
$329$	−4.81138	−	5.55262i	−0.265260	−	0.306126i
$330$	−2.48884	+	0.616423i	−0.137006	+	0.0339330i
$331$	4.42337	+	1.29882i	0.243131	+	0.0713896i	0.401027	−	0.916066i	$-0.368653\pi$
$331$	4.42337	+	1.29882i	0.243131	+	0.0713896i	−0.157897	+	0.987456i	$0.550471\pi$
$332$	−1.41393	+	1.63176i	−0.0775994	+	0.0895545i
$333$	3.57991	−	9.19654i	0.196178	−	0.503967i
$334$	−11.7019	−	7.52035i	−0.640299	−	0.411495i
$335$	3.04277	+	2.63658i	0.166244	+	0.144052i
$336$	−0.666566	+	3.54989i	−0.0363642	+	0.193662i
$337$	9.86785	−	1.41878i	0.537536	−	0.0772860i	0.131800	−	0.991276i	$-0.457924\pi$
$337$	9.86785	−	1.41878i	0.537536	−	0.0772860i	0.405736	+	0.913990i	$0.367015\pi$
$338$	0.0179157	−	0.0155241i	0.000974487	−	0.000844398i
$339$	−9.22620	−	15.8049i	−0.501098	−	0.858406i
$340$	−1.48828	+	0.436999i	−0.0807134	+	0.0236996i
$341$	−3.37931	+	7.39966i	−0.183000	+	0.400714i
$342$	−0.746920	−	13.0485i	−0.0403888	−	0.705582i
$343$	10.8811	+	16.9314i	0.587526	+	0.914208i
$344$	−0.980291			−0.0528537
$345$	−3.49524	−	7.53547i	−0.188177	−	0.405696i
$346$	−24.7612			−1.33117
$347$	1.66888	+	2.59683i	0.0895902	+	0.139405i	0.883156	−	0.469079i	$-0.155414\pi$
$347$	1.66888	+	2.59683i	0.0895902	+	0.139405i	−0.793566	+	0.608484i	$0.791778\pi$
$348$	−6.58308	−	0.281995i	−0.352890	−	0.0151165i
$349$	7.86557	−	17.2232i	0.421035	−	0.921937i	−0.573663	−	0.819092i	$-0.694478\pi$
$349$	7.86557	−	17.2232i	0.421035	−	0.921937i	0.994697	−	0.102845i	$-0.0327947\pi$
$350$	−2.00088	+	0.587510i	−0.106951	+	0.0314037i
$351$	12.4596	+	13.9685i	0.665045	+	0.745581i
$352$	1.11877	−	0.969422i	0.0596308	−	0.0516704i
$353$	11.4708	−	1.64926i	0.610532	−	0.0877812i	0.169888	−	0.985463i	$-0.445659\pi$
$353$	11.4708	−	1.64926i	0.610532	−	0.0877812i	0.440644	+	0.897682i	$0.354750\pi$
$354$	8.18070	+	1.53610i	0.434799	+	0.0816427i
$355$	−0.494533	−	0.428515i	−0.0262471	−	0.0227432i
$356$	6.16925	+	3.96473i	0.326969	+	0.210130i
$357$	−2.54333	+	4.99194i	−0.134608	+	0.264202i
$358$	9.50353	−	10.9677i	0.502277	−	0.579659i
$359$	−23.1957	−	6.81087i	−1.22422	−	0.359464i	−0.395156	−	0.918614i	$-0.629309\pi$
$359$	−23.1957	−	6.81087i	−1.22422	−	0.359464i	−0.829067	+	0.559150i	$0.811128\pi$
$360$	2.82547	−	1.00832i	0.148916	−	0.0531429i
$361$	−0.0130119	−	0.0150165i	−0.000684837	−	0.000790344i
$362$	−0.470449	−	1.03014i	−0.0247263	−	0.0541429i
$363$	−14.1367	+	5.73819i	−0.741983	+	0.301177i
$364$	6.83312	+	3.12058i	0.358153	+	0.163563i
$365$	0.883726	−	6.14645i	0.0462563	−	0.321720i
$366$	−10.2421	+	8.13421i	−0.535366	+	0.425182i
$367$			19.8734i			1.03738i	0.854962	+	0.518691i	$0.173580\pi$
$367$			19.8734i			1.03738i	−0.854962	+	0.518691i	$0.826420\pi$
$368$	3.77307	+	2.96039i	0.196685	+	0.154321i
$369$	−0.456277	−	2.25113i	−0.0237528	−	0.117189i
$370$	−2.76737	+	1.77848i	−0.143869	+	0.0924588i
$371$	0.144177	+	0.0207295i	0.00748529	+	0.00107622i
$372$	3.06989	−	9.00926i	0.159167	−	0.467109i
$373$	9.91044	+	33.7519i	0.513143	+	1.74761i	0.652924	+	0.757423i	$0.273542\pi$
$373$	9.91044	+	33.7519i	0.513143	+	1.74761i	−0.139781	+	0.990182i	$0.544640\pi$
$374$	2.08868	−	0.953870i	0.108003	−	0.0493235i
$375$	1.25925	+	1.18923i	0.0650276	+	0.0614118i
$376$	−0.501409	−	3.48738i	−0.0258582	−	0.179848i
$377$	−3.86082	+	13.1487i	−0.198842	+	0.677194i
$378$	4.35925	−	9.92023i	0.224216	−	0.510242i
$379$	12.6967	−	19.7565i	0.652187	−	1.01482i	−0.344907	−	0.938637i	$-0.612089\pi$
$379$	12.6967	−	19.7565i	0.652187	−	1.01482i	0.997094	−	0.0761858i	$-0.0242742\pi$
$380$	−2.35537	+	3.66502i	−0.120828	+	0.188012i
$381$	0.374067	−	0.530665i	0.0191640	−	0.0271868i
$382$	3.20176	−	10.9042i	0.163816	−	0.557907i
$383$	−3.06919	−	21.3467i	−0.156828	−	1.09077i	−0.904431	−	0.426619i	$-0.859704\pi$
$383$	−3.06919	−	21.3467i	−0.156828	−	1.09077i	0.747603	−	0.664146i	$-0.231205\pi$
$384$	−1.18923	+	1.25925i	−0.0606878	+	0.0642611i
$385$	2.80807	−	1.28240i	0.143112	−	0.0653573i
$386$	−3.72073	−	12.6716i	−0.189380	−	0.644970i
$387$	2.86448	+	0.665928i	0.145610	+	0.0338510i
$388$	−12.3420	−	1.77452i	−0.626571	−	0.0900874i
$389$	6.27074	−	4.02996i	0.317939	−	0.204327i	−0.371931	−	0.928260i	$-0.621304\pi$
