LMFDB - Embedded newform 950.2.u.g.199.5

Newspace parameters

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.5
Character	$\chi$	$=$	950.199
Dual form			950.2.u.g.549.5

$q$-expansion

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(0.712963 + 0.849676i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(-4.26875 - 2.46456i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.307311 - 1.74285i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(0.712963 + 0.849676i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(-4.26875 - 2.46456i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.307311 - 1.74285i) q^{9} +(-2.20561 - 3.82023i) q^{11} +(0.960572 + 0.554587i) q^{12} +(1.69691 - 2.02230i) q^{13} +(-4.63187 - 1.68586i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-4.94904 + 0.872649i) q^{17} -1.76973i q^{18} +(4.21347 - 1.11656i) q^{19} +(-0.949379 - 5.38420i) q^{21} +(-2.83548 - 3.37919i) q^{22} +(-0.351075 - 0.964570i) q^{23} +(1.04228 + 0.379360i) q^{24} +(1.31996 - 2.28624i) q^{26} +(4.58167 - 2.64523i) q^{27} +(-4.85424 - 0.855934i) q^{28} +(-0.462691 + 2.62405i) q^{29} +(-1.01615 + 1.76003i) q^{31} +(0.642788 - 0.766044i) q^{32} +(1.67344 - 4.59773i) q^{33} +(-4.72232 + 1.71878i) q^{34} +(-0.307311 - 1.74285i) q^{36} +2.00107i q^{37} +(3.95557 - 1.83126i) q^{38} +2.92813 q^{39} +(1.65005 - 1.38456i) q^{41} +(-1.86991 - 5.13754i) q^{42} +(-0.516578 + 1.41929i) q^{43} +(-3.37919 - 2.83548i) q^{44} +(-0.513237 - 0.888952i) q^{46} +(1.76317 + 0.310895i) q^{47} +(1.09232 + 0.192606i) q^{48} +(8.64815 + 14.9790i) q^{49} +(-4.26995 - 3.58291i) q^{51} +(0.902907 - 2.48072i) q^{52} +(1.92343 + 5.28457i) q^{53} +(4.05273 - 3.40064i) q^{54} -4.92913 q^{56} +(3.95276 + 2.78402i) q^{57} +2.66453i q^{58} +(-2.44041 - 13.8402i) q^{59} +(13.6360 - 4.96308i) q^{61} +(-0.695088 + 1.90974i) q^{62} +(-5.60720 + 6.68240i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.849627 - 4.81847i) q^{66} +(-13.4349 - 2.36894i) q^{67} +(-4.35211 + 2.51269i) q^{68} +(0.569269 - 0.986002i) q^{69} +(14.6575 + 5.33488i) q^{71} +(-0.605285 - 1.66301i) q^{72} +(8.10702 + 9.66157i) q^{73} +(0.347483 + 1.97067i) q^{74} +(3.57748 - 2.49031i) q^{76} +21.7435i q^{77} +(2.88365 - 0.508465i) q^{78} +(2.17143 - 1.82205i) q^{79} +(0.525132 + 0.191132i) q^{81} +(1.38456 - 1.65005i) q^{82} +(-6.30732 - 3.64153i) q^{83} +(-2.73363 - 4.73478i) q^{84} +(-0.262274 + 1.48743i) q^{86} +(-2.55947 + 1.47771i) q^{87} +(-3.82023 - 2.20561i) q^{88} +(-7.72995 - 6.48620i) q^{89} +(-12.2278 + 4.45054i) q^{91} +(-0.659805 - 0.786325i) q^{92} +(-2.21993 + 0.391433i) q^{93} +1.79037 q^{94} +1.10917 q^{96} +(-11.7266 + 2.06772i) q^{97} +(11.1179 + 13.2497i) q^{98} +(-7.33589 + 2.67005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36q + 36q^{9} + O(q^{10}) $	$ 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	0.712963	+	0.849676i	0.411629	+	0.490561i	0.931529	−	0.363667i	$-0.118475\pi$
$3$	0.712963	+	0.849676i	0.411629	+	0.490561i	−0.519900	+	0.854227i	$0.674031\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	0.849676	+	0.712963i	0.346879	+	0.291066i
$7$	−4.26875	−	2.46456i	−1.61344	−	0.931518i	−0.988566	−	0.150789i	$-0.951819\pi$
$7$	−4.26875	−	2.46456i	−1.61344	−	0.931518i	−0.624870	−	0.780729i	$-0.714848\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	0.307311	−	1.74285i	0.102437	−	0.580950i
$10$		0			0
$11$	−2.20561	−	3.82023i	−0.665016	−	1.15184i	−0.979281	−	0.202507i	$-0.935091\pi$