$389$	6.27074	−	4.02996i	0.317939	−	0.204327i	0.689870	+	0.723933i	$0.257668\pi$
$390$	−0.622826	−	6.20814i	−0.0315380	−	0.314361i
$391$	4.32171	+	6.05472i	0.218558	+	0.306200i
$392$			2.65133i			0.133912i
$393$	−16.5825	−	20.8798i	−0.836478	−	1.05325i
$394$	3.68818	−	25.6518i	0.185808	−	1.29232i
$395$	2.73614	+	1.24955i	0.137670	+	0.0628719i
$396$	−3.92768	+	2.07272i	−0.197373	+	0.104158i
$397$	7.08438	+	15.5126i	0.355555	+	0.778556i	0.999904	+	0.0138252i	$0.00440084\pi$
$397$	7.08438	+	15.5126i	0.355555	+	0.778556i	−0.644350	+	0.764731i	$0.722872\pi$
$398$	−13.9009	−	16.0425i	−0.696788	−	0.804137i
$399$	3.78306	+	15.2743i	0.189390	+	0.764670i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−12.3979	+	14.3080i	−0.619124	+	0.714507i	−0.975540	−	0.219820i	$-0.929453\pi$
$401$	−12.3979	+	14.3080i	−0.619124	+	0.714507i	0.356417	+	0.934327i	$0.383998\pi$
$402$	6.21355	+	3.16573i	0.309903	+	0.157892i
$403$	−16.6527	−	10.7020i	−0.829529	−	0.533106i
$404$	12.0110	+	10.4076i	0.597570	+	0.517798i
$405$	−8.94121	+	1.02699i	−0.444292	+	0.0510315i
$406$	7.85239	−	1.12900i	0.389708	−	0.0560315i
$407$	3.68029	−	3.18899i	0.182425	−	0.158072i
$408$	−2.32021	+	1.35443i	−0.114867	+	0.0670544i
$409$	−23.7146	+	6.96324i	−1.17261	+	0.344310i	−0.809321	−	0.587366i	$-0.800165\pi$
$409$	−23.7146	+	6.96324i	−1.17261	+	0.344310i	−0.363290	+	0.931676i	$0.618347\pi$
$410$	−0.318056	+	0.696446i	−0.0157077	+	0.0343950i
$411$	0.434604	−	10.1457i	0.0214374	−	0.500450i
$412$	1.59645	+	2.48413i	0.0786517	+	0.122384i
$413$	−10.0215			−0.493125
$414$	−9.01417	−	11.2136i	−0.443022	−	0.551118i
$415$	−2.15913			−0.105987
$416$	1.94753	+	3.03042i	0.0954855	+	0.148578i
$417$	−0.259387	+	6.05532i	−0.0127023	+	0.296530i
$418$	2.67914	−	5.86650i	0.131041	−	0.286940i
$419$	−11.2371	+	3.29950i	−0.548967	+	0.161191i	−0.544442	−	0.838799i	$-0.683259\pi$
$419$	−11.2371	+	3.29950i	−0.548967	+	0.161191i	−0.00452497	+	0.999990i	$0.501440\pi$
$420$	−3.11933	+	1.82092i	−0.152208	+	0.0888520i
$421$	−13.5840	+	11.7706i	−0.662042	+	0.573663i	−0.919723	−	0.392567i	$-0.871587\pi$
$421$	−13.5840	+	11.7706i	−0.662042	+	0.573663i	0.257681	+	0.966230i	$0.417042\pi$
$422$	−24.1936	+	3.47851i	−1.17773	+	0.169331i
$423$	−0.903876	+	10.5310i	−0.0439480	+	0.512035i
$424$	0.0527884	+	0.0457414i	0.00256363	+	0.00222140i
$425$	−1.30488	−	0.838595i	−0.0632959	−	0.0406778i
$426$	−1.00987	−	0.514516i	−0.0489283	−	0.0249284i
$427$	10.3122	−	11.9009i	0.499040	−	0.575923i
$428$	11.2442	+	3.30160i	0.543509	+	0.159589i
$429$	2.22052	+	8.96545i	0.107208	+	0.432856i
$430$	−0.641954	−	0.740854i	−0.0309578	−	0.0357272i
$431$	16.2694	+	35.6249i	0.783668	+	1.71599i	0.693947	+	0.720027i	$0.255870\pi$
$431$	16.2694	+	35.6249i	0.783668	+	1.71599i	0.0897214	+	0.995967i	$0.471402\pi$
$432$	4.33046	−	2.87177i	0.208350	−	0.138168i
$433$	7.15627	+	3.26816i	0.343908	+	0.157058i	0.579879	−	0.814703i	$-0.303100\pi$
$433$	7.15627	+	3.26816i	0.343908	+	0.157058i	−0.235971	+	0.971760i	$0.575827\pi$
$434$	−1.63084	+	11.3427i	−0.0782827	+	0.544468i
$435$	−4.09789	−	5.15983i	−0.196479	−	0.247395i
$436$		−	14.6312i		−	0.700709i
$437$	20.3101	+	4.90326i	0.971565	+	0.234555i
$438$	−1.07364	−	10.7017i	−0.0513005	−	0.511348i
$439$	−3.28588	+	2.11171i	−0.156827	+	0.100786i	−0.616700	−	0.787198i	$-0.711531\pi$
$439$	−3.28588	+	2.11171i	−0.156827	+	0.100786i	0.459874	+	0.887984i	$0.347895\pi$
$440$	1.46528	+	0.210676i	0.0698545	+	0.0100436i
$441$	1.80109	−	7.74739i	0.0857662	−	0.368923i
$442$	1.57418	+	5.36118i	0.0748763	+	0.255005i
$443$	−10.1679	+	4.64353i	−0.483092	+	0.220621i	−0.642047	−	0.766665i	$-0.721915\pi$
$443$	−10.1679	+	4.64353i	−0.483092	+	0.220621i	0.158955	+	0.987286i	$0.449187\pi$
$444$	−3.91208	+	4.14242i	−0.185659	+	0.196590i
$445$	1.04365	+	7.25875i	0.0494738	+	0.344098i
$446$	6.19311	−	21.0918i	0.293252	−	0.998725i
$447$	−23.4520	+	33.2699i	−1.10924	+	1.57361i
$448$	1.12742	−	1.75431i	0.0532658	−	0.0828831i
$449$	15.3247	−	23.8457i	0.723217	−	1.12535i	−0.263776	−	0.964584i	$-0.584968\pi$
$449$	15.3247	−	23.8457i	0.723217	−	1.12535i	0.986993	−	0.160764i	$-0.0513957\pi$
$450$	2.61233	+	1.47504i	0.123146	+	0.0695342i
$451$	0.319317	−	1.08749i	0.0150361	−	0.0512081i
$452$	1.50369	+	10.4584i	0.0707278	+	0.491922i
$453$	−28.8223	−	27.2196i	−1.35419	−	1.27889i
$454$	−12.5094	+	5.71284i	−0.587094	+	0.268117i
$455$	2.11637	+	7.20768i	0.0992167	+	0.337901i
$456$	−2.43383	+	7.14261i	−0.113975	+	0.334483i
$457$	19.2217	+	2.76366i	0.899151	+	0.129278i	0.576364	−	0.817193i	$-0.304471\pi$
$457$	19.2217	+	2.76366i	0.899151	+	0.129278i	0.322787	+	0.946472i	$0.395380\pi$
$458$	13.5831	−	8.72936i	0.634699	−	0.407896i
$459$	7.69991	−	2.38160i	0.359401	−	0.111163i
$460$	0.233526	+	4.79014i	0.0108882	+	0.223342i
$461$			40.1433i			1.86966i	0.355096	+	0.934830i	$0.384448\pi$
$461$			40.1433i			1.86966i	−0.355096	+	0.934830i	$0.615552\pi$
$462$	4.18707	−	3.32533i	0.194800	−	0.154708i
$463$	1.28799	−	8.95815i	0.0598578	−	0.416320i	−0.937757	−	0.347292i	$-0.887101\pi$
$463$	1.28799	−	8.95815i	0.0598578	−	0.416320i	0.997615	−	0.0690280i	$-0.0219898\pi$
$464$	3.46045	+	1.58033i	0.160647	+	0.0733652i
$465$	8.81910	−	3.57974i	0.408976	−	0.166007i
$466$	−1.21692	−	2.66469i	−0.0563729	−	0.123439i
$467$	−11.1357	−	12.8513i	−0.515300	−	0.594688i	0.437148	−	0.899390i	$-0.355989\pi$
$467$	−11.1357	−	12.8513i	−0.515300	−	0.594688i	−0.952448	+	0.304702i	$0.901443\pi$
$468$	−3.63222	−	10.1781i	−0.167899	−	0.470483i
$469$	−8.05585	−	2.36541i	−0.371985	−	0.109225i
$470$	2.30723	−	2.66269i	0.106425	−	0.122821i
$471$	−12.8336	+	25.1892i	−0.591340	+	1.16066i
$472$	−4.04279	−	2.59814i	−0.186084	−	0.119589i
$473$	1.09672	+	0.950316i	0.0504274	+	0.0436956i
$474$	5.12046	+	0.961474i	0.235191	+	0.0441620i
$475$	−4.31228	+	0.620012i	−0.197861	+	0.0284481i
$476$	2.44455	−	2.11822i	0.112046	−	0.0970883i
$477$	−0.123179	−	0.169520i	−0.00563997	−	0.00776178i
$478$	−8.46908	+	2.48675i	−0.387367	+	0.113741i
$479$	5.35009	−	11.7151i	0.244452	−	0.535275i	−0.747142	−	0.664665i	$-0.768574\pi$
$479$	5.35009	−	11.7151i	0.244452	−	0.535275i	0.991594	+	0.129389i	$0.0413017\pi$
$480$	−1.73046	−	0.0741266i	−0.0789845	−	0.00338340i
$481$	6.40656	+	9.96880i	0.292114	+	0.454538i
$482$	−6.22084			−0.283352
$483$	13.1580	+	11.2662i	0.598708	+	0.512628i
$484$	8.80857			0.400390
$485$	−6.74122	−	10.4895i	−0.306103	−	0.476306i
$486$	−14.6048	+	5.44978i	−0.662487	+	0.247207i
$487$	15.7967	−	34.5900i	0.715817	−	1.56742i	−0.103857	−	0.994592i	$-0.533119\pi$
$487$	15.7967	−	34.5900i	0.715817	−	1.56742i	0.819675	−	0.572829i	$-0.194154\pi$
$488$	7.24543	−	2.12745i	0.327985	−	0.0963052i
$489$	−2.16629	−	3.71096i	−0.0979631	−	0.167816i
$490$	−2.00374	+	1.73625i	−0.0905198	+	0.0784358i
$491$	34.0125	−	4.89026i	1.53496	−	0.220694i	0.677609	−	0.735422i	$-0.263016\pi$
$491$	34.0125	−	4.89026i	1.53496	−	0.220694i	0.857354	+	0.514728i	$0.172107\pi$
$492$	−0.244730	+	1.30334i	−0.0110333	+	0.0587591i
$493$	4.45952	+	3.86419i	0.200847	+	0.174035i
$494$	13.2024	+	8.48465i	0.594003	+	0.381742i
$495$	−4.13855	−	1.61100i	−0.186014	−	0.0724090i
$496$	−3.59858	+	4.15298i	−0.161581	+	0.186474i
$497$	1.30929	+	0.384443i	0.0587299	+	0.0172446i
$498$	−3.63004	+	0.899070i	−0.162666	+	0.0402883i
$499$	−24.0198	−	27.7203i	−1.07527	−	1.24093i	−0.969123	−	0.246580i	$-0.920693\pi$
$499$	−24.0198	−	27.7203i	−1.07527	−	1.24093i	−0.106149	−	0.994350i	$-0.533852\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	−9.06147	−	22.3240i	−0.404837	−	0.997361i
$502$	1.68737	+	0.770594i	0.0753108	+	0.0343933i
$503$	−5.29059	+	36.7968i	−0.235896	+	1.64069i	0.435930	+	0.899980i	$0.356419\pi$
$503$	−5.29059	+	36.7968i	−0.235896	+	1.64069i	−0.671826	+	0.740709i	$0.734490\pi$
$504$	−4.48615	+	4.36034i	−0.199829	+	0.194225i
$505$			15.8929i			0.707223i
$506$	−1.35135	−	6.96970i	−0.0600747	−	0.309841i
$507$	0.0408548	−	0.00409872i	0.00181442	−	0.000182030i
$508$	−0.315342	+	0.202658i	−0.0139910	+	0.00899148i
$509$	9.32660	+	1.34096i	0.413394	+	0.0594371i	0.345874	−	0.938281i	$-0.387582\pi$
$509$	9.32660	+	1.34096i	0.413394	+	0.0594371i	0.0675199	+	0.997718i	$0.478491\pi$
$510$	−2.54302	−	0.866532i	−0.112607	−	0.0383707i