$11$	−2.20561	−	3.82023i	−0.665016	−	1.15184i	0.314264	−	0.949336i	$-0.398242\pi$
$12$	0.960572	+	0.554587i	0.277293	+	0.160095i
$13$	1.69691	−	2.02230i	0.470638	−	0.560884i	−0.477546	−	0.878607i	$-0.658474\pi$
$13$	1.69691	−	2.02230i	0.470638	−	0.560884i	0.948184	+	0.317722i	$0.102918\pi$
$14$	−4.63187	−	1.68586i	−1.23792	−	0.450565i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−4.94904	+	0.872649i	−1.20032	+	0.211649i	−0.737836	−	0.674980i	$-0.764152\pi$
$17$	−4.94904	+	0.872649i	−1.20032	+	0.211649i	−0.462483	+	0.886628i	$0.653041\pi$
$18$		−	1.76973i		−	0.417131i
$19$	4.21347	−	1.11656i	0.966635	−	0.256156i
$19$	4.21347	−	1.11656i	0.966635	−	0.256156i
$20$		0			0
$21$	−0.949379	−	5.38420i	−0.207172	−	1.17493i
$22$	−2.83548	−	3.37919i	−0.604526	−	0.720446i
$23$	−0.351075	−	0.964570i	−0.0732041	−	0.201127i	0.897694	−	0.440619i	$-0.145241\pi$
$23$	−0.351075	−	0.964570i	−0.0732041	−	0.201127i	−0.970898	+	0.239493i	$0.923019\pi$
$24$	1.04228	+	0.379360i	0.212755	+	0.0774364i
$25$		0			0
$26$	1.31996	−	2.28624i	0.258866	−	0.448368i
$27$	4.58167	−	2.64523i	0.881744	−	0.509075i
$28$	−4.85424	−	0.855934i	−0.917366	−	0.161756i
$29$	−0.462691	+	2.62405i	−0.0859196	+	0.487274i	0.911235	+	0.411887i	$0.135130\pi$
$29$	−0.462691	+	2.62405i	−0.0859196	+	0.487274i	−0.997154	+	0.0753868i	$0.975981\pi$
$30$		0			0
$31$	−1.01615	+	1.76003i	−0.182506	+	0.316110i	−0.942733	−	0.333547i	$-0.891754\pi$
$31$	−1.01615	+	1.76003i	−0.182506	+	0.316110i	0.760227	+	0.649657i	$0.225088\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	1.67344	−	4.59773i	0.291308	−	0.800363i
$34$	−4.72232	+	1.71878i	−0.809871	+	0.294769i
$35$		0			0
$36$	−0.307311	−	1.74285i	−0.0512185	−	0.290475i
$37$			2.00107i			0.328975i	0.986379	+	0.164487i	$0.0525970\pi$
$37$			2.00107i			0.328975i	−0.986379	+	0.164487i	$0.947403\pi$
$38$	3.95557	−	1.83126i	0.641678	−	0.297069i
$39$	2.92813			0.468876
$40$		0			0
$41$	1.65005	−	1.38456i	0.257695	−	0.216232i	−0.504782	−	0.863247i	$-0.668427\pi$
$41$	1.65005	−	1.38456i	0.257695	−	0.216232i	0.762477	+	0.647015i	$0.223983\pi$
$42$	−1.86991	−	5.13754i	−0.288534	−	0.792740i
$43$	−0.516578	+	1.41929i	−0.0787775	+	0.216439i	−0.972829	−	0.231525i	$-0.925629\pi$
$43$	−0.516578	+	1.41929i	−0.0787775	+	0.216439i	0.894052	+	0.447964i	$0.147851\pi$
$44$	−3.37919	−	2.83548i	−0.509432	−	0.427464i
$45$		0			0
$46$	−0.513237	−	0.888952i	−0.0756727	−	0.131069i
$47$	1.76317	+	0.310895i	0.257185	+	0.0453486i	0.300754	−	0.953702i	$-0.402762\pi$
$47$	1.76317	+	0.310895i	0.257185	+	0.0453486i	−0.0435690	+	0.999050i	$0.513873\pi$
$48$	1.09232	+	0.192606i	0.157663	+	0.0278003i
$49$	8.64815	+	14.9790i	1.23545	+	2.13986i
$50$		0			0
$51$	−4.26995	−	3.58291i	−0.597913	−	0.501708i
$52$	0.902907	−	2.48072i	0.125211	−	0.344013i
$53$	1.92343	+	5.28457i	0.264203	+	0.725891i	0.998873	+	0.0474667i	$0.0151148\pi$
$53$	1.92343	+	5.28457i	0.264203	+	0.725891i	−0.734670	+	0.678425i	$0.762663\pi$
$54$	4.05273	−	3.40064i	0.551507	−	0.462769i
$55$		0			0
$56$	−4.92913			−0.658683
$57$	3.95276	+	2.78402i	0.523555	+	0.368752i
$58$			2.66453i			0.349870i
$59$	−2.44041	−	13.8402i	−0.317714	−	1.80184i	−0.556583	−	0.830792i	$-0.687888\pi$
$59$	−2.44041	−	13.8402i	−0.317714	−	1.80184i	0.238869	−	0.971052i	$-0.423223\pi$
$60$		0			0
$61$	13.6360	−	4.96308i	1.74590	−	0.635457i	0.746358	−	0.665545i	$-0.231801\pi$
$61$	13.6360	−	4.96308i	1.74590	−	0.635457i	0.999547	+	0.0300876i	$0.00957861\pi$