$511$	3.64823	+	12.4247i	0.161388	+	0.549638i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	11.9639	−	19.2179i	0.528221	−	0.848491i
$514$	−1.44093	−	10.0219i	−0.0635568	−	0.442047i
$515$	−0.831926	+	2.83328i	−0.0366590	+	0.124849i
$516$	−1.38778	−	0.978251i	−0.0610937	−	0.0430651i
$517$	−2.81978	+	4.38766i	−0.124014	+	0.192969i
$518$	3.70875	−	5.77093i	0.162953	−	0.253560i
$519$	−35.0540	−	24.7096i	−1.53870	−	1.08463i
$520$	−1.01487	+	3.45635i	−0.0445052	+	0.151571i
$521$	1.17728	+	8.18815i	0.0515775	+	0.358729i	0.999223	+	0.0394060i	$0.0125466\pi$
$521$	1.17728	+	8.18815i	0.0515775	+	0.358729i	−0.947646	+	0.319323i	$0.896544\pi$
$522$	−9.03815	−	6.96860i	−0.395589	−	0.305007i
$523$	11.5841	−	5.29027i	0.506536	−	0.231327i	−0.145720	−	0.989326i	$-0.546550\pi$
$523$	11.5841	−	5.29027i	0.506536	−	0.231327i	0.652256	+	0.757999i	$0.273823\pi$
$524$	4.33705	+	14.7707i	0.189465	+	0.645259i
$525$	−3.41889	−	1.16498i	−0.149213	−	0.0508440i
$526$	22.8942	+	3.29168i	0.998233	+	0.143524i
$527$	−7.17055	+	4.60823i	−0.312354	+	0.200738i
$528$	2.55123	−	0.255950i	0.111028	−	0.0111388i
$529$	21.3334	−	8.59574i	0.927538	−	0.373728i
$530$			0.0698491i			0.00303405i
$531$	10.0484	+	10.3383i	0.436062	+	0.448644i
$532$	1.29294	−	8.99259i	0.0560560	−	0.389878i
$533$	2.50878	+	1.14572i	0.108667	+	0.0496267i
$534$	4.77721	+	11.7692i	0.206730	+	0.509304i
$535$	4.86821	+	10.6599i	0.210471	+	0.460867i
$536$	−2.63658	−	3.04277i	−0.113883	−	0.131428i
$537$	24.3988	−	6.04297i	1.05289	−	0.260774i
$538$	28.0045	+	8.22286i	1.20736	+	0.354513i
$539$	2.57026	−	2.96623i	0.110709	−	0.127765i
$540$	5.00619	+	1.39214i	0.215432	+	0.0599080i
$541$	−23.5674	−	15.1459i	−1.01324	−	0.651172i	−0.0750124	−	0.997183i	$-0.523900\pi$
$541$	−23.5674	−	15.1459i	−1.01324	−	0.651172i	−0.938230	+	0.346011i	$0.887536\pi$
$542$	18.7991	+	16.2895i	0.807491	+	0.699695i
$543$	0.361989	−	1.92782i	0.0155344	−	0.0827307i
$544$	1.53532	−	0.220746i	0.0658265	−	0.00946442i
$545$	11.0576	−	9.58142i	0.473653	−	0.410423i
$546$	6.55945	+	11.2367i	0.280719	+	0.480885i
$547$	4.57827	−	1.34430i	0.195753	−	0.0574782i	−0.182387	−	0.983227i	$-0.558382\pi$
$547$	4.57827	−	1.34430i	0.195753	−	0.0574782i	0.378139	+	0.925749i	$0.376564\pi$
$548$	−2.43558	+	5.33317i	−0.104043	+	0.227822i
$549$	−22.6169	+	1.29463i	−0.965266	+	0.0552536i
$550$	0.800337	+	1.24535i	0.0341265	+	0.0531018i
$551$	16.5736			0.706058
$552$	2.38725	+	7.95619i	0.101608	+	0.338638i
$553$	−6.27265			−0.266740
$554$	8.97213	+	13.9609i	0.381189	+	0.593142i
$555$	−5.69250	−	0.243845i	−0.241633	−	0.0103507i
$556$	1.45364	−	3.18303i	0.0616481	−	0.134990i
$557$	17.6154	−	5.17236i	0.746391	−	0.219160i	0.113647	−	0.993521i	$-0.463747\pi$
$557$	17.6154	−	5.17236i	0.746391	−	0.219160i	0.632744	+	0.774361i	$0.281929\pi$
$558$	13.3365	−	9.69075i	0.564579	−	0.410242i
$559$	−2.66875	+	2.31249i	−0.112876	+	0.0978078i
$560$	2.06412	−	0.296776i	0.0872250	−	0.0125411i
$561$	3.90880	+	0.733960i	0.165030	+	0.0309878i
$562$	20.8943	+	18.1050i	0.881372	+	0.763713i
$563$	15.4353	+	9.91963i	0.650518	+	0.418063i	0.823856	−	0.566800i	$-0.191819\pi$
$563$	15.4353	+	9.91963i	0.650518	+	0.418063i	−0.173337	+	0.984863i	$0.555455\pi$
$564$	2.77028	−	5.43739i	0.116650	−	0.228955i
$565$	−6.91923	+	7.98522i	−0.291094	+	0.335941i
$566$	−8.04305	−	2.36165i	−0.338074	−	0.0992676i
$567$	16.0709	−	9.69372i	0.674915	−	0.407098i
$568$	0.428515	+	0.494533i	0.0179801	+	0.0207501i
$569$	−3.13536	−	6.86547i	−0.131441	−	0.287816i	0.832456	−	0.554091i	$-0.186934\pi$
$569$	−3.13536	−	6.86547i	−0.131441	−	0.287816i	−0.963897	+	0.266276i	$0.914207\pi$
$570$	−6.99184	+	2.83804i	−0.292856	+	0.118873i
$571$	−29.5680	−	13.5033i	−1.23738	−	0.565094i	−0.314165	−	0.949369i	$-0.601724\pi$
$571$	−29.5680	−	13.5033i	−1.23738	−	0.565094i	−0.923219	+	0.384274i	$0.874452\pi$
$572$	0.758909	−	5.27832i	0.0317316	−	0.220698i
$573$	15.4142	−	12.2418i	0.643936	−	0.511408i
$574$		−	1.59661i		−	0.0666414i
$575$	−3.46722	+	3.31336i	−0.144593	+	0.138177i
$576$	−2.94021	+	0.595947i	−0.122509	+	0.0248311i
$577$	−5.97002	+	3.83670i	−0.248535	+	0.159724i	−0.658977	−	0.752163i	$-0.729011\pi$
$577$	−5.97002	+	3.83670i	−0.248535	+	0.159724i	0.410442	+	0.911887i	$0.365374\pi$
$578$	−14.4455	−	2.07695i	−0.600854	−	0.0863897i
$579$	7.37790	−	21.6520i	0.306615	−	0.899827i
$580$	1.07178	+	3.65013i	0.0445031	+	0.151563i
$581$	4.09565	−	1.87042i	0.169916	−	0.0775981i
$582$	−15.7016	−	14.8285i	−0.650851	−	0.614661i
$583$	−0.0147155	−	0.102348i	−0.000609453	−	0.00423884i
$584$	−1.74946	+	5.95812i	−0.0723932	+	0.246549i
$585$	5.31349	−	9.41028i	0.219686	−	0.389067i
$586$	−7.56208	+	11.7668i	−0.312386	+	0.486083i
$587$	−7.50009	+	11.6704i	−0.309562	+	0.481688i	−0.960822	−	0.277167i	$-0.910604\pi$
$587$	−7.50009	+	11.6704i	−0.309562	+	0.481688i	0.651260	+	0.758855i	$0.274241\pi$
$588$	−2.64581	+	3.75344i	−0.109111	+	0.154789i
$589$	−6.74479	+	22.9707i	−0.277914	+	0.946489i
$590$	−0.683918	−	4.75676i	−0.0281565	−	0.195833i
$591$	30.8197	−	32.6344i	1.26775	−	1.34240i
$592$	2.99231	−	1.36654i	0.122983	−	0.0561645i
$593$	2.68805	+	9.15464i	0.110385	+	0.375936i	0.996093	−	0.0883054i	$-0.0281452\pi$
$593$	2.68805	+	9.15464i	0.110385	+	0.375936i	−0.885709	+	0.464242i	$0.846327\pi$
$594$	−7.62876	−	0.985187i	−0.313012	−	0.0404227i
$595$	3.20168	+	0.460333i	0.131256	+	0.0188718i
$596$	19.7702	−	12.7056i	0.809821	−	0.520440i
$597$	−3.67016	−	36.5830i	−0.150210	−	1.49724i
$598$	17.2554	−	0.841220i	0.705624	−	0.0344001i
$599$		−	19.3843i		−	0.792022i	−0.918246	−	0.396011i	$-0.870394\pi$
$599$		−	19.3843i		−	0.792022i	0.918246	−	0.396011i	$-0.129606\pi$
$600$	−1.07719	−	1.35634i	−0.0439762	−	0.0553723i
$601$	3.70050	−	25.7375i	0.150947	−	1.04986i	−0.763691	−	0.645582i	$-0.776615\pi$
$601$	3.70050	−	25.7375i	0.150947	−	1.04986i	0.914638	−	0.404275i	$-0.132476\pi$
$602$	1.85951	+	0.849211i	0.0757881	+	0.0346112i
$603$	5.63727	+	10.6823i	0.229567	+	0.435016i
$604$	9.50817	+	20.8200i	0.386882	+	0.847154i
$605$	5.76839	+	6.65707i	0.234518	+	0.270648i
$606$	6.61785	+	26.7199i	0.268832	+	1.08542i
$607$	9.04227	+	2.65505i	0.367014	+	0.107765i	0.460039	−	0.887899i	$-0.347835\pi$
$607$	9.04227	+	2.65505i	0.367014	+	0.107765i	−0.0930248	+	0.995664i	$0.529654\pi$
$608$	2.85298	−	3.29251i	0.115704	−	0.133529i
$609$	12.2431	+	6.23774i	0.496117	+	0.252766i
$610$	6.35257	+	4.08255i	0.257208	+	0.165298i
$611$	−9.59169	−	8.31125i	−0.388038	−	0.336237i
$612$	−4.63629	−	0.397933i	−0.187411	−	0.0160855i
$613$	−22.3810	+	3.21790i	−0.903960	+	0.129970i	−0.578591	−	0.815617i	$-0.696397\pi$
$613$	−22.3810	+	3.21790i	−0.903960	+	0.129970i	−0.325368	+	0.945587i	$0.605488\pi$
$614$	−20.4542	+	17.7237i	−0.825464	+	0.715269i
$615$	−1.14526	+	0.668552i	−0.0461815	+	0.0269586i
$616$	−2.96199	+	0.869719i	−0.119342	+	0.0350420i
$617$	15.9515	−	34.9289i	0.642184	−	1.40619i	−0.256048	−	0.966664i	$-0.582420\pi$
$617$	15.9515	−	34.9289i	0.642184	−	1.40619i	0.898232	−	0.439522i	$-0.144852\pi$
$618$	−0.218888	+	5.10987i	−0.00880497	+	0.205549i
$619$	−4.78511	−	7.44578i	−0.192330	−	0.299271i	0.731674	−	0.681655i	$-0.238740\pi$
$619$	−4.78511	−	7.44578i	−0.192330	−	0.299271i	−0.924004	+	0.382384i	$0.875103\pi$
$620$	−5.49518			−0.220692
$621$	−1.57095	−	24.8703i	−0.0630402	−	0.998011i
$622$	1.97901			0.0793511
$623$	−8.26784	−	12.8650i	−0.331244	−	0.515426i
$624$	−0.267024	+	6.23358i	−0.0106895	+	0.249543i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	5.69694	−	1.67277i	0.227696	−	0.0668574i
$627$	9.64711	−	5.63154i	0.385268	−	0.224902i
$628$	12.3351	−	10.6884i	0.492225	−	0.426515i
$629$	5.05057	−	0.726163i	0.201379	−	0.0289540i
$630$	−6.23312	−	0.534989i	−0.248334	−	0.0213145i
$631$	23.3976	+	20.2741i	0.931443	+	0.807100i	0.981464	−	0.191648i	$-0.0613832\pi$
$631$	23.3976	+	20.2741i	0.931443	+	0.807100i	−0.0500205	+	0.998748i	$0.515929\pi$
$632$	−2.53046	−	1.62623i	−0.100656	−	0.0646879i
$633$	−37.7217	−	19.2188i	−1.49930	−	0.763877i
$634$	9.19065	−	10.6066i	0.365007	−	0.421241i
$635$	−0.359663	−	0.105607i	−0.0142728	−	0.00419087i
$636$	0.0290854	+	0.117434i	0.00115331	+	0.00465656i
$637$	6.25443	+	7.21800i	0.247810	+	0.285988i
$638$	−2.33945	−	5.12267i	−0.0926195	−	0.202808i
$639$	−0.916209	−	1.73616i	−0.0362447	−	0.0686814i
$640$	0.909632	+	0.415415i	0.0359564	+	0.0164207i