$62$	−0.695088	+	1.90974i	−0.0882763	+	0.242537i
$63$	−5.60720	+	6.68240i	−0.706441	+	0.841903i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	0.849627	−	4.81847i	0.104582	−	0.593113i
$67$	−13.4349	−	2.36894i	−1.64134	−	0.289412i	−0.724679	−	0.689086i	$-0.758012\pi$
$67$	−13.4349	−	2.36894i	−1.64134	−	0.289412i	−0.916657	+	0.399674i	$0.869123\pi$
$68$	−4.35211	+	2.51269i	−0.527771	+	0.304709i
$69$	0.569269	−	0.986002i	0.0685319	−	0.118701i
$70$		0			0
$71$	14.6575	+	5.33488i	1.73952	+	0.633134i	0.999233	−	0.0391574i	$-0.0124674\pi$
$71$	14.6575	+	5.33488i	1.73952	+	0.633134i	0.740287	+	0.672291i	$0.234690\pi$
$72$	−0.605285	−	1.66301i	−0.0713335	−	0.195987i
$73$	8.10702	+	9.66157i	0.948855	+	1.13080i	0.991289	+	0.131702i	$0.0420441\pi$
$73$	8.10702	+	9.66157i	0.948855	+	1.13080i	−0.0424348	+	0.999099i	$0.513511\pi$
$74$	0.347483	+	1.97067i	0.0403941	+	0.229086i
$75$		0			0
$76$	3.57748	−	2.49031i	0.410365	−	0.285658i
$77$			21.7435i			2.47790i
$78$	2.88365	−	0.508465i	0.326509	−	0.0575723i
$79$	2.17143	−	1.82205i	0.244305	−	0.204996i	−0.512410	−	0.858741i	$-0.671247\pi$
$79$	2.17143	−	1.82205i	0.244305	−	0.204996i	0.756716	+	0.653744i	$0.226803\pi$
$80$		0			0
$81$	0.525132	+	0.191132i	0.0583480	+	0.0212369i
$82$	1.38456	−	1.65005i	0.152899	−	0.182218i
$83$	−6.30732	−	3.64153i	−0.692318	−	0.399710i	0.112162	−	0.993690i	$-0.464222\pi$
$83$	−6.30732	−	3.64153i	−0.692318	−	0.399710i	−0.804480	+	0.593980i	$0.797556\pi$
$84$	−2.73363	−	4.73478i	−0.298263	−	0.516607i
$85$		0			0
$86$	−0.262274	+	1.48743i	−0.0282817	+	0.160394i
$87$	−2.55947	+	1.47771i	−0.274404	+	0.158428i
$88$	−3.82023	−	2.20561i	−0.407238	−	0.235119i
$89$	−7.72995	−	6.48620i	−0.819373	−	0.687536i	0.133452	−	0.991055i	$-0.457394\pi$
$89$	−7.72995	−	6.48620i	−0.819373	−	0.687536i	−0.952825	+	0.303520i	$0.901838\pi$
$90$		0			0
$91$	−12.2278	+	4.45054i	−1.28182	+	0.466544i
$92$	−0.659805	−	0.786325i	−0.0687894	−	0.0819800i
$93$	−2.21993	+	0.391433i	−0.230196	+	0.0405897i
$94$	1.79037			0.184663
$95$		0			0
$96$	1.10917			0.113205
$97$	−11.7266	+	2.06772i	−1.19066	+	0.209945i	−0.733656	−	0.679521i	$-0.762188\pi$
$97$	−11.7266	+	2.06772i	−1.19066	+	0.209945i	−0.457002	+	0.889466i	$0.651077\pi$
$98$	11.1179	+	13.2497i	1.12307	+	1.33843i
$99$	−7.33589	+	2.67005i	−0.737285	+	0.268350i
$100$		0			0
$101$	−1.10632	−	0.928316i	−0.110083	−	0.0923709i	0.586085	−	0.810250i	$-0.300669\pi$
$101$	−1.10632	−	0.928316i	−0.110083	−	0.0923709i	−0.696168	+	0.717879i	$0.745113\pi$
$102$	−4.82725	−	2.78701i	−0.477969	−	0.275955i
$103$	3.86364	−	2.23068i	0.380696	−	0.219795i	−0.297425	−	0.954745i	$-0.596128\pi$
$103$	3.86364	−	2.23068i	0.380696	−	0.219795i	0.678121	+	0.734950i	$0.262794\pi$
$104$	0.458418	−	2.59982i	0.0449515	−	0.254933i
$105$		0			0
$106$	2.81186	+	4.87029i	0.273112	+	0.473044i
$107$	6.80951	+	3.93147i	0.658300	+	0.380070i	0.791629	−	0.611002i	$-0.209233\pi$
$107$	6.80951	+	3.93147i	0.658300	+	0.380070i	−0.133329	+	0.991072i	$0.542567\pi$
$108$	3.40064	−	4.05273i	0.327227	−	0.389974i
$109$	−2.37019	−	0.862678i	−0.227023	−	0.0826296i	0.226004	−	0.974126i	$-0.427434\pi$
$109$	−2.37019	−	0.862678i	−0.227023	−	0.0826296i	−0.453027	+	0.891497i	$0.649656\pi$
$110$		0			0
$111$	−1.70027	+	1.42669i	−0.161382	+	0.135416i
$112$	−4.85424	+	0.855934i	−0.458683	+	0.0808782i
$113$		−	2.59814i		−	0.244413i	−0.992505	−	0.122206i	$-0.961003\pi$