$641$	−3.64547	+	25.3548i	−0.143988	+	1.00146i	0.781832	+	0.623489i	$0.214285\pi$
$641$	−3.64547	+	25.3548i	−0.143988	+	1.00146i	−0.925819	+	0.377966i	$0.876624\pi$
$642$	12.6235	+	15.8948i	0.498210	+	0.627318i
$643$		−	34.6081i		−	1.36481i	−0.730974	−	0.682406i	$-0.760934\pi$
$643$		−	34.6081i		−	1.36481i	0.730974	−	0.682406i	$-0.239066\pi$
$644$	−4.59260	−	8.88411i	−0.180974	−	0.350083i
$645$	−0.169491	−	1.68943i	−0.00667370	−	0.0665214i
$646$	5.68486	−	3.65344i	0.223668	−	0.143743i
$647$	27.5272	+	3.95781i	1.08220	+	0.155597i	0.660270	−	0.751029i	$-0.270442\pi$
$647$	27.5272	+	3.95781i	1.08220	+	0.155597i	0.421935	+	0.906626i	$0.361351\pi$
$648$	8.99636	+	0.255932i	0.353410	+	0.0100540i
$649$	2.00426	+	6.82590i	0.0786743	+	0.267940i
$650$	−3.27673	+	1.49643i	−0.128524	+	0.0586950i
$651$	−13.6279	+	14.4303i	−0.534118	+	0.565566i
$652$	0.353064	+	2.45561i	0.0138270	+	0.0961692i
$653$	8.18759	−	27.8844i	0.320405	−	1.09120i	−0.629067	−	0.777351i	$-0.716563\pi$
$653$	8.18759	−	27.8844i	0.320405	−	1.09120i	0.949473	−	0.313849i	$-0.101619\pi$
$654$	14.6008	−	20.7132i	0.570936	−	0.809950i
$655$	−8.32275	+	12.9504i	−0.325197	+	0.506016i
$656$	0.413933	−	0.644093i	0.0161614	−	0.0251476i
$657$	9.15951	−	16.2216i	0.357346	−	0.632867i
$658$	−2.06994	+	7.04956i	−0.0806946	+	0.274821i
$659$	1.36848	+	9.51801i	0.0533085	+	0.370769i	0.998960	+	0.0455880i	$0.0145161\pi$
$659$	1.36848	+	9.51801i	0.0533085	+	0.370769i	−0.945652	+	0.325181i	$0.894575\pi$
$660$	1.86414	+	1.76048i	0.0725614	+	0.0685266i
$661$	−31.2494	+	14.2711i	−1.21546	+	0.555082i	−0.916826	−	0.399286i	$-0.869258\pi$
$661$	−31.2494	+	14.2711i	−1.21546	+	0.555082i	−0.298633	+	0.954368i	$0.596531\pi$
$662$	−1.29882	−	4.42337i	−0.0504801	−	0.171919i
$663$	−3.12148	+	9.16064i	−0.121228	+	0.355770i
$664$	2.13715	+	0.307276i	0.0829376	+	0.0119246i
$665$	7.64284	−	4.91175i	0.296377	−	0.190470i
$666$	−9.67206	+	1.96041i	−0.374785	+	0.0759645i
$667$	14.8497	−	10.5993i	0.574983	−	0.410408i
$668$			13.9101i			0.538197i
$669$	29.8154	−	23.6791i	1.15273	−	0.915486i
$670$	0.572983	−	3.98518i	0.0221363	−	0.153961i
$671$	−10.1684	−	4.64375i	−0.392546	−	0.179270i
$672$	3.34673	−	1.35846i	0.129103	−	0.0524039i
$673$	14.1459	+	30.9752i	0.545284	+	1.19400i	0.958950	+	0.283576i	$0.0915208\pi$
$673$	14.1459	+	30.9752i	0.545284	+	1.19400i	−0.413666	+	0.910429i	$0.635752\pi$
$674$	−6.52852	−	7.53431i	−0.251469	−	0.290211i
$675$	2.22625	+	4.69508i	0.0856885	+	0.180714i
$676$	−0.0227457	−	0.00667873i	−0.000874833	−	0.000256874i
$677$	−25.7333	+	29.6978i	−0.989012	+	1.14138i	0.000942858		1.00000i	$0.499700\pi$
$677$	−25.7333	+	29.6978i	−0.989012	+	1.14138i	−0.989955	+	0.141382i	$0.954846\pi$
$678$	−8.30790	+	16.3064i	−0.319063	+	0.626242i
$679$	21.8743	+	14.0578i	0.839460	+	0.539488i
$680$	1.17225	+	1.01576i	0.0449538	+	0.0389527i
$681$	−23.4103	−	4.39577i	−0.897083	−	0.168446i
$682$	8.05198	−	1.15770i	0.308326	−	0.0443306i
$683$	12.3670	−	10.7160i	0.473209	−	0.410038i	−0.385336	−	0.922776i	$-0.625914\pi$
$683$	12.3670	−	10.7160i	0.473209	−	0.410038i	0.858545	+	0.512739i	$0.171369\pi$
$684$	−10.5733	+	7.68290i	−0.404279	+	0.293763i
$685$	−5.62550	+	1.65180i	−0.214939	+	0.0631119i
$686$	8.36080	−	18.3076i	0.319217	−	0.698987i
$687$	27.9406	+	1.19687i	1.06600	+	0.0456635i
$688$	0.529985	+	0.824673i	0.0202055	+	0.0314404i
$689$	0.251615			0.00958575
$690$	−4.44957	+	7.01436i	−0.169392	+	0.267032i
$691$	−48.2082			−1.83393			−0.916963	−	0.398972i	$-0.869367\pi$
$691$	−48.2082			−1.83393			−0.916963	+	0.398972i	$0.869367\pi$
$692$	13.3869	+	20.8304i	0.508894	+	0.791854i
$693$	9.24598	−	0.529257i	0.351226	−	0.0201048i
$694$	1.28233	−	2.80790i	0.0486765	−	0.106587i
$695$	3.35750	−	0.985852i	0.127357	−	0.0373955i
$696$	3.32185	+	5.69050i	0.125915	+	0.215698i
$697$	0.897517	−	0.777703i	0.0339959	−	0.0294576i
$698$	−18.7415	+	2.69463i	−0.709377	+	0.101993i
$699$	0.936366	−	4.98674i	0.0354166	−	0.188616i
$700$	1.57600	+	1.36561i	0.0595672	+	0.0516153i
$701$	−36.8554	−	23.6855i	−1.39201	−	0.894590i	−0.392328	−	0.919825i	$-0.628330\pi$
$701$	−36.8554	−	23.6855i	−1.39201	−	0.894590i	−0.999682	+	0.0252349i	$0.991967\pi$
$702$	5.01484	−	18.0336i	0.189273	−	0.680635i
$703$	9.38510	−	10.8310i	0.353966	−	0.408498i
$704$	−1.42038	−	0.417062i	−0.0535327	−	0.0157186i
$705$	5.92345	−	1.46709i	0.223090	−	0.0552538i
$706$	−7.58905	−	8.75823i	−0.285618	−	0.329620i
$707$	−13.7677	−	30.1471i	−0.517789	−	1.13380i
$708$	−3.13057	−	7.71252i	−0.117654	−	0.289854i
$709$	−38.0324	−	17.3688i	−1.42834	−	0.652299i	−0.456881	−	0.889528i	$-0.651034\pi$
$709$	−38.0324	−	17.3688i	−1.42834	−	0.652299i	−0.971454	+	0.237229i	$0.923761\pi$
$710$	−0.0931252	+	0.647700i	−0.00349493	+	0.0243078i
$711$	6.28948	+	6.47095i	0.235874	+	0.242679i
$712$		−	7.33340i		−	0.274831i
$713$	8.64725	+	24.8949i	0.323842	+	0.932322i
$714$	5.57452	−	0.559259i	0.208621	−	0.0209297i
$715$	4.48607	−	2.88302i	0.167770	−	0.107819i
$716$	−14.3646	−	2.06531i	−0.536829	−	0.0771844i
$717$	−14.4711	−	4.93101i	−0.540434	−	0.184152i
$718$	6.81087	+	23.1957i	0.254180	+	0.865656i
$719$	24.2600	−	11.0792i	0.904744	−	0.413183i	0.0919699	−	0.995762i	$-0.470684\pi$
$719$	24.2600	−	11.0792i	0.904744	−	0.413183i	0.812774	+	0.582579i	$0.197956\pi$
$720$	−2.37582	−	1.83180i	−0.0885414	−	0.0682672i
$721$	−0.876347	−	6.09513i	−0.0326369	−	0.226994i
$722$	−0.00559795	+	0.0190649i	−0.000208334	+	0.000709521i
$723$	−8.80674	−	6.20789i	−0.327526	−	0.230874i
$724$	−0.612265	+	0.952702i	−0.0227546	+	0.0354069i
$725$	−2.05672	+	3.20032i	−0.0763847	+	0.118857i
$726$	12.4701	+	8.79024i	0.462810	+	0.326236i
$727$	−10.0118	+	34.0971i	−0.371317	+	1.26459i	0.536026	+	0.844201i	$0.319925\pi$
$727$	−10.0118	+	34.0971i	−0.371317	+	1.26459i	−0.907344	+	0.420389i	$0.861893\pi$
$728$	−1.06906	−	7.43550i	−0.0396222	−	0.275578i
$729$	−26.1142	−	6.85923i	−0.967192	−	0.254045i
$730$	−5.64850	+	2.57958i	−0.209060	+	0.0954747i
$731$	0.428386	+	1.45895i	0.0158444	+	0.0539612i
$732$	12.3803	+	4.21856i	0.457587	+	0.155922i
$733$	17.4721	+	2.51211i	0.645347	+	0.0927869i	0.457214	−	0.889357i	$-0.348847\pi$
$733$	17.4721	+	2.51211i	0.645347	+	0.0927869i	0.188133	+	0.982144i	$0.439756\pi$
$734$	16.7185	−	10.7444i	0.617093	−	0.396582i
$735$	−4.56930	+	0.458411i	−0.168541	+	0.0169087i
$736$	0.450560	−	4.77462i	0.0166079	−	0.175995i
$737$			5.96012i			0.219544i
$738$	−1.64709	+	1.60090i	−0.0606301	+	0.0589298i
$739$	4.50273	−	31.3172i	0.165636	−	1.15202i	−0.722141	−	0.691746i	$-0.756842\pi$
$739$	4.50273	−	31.3172i	0.165636	−	1.15202i	0.887776	−	0.460275i	$-0.152249\pi$
$740$	2.99231	+	1.36654i	0.109999	+	0.0502350i
$741$	10.2234	+	25.1865i	0.375565	+	0.925248i
$742$	−0.0605091	−	0.132497i	−0.00222136	−	0.00486410i
$743$	−20.3994	−	23.5422i	−0.748382	−	0.863679i	0.246028	−	0.969263i	$-0.420874\pi$
$743$	−20.3994	−	23.5422i	−0.748382	−	0.863679i	−0.994410	+	0.105583i	$0.966329\pi$
$744$	−9.23878	+	2.28822i	−0.338710	+	0.0838901i
$745$	22.5490	+	6.62098i	0.826131	+	0.242574i
$746$	23.0359	−	26.5848i	0.843404	−	0.973340i
$747$	−6.03618	−	2.34969i	−0.220852	−	0.0859705i
$748$	−1.93167	−	1.24141i	−0.0706290	−	0.0453905i
$749$	−18.4690	−	16.0035i	−0.674842	−	0.584754i
$750$	0.319643	−	1.70230i	0.0116717	−	0.0621592i
$751$	−37.4182	+	5.37993i	−1.36541	+	0.196316i	−0.785752	−	0.618542i	$-0.787724\pi$
$751$	−37.4182	+	5.37993i	−1.36541	+	0.196316i	−0.579660	+	0.814859i	$0.696814\pi$
$752$	−2.66269	+	2.30723i	−0.0970982	+	0.0841361i
$753$	1.61978	+	2.77477i	0.0590282	+	0.101118i
$754$	13.1487	−	3.86082i	0.478849	−	0.140603i
$755$	−9.50817	+	20.8200i	−0.346038	+	0.757717i
$756$	−10.7022	+	1.69605i	−0.389236	+	0.0616846i
$757$	−3.67189	−	5.71358i	−0.133457	−	0.207664i	0.768093	−	0.640339i	$-0.221206\pi$
$757$	−3.67189	−	5.71358i	−0.133457	−	0.207664i	−0.901550	+	0.432675i	$0.857570\pi$
$758$	−23.4846			−0.852999
$759$	5.04212	−	11.2154i	0.183017	−	0.407094i
$760$	4.35662			0.158031
$761$	−22.2770	−	34.6637i	−0.807541	−	1.25656i	−0.963210	−	0.268749i	$-0.913390\pi$
$761$	−22.2770	−	34.6637i	−0.807541	−	1.25656i	0.155670	−	0.987809i	$-0.450246\pi$
$762$	−0.648660	−	0.0277862i	−0.0234985	−	0.00100659i
$763$	−12.6748	+	27.7540i	−0.458859	+	1.00476i
$764$	−10.9042	+	3.20176i	−0.394500	+	0.115836i