$113$		−	2.59814i		−	0.244413i	0.992505	−	0.122206i	$-0.0389970\pi$
$114$	4.37615	+	2.05533i	0.409864	+	0.192499i
$115$		0			0
$116$	0.462691	+	2.62405i	0.0429598	+	0.243637i
$117$	−3.00308	−	3.57893i	−0.277635	−	0.330872i
$118$	−4.80666	−	13.2062i	−0.442489	−	1.21573i
$119$	23.2769	+	8.47211i	2.13379	+	0.776637i
$120$		0			0
$121$	−4.22943	+	7.32559i	−0.384494	+	0.665963i
$122$	12.5670	−	7.25554i	1.13776	−	0.656886i
$123$	2.35285	+	0.414871i	0.212150	+	0.0374077i
$124$	−0.352906	+	2.00143i	−0.0316919	+	0.179733i
$125$		0			0
$126$	−4.36163	+	7.55456i	−0.388564	+	0.673013i
$127$	13.3209	−	15.8752i	1.18204	−	1.40869i	0.289822	−	0.957080i	$-0.406404\pi$
$127$	13.3209	−	15.8752i	1.18204	−	1.40869i	0.892213	−	0.451614i	$-0.149152\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	−1.57424	+	0.572975i	−0.138604	+	0.0504476i
$130$		0			0
$131$	−0.301638	−	1.71068i	−0.0263543	−	0.149462i	0.968791	−	0.247879i	$-0.0797334\pi$
$131$	−0.301638	−	1.71068i	−0.0263543	−	0.149462i	−0.995145	+	0.0984163i	$0.968622\pi$
$132$		−	4.89281i		−	0.425864i
$133$	−20.7381	−	5.61805i	−1.79822	−	0.487147i
$134$	−13.6422			−1.17850
$135$		0			0
$136$	−3.84967	+	3.23026i	−0.330107	+	0.276992i
$137$	−0.854249	−	2.34703i	−0.0729834	−	0.200520i	0.897837	−	0.440328i	$-0.145138\pi$
$137$	−0.854249	−	2.34703i	−0.0729834	−	0.200520i	−0.970820	+	0.239808i	$0.922916\pi$
$138$	0.389403	−	1.06988i	0.0331482	−	0.0910738i
$139$	−9.06390	−	7.60552i	−0.768790	−	0.645092i	0.171609	−	0.985165i	$-0.445104\pi$
$139$	−9.06390	−	7.60552i	−0.768790	−	0.645092i	−0.940399	+	0.340074i	$0.889548\pi$
$140$		0			0
$141$	0.992916	+	1.71978i	0.0836186	+	0.144832i
$142$	15.3612	+	2.70859i	1.28908	+	0.227300i
$143$	−11.4684	−	2.02218i	−0.959032	−	0.169103i
$144$	−0.884867	−	1.53264i	−0.0737390	−	0.127720i
$145$		0			0
$146$	9.66157	+	8.10702i	0.799597	+	0.670942i
$147$	−6.56152	+	18.0276i	−0.541185	+	1.48689i
$148$	0.684408	+	1.88040i	0.0562580	+	0.154568i
$149$	15.4299	−	12.9472i	1.26406	−	1.06068i	0.268828	−	0.963188i	$-0.413364\pi$
$149$	15.4299	−	12.9472i	1.26406	−	1.06068i	0.995237	−	0.0974880i	$-0.0310808\pi$
$150$		0			0
$151$	−7.67871			−0.624885			−0.312442	−	0.949937i	$-0.601147\pi$
$151$	−7.67871			−0.624885			−0.312442	+	0.949937i	$0.601147\pi$
$152$	3.09069	−	3.07370i	0.250688	−	0.249310i
$153$			8.89360i			0.719005i
$154$	3.77571	+	21.4131i	0.304256	+	1.72552i
$155$		0			0
$156$	2.75154	−	1.00148i	0.220300	−	0.0801825i
$157$	−1.98396	+	5.45088i	−0.158337	+	0.435027i	−0.993340	−	0.115218i	$-0.963243\pi$
$157$	−1.98396	+	5.45088i	−0.158337	+	0.435027i	0.835003	+	0.550245i	$0.185466\pi$
$158$	1.82205	−	2.17143i	0.144954	−	0.172750i
$159$	−3.11884	+	5.40199i	−0.247340	+	0.428406i
$160$		0			0
$161$	−0.878594	+	4.98275i	−0.0692429	+	0.392696i
$162$	0.550344	+	0.0970404i	0.0432391	+	0.00762422i
$163$	9.28767	−	5.36224i	0.727466	−	0.420003i	−0.0900283	−	0.995939i	$-0.528696\pi$
$163$	9.28767	−	5.36224i	0.727466	−	0.420003i	0.817495	+	0.575936i	$0.195362\pi$
$164$	1.07700	−	1.86541i	0.0840992	−	0.145664i
$165$		0			0
$166$	−6.84384	−	2.49095i	−0.531185	−	0.193335i
$167$	−3.38367	−	9.29655i	−0.261836	−	0.719389i	−0.999044	−	0.0437226i	$-0.986078\pi$
$167$	−3.38367	−	9.29655i	−0.261836	−	0.719389i	0.737208	−	0.675666i	$-0.236144\pi$
$168$	−3.51429	−	4.18816i	−0.271133	−	0.323124i
$169$	1.04724	+	5.93919i	0.0805569	+	0.456861i
$170$		0			0
$171$	−0.651146	−	7.68657i	−0.0497944	−	0.587806i
$172$			1.51037i			0.115165i
$173$	−15.4634	+	2.72662i	−1.17566	+	0.207301i	−0.727151	−	0.686477i	$-0.759156\pi$
$173$	−15.4634	+	2.72662i	−1.17566	+	0.207301i	−0.448510	+	0.893778i	$0.648045\pi$
$174$	−2.26399	+	1.89971i	−0.171633	+	0.144017i
$175$		0			0
$176$	−4.14519	−	1.50873i	−0.312456	−	0.113725i
$177$	10.0198	−	11.9411i	0.753134	−	0.897550i
$178$	−8.73883	−	5.04537i	−0.655003	−	0.378166i
$179$	5.05642	+	8.75798i	0.377935	+	0.654602i	0.990762	−	0.135615i	$-0.0433010\pi$
$179$	5.05642	+	8.75798i	0.377935	+	0.654602i	−0.612827	+	0.790217i	$0.709968\pi$
$180$		0			0
$181$	0.465151	−	2.63800i	0.0345744	−	0.196081i	−0.962628	−	0.270826i	$-0.912703\pi$
$181$	0.465151	−	2.63800i	0.0345744	−	0.196081i	0.997203	+	0.0747449i	$0.0238142\pi$
$182$	−11.2692	+	6.50626i	−0.835326	+	0.482276i
$183$	13.9389	+	8.04765i	1.03040	+	0.594899i
$184$	−0.786325	−	0.659805i	−0.0579686	−	0.0486414i
$185$		0			0
$186$	−2.11823	+	0.770973i	−0.155316	+	0.0565305i
$187$	14.2494	+	16.9817i	1.04202	+	1.24183i
$188$	1.76317	−	0.310895i	0.128592	−	0.0226743i
$189$	−26.0774			−1.89685
$190$		0			0
$191$	3.75100			0.271413			0.135706	−	0.990749i	$-0.456670\pi$
$191$	3.75100			0.271413			0.135706	+	0.990749i	$0.456670\pi$
$192$	1.09232	−	0.192606i	0.0788316	−	0.0139001i
$193$	9.27700	+	11.0559i	0.667773	+	0.795821i	0.988479	−	0.151358i	$-0.0483645\pi$
$193$	9.27700	+	11.0559i	0.667773	+	0.795821i	−0.320706	+	0.947179i	$0.603920\pi$
$194$	−11.1894	+	4.07261i	−0.803353	+	0.292397i
$195$		0			0
$196$	13.2497	+	11.1179i	0.946410	+	0.794132i
$197$	17.1473	+	9.89999i	1.22169	+	0.705345i	0.965279	−	0.261222i	$-0.0841254\pi$
$197$	17.1473	+	9.89999i	1.22169	+	0.705345i	0.256415	+	0.966567i	$0.417459\pi$
$198$	−6.76079	+	3.90335i	−0.480469	+	0.277399i
$199$	−3.46951	+	19.6766i	−0.245947	+	1.39484i	0.572335	+	0.820020i	$0.306038\pi$
$199$	−3.46951	+	19.6766i	−0.245947	+	1.39484i	−0.818282	+	0.574817i	$0.805073\pi$
$200$		0			0
$201$	−7.56577	−	13.1043i	−0.533648	−	0.924305i
$202$	−1.25072	−	0.722101i	−0.0880001	−	0.0508069i
$203$	8.44226	−	10.0611i	0.592530	−	0.706150i
$204$	−5.23787	−	1.90643i	−0.366724	−	0.133477i
$205$		0			0
$206$	3.41759	−	2.86770i	0.238115	−	0.199802i
$207$	−1.78899	+	0.315447i	−0.124343	+	0.0219251i
$208$		−	2.63992i		−	0.183046i
$209$	−13.5588	−	13.6337i	−0.937880	−	0.943064i
$210$		0			0
$211$	2.37072	+	13.4450i	0.163207	+	0.925594i	0.950894	+	0.309518i	$0.100168\pi$
$211$	2.37072	+	13.4450i	0.163207	+	0.925594i	−0.787687	+	0.616076i	$0.788721\pi$
$212$	3.61486	+	4.30802i	0.248269	+	0.295876i
$213$	5.91730	+	16.2577i	0.405447	+	1.11396i
$214$	7.38875	+	2.68928i	0.505084	+	0.183836i
$215$		0			0
$216$	2.64523	−	4.58167i	0.179985	−	0.311743i
$217$	8.67539	−	5.00874i	0.588924	−	0.340015i
$218$	−2.48398	−	0.437993i	−0.168237	−	0.0296646i
$219$	−2.42920	+	13.7767i	−0.164150	+	0.930941i
$220$		0			0
$221$	−6.63332	+	11.4892i	−0.446205	+	0.772850i
$222$	−1.42669	+	1.70027i	−0.0957533	+	0.114114i
$223$	7.92835	−	21.7830i	0.530922	−	1.45870i	−0.327054	−	0.945006i	$-0.606056\pi$
$223$	7.92835	−	21.7830i	0.530922	−	1.45870i	0.857976	−	0.513690i	$-0.171722\pi$
$224$	−4.63187	+	1.68586i	−0.309480	+	0.112641i
$225$		0			0
$226$	−0.451163	−	2.55867i	−0.0300109	−	0.170200i
$227$		−	7.37892i		−	0.489756i	−0.969554	−	0.244878i	$-0.921252\pi$
$227$		−	7.37892i		−	0.489756i	0.969554	−	0.244878i	$-0.0787479\pi$
$228$	4.66657	+	1.26420i	0.309051	+	0.0837235i
$229$	13.2440			0.875188			0.437594	−	0.899173i	$-0.355831\pi$