$765$	−2.73539	−	3.76447i	−0.0988981	−	0.136105i
$766$	−16.2987	+	14.1229i	−0.588894	+	0.510280i
$767$	−17.1351	+	2.46365i	−0.618712	+	0.0889574i
$768$	1.70230	+	0.319643i	0.0614265	+	0.0115341i
$769$	19.8289	+	17.1818i	0.715047	+	0.619592i	0.934472	−	0.356038i	$-0.115873\pi$
$769$	19.8289	+	17.1818i	0.715047	+	0.619592i	−0.219425	+	0.975629i	$0.570418\pi$
$770$	−2.59698	−	1.66898i	−0.0935888	−	0.0601458i
$771$	7.96114	−	15.6258i	0.286713	−	0.562748i
$772$	−8.64849	+	9.98089i	−0.311266	+	0.359220i
$773$	43.1204	+	12.6613i	1.55093	+	0.455395i	0.941379	−	0.337351i	$-0.109531\pi$
$773$	43.1204	+	12.6613i	1.55093	+	0.455395i

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(0.0741266 - 1.73046i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.49583 + 0.873200i) q^{6} +(1.57600 - 1.36561i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98901 - 0.256547i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(0.0741266 - 1.73046i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.49583 + 0.873200i) q^{6} +(1.57600 - 1.36561i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98901 - 0.256547i) q^{9} +(0.755750 + 0.654861i) q^{10} +(-1.24535 - 0.800337i) q^{11} +(1.54329 + 0.786289i) q^{12} +(2.35898 - 2.72241i) q^{13} +(-2.00088 - 0.587510i) q^{14} +(0.416404 + 1.68125i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.644355 - 1.41094i) q^{17} +(1.40016 + 2.65322i) q^{18} +(-3.96292 - 1.80980i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-2.24632 - 2.82844i) q^{21} +1.48035i q^{22} +(-4.70815 + 0.912857i) q^{23} +(-0.172899 - 1.72340i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-3.56560 - 0.512655i) q^{26} +(-0.665511 + 5.15336i) q^{27} +(0.587510 + 2.00088i) q^{28} +(-3.46045 + 1.58033i) q^{29} +(1.18923 - 1.25925i) q^{30} +(-0.782046 - 5.43925i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-1.47727 + 2.09570i) q^{33} +(-0.838595 + 1.30488i) q^{34} +(-1.12742 + 1.75431i) q^{35} +(1.47504 - 2.61233i) q^{36} +(-0.926782 + 3.15633i) q^{37} +(0.620012 + 4.31228i) q^{38} +(-4.53617 - 4.28393i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(0.215704 + 0.734621i) q^{41} +(-1.16498 + 3.41889i) q^{42} +(-0.970313 - 0.139510i) q^{43} +(1.24535 - 0.800337i) q^{44} +(2.94021 - 0.595947i) q^{45} +(3.31336 + 3.46722i) q^{46} -3.52324i q^{47} +(-1.35634 + 1.07719i) q^{48} +(-0.377323 + 2.62434i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(-2.48935 + 1.01045i) q^{51} +(1.49643 + 3.27673i) q^{52} +(0.0457414 + 0.0527884i) q^{53} +(4.69508 - 2.22625i) q^{54} +(1.42038 + 0.417062i) q^{55} +(1.36561 - 1.57600i) q^{56} +(-3.42556 + 6.72354i) q^{57} +(3.20032 + 2.05672i) q^{58} +(-3.63188 - 3.14705i) q^{59} +(-1.70230 - 0.319643i) q^{60} +(7.47445 - 1.07466i) q^{61} +(-4.15298 + 3.59858i) q^{62} +(-5.06102 + 3.67751i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.49643 + 3.27673i) q^{65} +(2.56169 + 0.109733i) q^{66} +(-2.17671 - 3.38702i) q^{67} +1.55111 q^{68} +(1.23067 + 8.21495i) q^{69} +2.08535 q^{70} +(0.353774 + 0.550483i) q^{71} +(-2.99510 + 0.171445i) q^{72} +(-2.57958 + 5.64850i) q^{73} +(3.15633 - 0.926782i) q^{74} +(-0.873200 - 1.49583i) q^{75} +(3.29251 - 2.85298i) q^{76} +(-3.05562 + 0.439332i) q^{77} +(-1.15144 + 6.13213i) q^{78} +(-2.27327 - 1.96980i) q^{79} +(0.841254 + 0.540641i) q^{80} +(8.86837 + 1.53364i) q^{81} +(0.501384 - 0.578628i) q^{82} +(2.07167 + 0.608297i) q^{83} +(3.50599 - 0.868347i) q^{84} +(1.01576 + 1.17225i) q^{85} +(0.407228 + 0.891704i) q^{86} +(2.47820 + 6.10533i) q^{87} +(-1.34657 - 0.614959i) q^{88} +(1.04365 - 7.25875i) q^{89} +(-2.09094 - 2.15127i) q^{90} -7.51197i q^{91} +(1.12547 - 4.66190i) q^{92} +(-9.47039 + 0.950109i) q^{93} +(-2.96394 + 1.90481i) q^{94} +(4.31228 + 0.620012i) q^{95} +(1.63948 + 0.558652i) q^{96} +(3.51291 + 11.9639i) q^{97} +(2.41173 - 1.10140i) q^{98} +(3.51703 + 2.71171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) \)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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Groups

Properties

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