$229$	13.2440			0.875188			0.437594	+	0.899173i	$0.355831\pi$
$230$		0			0
$231$	−18.4749	+	15.5023i	−1.21556	+	1.01998i
$232$	0.911323	+	2.50384i	0.0598313	+	0.164385i
$233$	−5.17822	+	14.2271i	−0.339237	+	0.932045i	0.646375	+	0.763020i	$0.276284\pi$
$233$	−5.17822	+	14.2271i	−0.339237	+	0.932045i	−0.985612	+	0.169025i	$0.945938\pi$
$234$	−3.57893	−	3.00308i	−0.233962	−	0.196317i
$235$		0			0
$236$	−7.02687	−	12.1709i	−0.457410	−	0.792258i
$237$	3.09630	+	0.545962i	0.201126	+	0.0354640i
$238$	24.3945	+	4.30140i	1.58126	+	0.278818i
$239$	5.84319	+	10.1207i	0.377964	+	0.654653i	0.990766	−	0.135583i	$-0.0432909\pi$
$239$	5.84319	+	10.1207i	0.377964	+	0.654653i	−0.612802	+	0.790237i	$0.709958\pi$
$240$		0			0
$241$	9.77297	+	8.20049i	0.629532	+	0.528240i	0.900784	−	0.434268i	$-0.142993\pi$
$241$	9.77297	+	8.20049i	0.629532	+	0.528240i	−0.271251	+	0.962509i	$0.587437\pi$
$242$	−2.89310	+	7.94873i	−0.185976	+	0.510964i
$243$	−5.21633	−	14.3318i	−0.334628	−	0.919383i
$244$	11.1161	−	9.32754i	0.711637	−	0.597135i
$245$		0			0
$246$	2.38915			0.152327
$247$	4.89186	−	10.4156i	0.311261	−	0.662727i
$248$			2.03230i			0.129051i
$249$	−1.40276	−	7.95545i	−0.0888963	−	0.504156i
$250$		0			0
$251$	−25.2367	+	9.18541i	−1.59293	+	0.579778i	−0.977963	−	0.208778i	$-0.933051\pi$
$251$	−25.2367	+	9.18541i	−1.59293	+	0.579778i	−0.614964	+	0.788556i	$0.710829\pi$
$252$	−2.98353	+	8.19717i	−0.187945	+	0.516373i
$253$	−2.91054	+	3.46865i	−0.182984	+	0.218072i
$254$	10.3618	−	17.9471i	0.650157	−	1.12610i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.157270	−	0.0277309i	−0.00981023	−	0.00172981i	0.168741	−	0.985660i	$-0.446030\pi$
$257$	−0.157270	−	0.0277309i	−0.00981023	−	0.00172981i	−0.178551	+	0.983931i	$0.557141\pi$
$258$	−1.45082	+	0.837633i	−0.0903243	+	0.0521488i
$259$	4.93178	−	8.54209i	0.306446	−	0.530780i
$260$		0			0
$261$	4.43113	+	1.61280i	0.274280	+	0.0998299i
$262$	−0.594111	−	1.63231i	−0.0367043	−	0.100844i
$263$	−5.95157	−	7.09280i	−0.366990	−	0.437361i	0.550673	−	0.834721i	$-0.314371\pi$
$263$	−5.95157	−	7.09280i	−0.366990	−	0.437361i	−0.917663	+	0.397360i	$0.869927\pi$
$264$	−0.849627	−	4.81847i	−0.0522909	−	0.296557i
$265$		0			0
$266$	−21.3986	−	1.93157i	−1.31203	−	0.118432i
$267$		−	11.1924i		−	0.684962i
$268$	−13.4349	+	2.36894i	−0.820668	+	0.144706i
$269$	−9.55896	+	8.02092i	−0.582820	+	0.489044i	−0.885872	−	0.463930i	$-0.846439\pi$
$269$	−9.55896	+	8.02092i	−0.582820	+	0.489044i	0.303052	+	0.952974i	$0.401995\pi$
$270$		0			0
$271$	26.5079	+	9.64808i	1.61024	+	0.586079i	0.981487	−	0.191526i	$-0.0613437\pi$
$271$	26.5079	+	9.64808i	1.61024	+	0.586079i	0.628752	+	0.777606i	$0.283566\pi$
$272$	−3.23026	+	3.84967i	−0.195863	+	0.233421i
$273$	−12.4995	−	7.21657i	−0.756502	−	0.436766i
$274$	−1.24883	−	2.16303i	−0.0754445	−	0.130674i
$275$		0			0
$276$	0.197705	−	1.12124i	0.0119004	−	0.0674907i
$277$	7.28486	−	4.20592i	0.437705	−	0.252709i	−0.264919	−	0.964271i	$-0.585345\pi$
$277$	7.28486	−	4.20592i	0.437705	−	0.252709i	0.702624	+	0.711562i	$0.252012\pi$
$278$	−10.2469	−	5.91604i	−0.614567	−	0.354821i
$279$	2.75518	+	2.31187i	0.164948	+	0.138408i
$280$		0			0
$281$	−20.9967	+	7.64218i	−1.25256	+	0.455894i	−0.881266	−	0.472621i	$-0.843308\pi$
$281$	−20.9967	+	7.64218i	−1.25256	+	0.455894i	−0.371294	+	0.928515i	$0.621086\pi$
$282$	1.27647	+	1.52123i	0.0760125	+	0.0905882i
$283$	12.5725	−	2.21687i	0.747357	−	0.131779i	0.213016	−	0.977049i	$-0.431671\pi$
$283$	12.5725	−	2.21687i	0.747357	−	0.131779i	0.534340	+	0.845269i	$0.320560\pi$
$284$	15.5981			0.925579
$285$		0			0
$286$	−11.6453			−0.688600
$287$	−10.4560	+	1.84368i	−0.617198	+	0.108829i
$288$	−1.13756	−	1.35570i	−0.0670316	−	0.0798851i
$289$	7.75671	−	2.82321i	0.456277	−	0.166071i
$290$		0			0
$291$	−10.1175	−	8.48962i	−0.593100	−	0.497670i
$292$	10.9226	+	6.30614i	0.639194	+	0.369039i
$293$	25.0376	−	14.4554i	1.46271	−	0.844496i	0.463575	−	0.886058i	$-0.346567\pi$
$293$	25.0376	−	14.4554i	1.46271	−	0.844496i	0.999136	+	0.0415616i	$0.0132333\pi$
$294$	−3.33137	+	18.8931i	−0.194289	+	1.10187i
$295$		0			0
$296$	1.00054	+	1.73298i	0.0581551	+	0.100728i
$297$	−20.2108	−	11.6687i	−1.17275	−	0.677086i
$298$	12.9472	−	15.4299i	0.750011	−	0.893829i
$299$	−2.54639	−	0.926810i	−0.147261	−	0.0535988i
$300$		0			0
$301$	5.70307	−	4.78544i	0.328719	−	0.275828i
$302$	−7.56206	+	1.33339i	−0.435147	+	0.0767282i
$303$		−	1.60187i		−	0.0920251i
$304$	2.50999	−	3.56370i	0.143958	−	0.204392i
$305$		0			0
$306$	1.54436	+	8.75849i	0.0882851	+	0.500690i
$307$	15.0835	+	17.9758i	0.860860	+	1.02593i	0.999367	+	0.0355713i	$0.0113251\pi$
$307$	15.0835	+	17.9758i	0.860860	+	1.02593i	−0.138507	+	0.990361i	$0.544230\pi$
$308$	7.43671	+	20.4322i	0.423746	+	1.16423i
$309$	4.64999	+	1.69246i	0.264528	+	0.0962805i
$310$		0			0
$311$	−2.12258	+	3.67642i	−0.120360	+	0.208470i	−0.919910	−	0.392130i	$-0.871738\pi$
$311$	−2.12258	+	3.67642i	−0.120360	+	0.208470i	0.799549	+	0.600600i	$0.205072\pi$
$312$	2.53584	−	1.46407i	0.143563	−	0.0828864i
$313$	11.4384	+	2.01689i	0.646534	+	0.114001i	0.487293	−	0.873238i	$-0.337984\pi$
$313$	11.4384	+	2.01689i	0.646534	+	0.114001i	0.159241	+	0.987240i	$0.449095\pi$
$314$	−1.00728	+	5.71258i	−0.0568442	+	0.322379i
$315$		0			0
$316$	1.41730	−	2.45484i	0.0797295	−	0.138096i
$317$	1.43742	−	1.71306i	0.0807338	−	0.0962148i	−0.724165	−	0.689626i	$-0.757775\pi$
$317$	1.43742	−	1.71306i	0.0807338	−	0.0962148i	0.804899	+	0.593411i	$0.202219\pi$
$318$	−2.13341	+	5.86150i	−0.119636	+	0.328697i
$319$	11.0450	−	4.02005i	0.618401	−	0.225080i
$320$		0			0
$321$	1.51445	+	8.58887i	0.0845283	+	0.479384i
$322$			5.05962i			0.281962i
$323$	−19.8783	+	9.20277i	−1.10606	+	0.512056i
$324$	0.558833			0.0310463
$325$		0			0
$326$	8.21542	−	6.89356i	0.455010	−	0.381799i
$327$	−0.956860	−	2.62895i	−0.0529145	−	0.145381i
$328$	0.736709	−	2.02409i	0.0406779	−	0.111762i
$329$	−6.76032	−	5.67258i	−0.372708	−	0.312739i
$330$		0			0
$331$	0.254634	+	0.441039i	0.0139959	+	0.0242417i	0.872939	−	0.487830i	$-0.162211\pi$
$331$	0.254634	+	0.441039i	0.0139959	+	0.0242417i	−0.858943	+	0.512072i	$0.828878\pi$
$332$	−7.17241	−	1.26469i	−0.393637	−	0.0694089i
$333$	3.48757	+	0.614953i	0.191118	+	0.0336992i
$334$	−4.94659	−	8.56775i	−0.270666	−	0.468806i
$335$		0			0
$336$	−4.18816	−	3.51429i	−0.228483	−	0.191720i
$337$	−5.15806	+	14.1717i	−0.280977	+	0.771979i	0.716269	+	0.697824i	$0.245848\pi$
$337$	−5.15806	+	14.1717i	−0.280977	+	0.771979i	−0.997247	+	0.0741552i	$0.976374\pi$
$338$	2.06266	+	5.66711i	0.112194	+	0.308250i
$339$	2.20758	−	1.85238i	0.119899	−	0.100607i
$340$		0			0
$341$	8.96493			0.485478
$342$	−1.97601	−	7.45672i	−0.106850	−	0.403213i
$343$		−	50.7518i		−	2.74034i
$344$	0.262274	+	1.48743i	0.0141409	+	0.0801968i
$345$		0			0
$346$	−14.7550	+	5.37038i	−0.793234	+	0.288714i
$347$	11.5530	−	31.7415i	0.620196	−	1.70398i	−0.0863093	−	0.996268i	$-0.527507\pi$
$347$	11.5530	−	31.7415i	0.620196	−	1.70398i	0.706506	−	0.707707i	$-0.250270\pi$
$348$	−1.89971	+	2.26399i	−0.101835	+	0.121363i
$349$	−0.0164139	+	0.0284297i	−0.000878615	+	0.00152181i	−0.866464	−	0.499239i	$-0.833613\pi$
$349$	−0.0164139	+	0.0284297i	−0.000878615	+	0.00152181i	0.865586	+	0.500761i	$0.166946\pi$
$350$		0			0
$351$	2.42524	−	13.7542i	0.129450	−	0.734146i
$352$	−4.34420	−	0.766000i	−0.231547	−	0.0408280i
$353$	0.243332	−	0.140488i	0.0129512	−	0.00747740i	−0.493510	−	0.869740i	$-0.664287\pi$
$353$	0.243332	−	0.140488i	0.0129512	−	0.00747740i	0.506462	+	0.862262i	$0.330953\pi$
$354$	7.79401	−	13.4996i	0.414247	−	0.717497i
$355$		0			0
$356$	−9.48219	−	3.45123i	−0.502555	−	0.182915i
$357$	9.39703	+	25.8181i	0.497344	+	1.36644i
$358$	6.50041	+	7.74689i	0.343557	+	0.409436i
$359$	−2.29364	−	13.0079i	−0.121054	−	0.686530i	−0.983574	−	0.180507i	$-0.942226\pi$
$359$	−2.29364	−	13.0079i	−0.121054	−	0.686530i	0.862520	−	0.506023i	$-0.168885\pi$
$360$		0			0
$361$	16.5066	−	9.40916i	0.868768	−	0.495219i
$362$		−	2.67870i		−	0.140789i
$363$	−9.23981	+	1.62923i	−0.484964	+	0.0855122i
$364$	−9.96816	+	8.36428i	−0.522474	+	0.438408i
$365$		0			0
$366$	15.1246	+	5.50492i	0.790577	+	0.287747i
$367$	−6.62354	+	7.89363i	−0.345746	+	0.412044i	−0.910693	−	0.413083i	$-0.864452\pi$
$367$	−6.62354	+	7.89363i	−0.345746	+	0.412044i	0.564948	+	0.825127i	$0.308896\pi$
$368$	−0.888952	−	0.513237i	−0.0463398	−	0.0267543i
$369$	−1.90600	−	3.30128i	−0.0992222	−	0.171858i
$370$		0			0
$371$	4.81354	−	27.2989i	0.249906	−	1.41729i
$372$	−1.95217	+	1.12709i	−0.101215	+	0.0584368i
$373$	24.5861	+	14.1948i	1.27302	+	0.734977i	0.975555	−	0.219756i	$-0.0705261\pi$
$373$	24.5861	+	14.1948i	1.27302	+	0.734977i	0.297463	+	0.954733i	$0.403859\pi$
$374$	16.9817	+	14.2494i	0.878105	+	0.736818i
$375$		0			0
$376$	1.68240	−	0.612343i	0.0867631	−	0.0315792i
$377$	4.52147	+	5.38848i	0.232867	+	0.277521i
$378$	−25.6812	+	4.52829i	−1.32090	+	0.232910i
$379$	−19.1984			−0.986157			−0.493079	−	0.869985i	$-0.664129\pi$
$379$	−19.1984			−0.986157			−0.493079	+	0.869985i	$0.664129\pi$
$380$		0			0
$381$	22.9860			1.17761
$382$	3.69402	−	0.651355i	0.189002	−	0.0333262i
$383$	−13.4201	−	15.9934i	−0.685734	−	0.817226i	0.305099	−	0.952321i	$-0.401311\pi$
$383$	−13.4201	−	15.9934i	−0.685734	−	0.817226i	−0.990833	+	0.135095i	$0.956866\pi$
$384$	1.04228	−	0.379360i	0.0531887	−	0.0193591i
$385$		0			0
$386$	11.0559	+	9.27700i	0.562731	+	0.472187i
$387$	2.31485	+	1.33648i	0.117671	+	0.0679371i
$388$	−10.3122	+	5.95376i	−0.523523	+	0.302256i
$389$	−2.69629	+	15.2914i	−0.136707	+	0.775304i	0.836949	+	0.547281i	$0.184337\pi$
$389$	−2.69629	+	15.2914i	−0.136707	+	0.775304i	−0.973656	+	0.228023i	$0.926774\pi$
$390$		0			0
$391$	2.57921	+	4.46733i	0.130436	+	0.225923i
$392$	14.9790	+	8.64815i	0.756556	+	0.436798i
$393$	1.23846	−	1.47594i	0.0624722	−	0.0744515i
$394$	18.6059	+	6.77199i	0.937351	+	0.341168i
$395$		0			0
$396$	−5.98027	+	5.01804i	−0.300520	+	0.252166i
$397$	−4.74331	+	0.836373i	−0.238060	+	0.0419764i	−0.291405	−	0.956600i	$-0.594123\pi$
$397$	−4.74331	+	0.836373i	−0.238060	+	0.0419764i	0.0533453	+	0.998576i	$0.483012\pi$
$398$			19.9801i			1.00151i
$399$	−10.0119	−	21.6261i	−0.501224	−	1.08266i
$400$		0			0
$401$	−2.15856	−	12.2418i	−0.107793	−	0.611326i	−0.990068	−	0.140591i	$-0.955100\pi$
$401$	−2.15856	−	12.2418i	−0.107793	−	0.611326i	0.882275	−	0.470735i	$-0.156011\pi$
$402$	−9.72636	−	11.5914i	−0.485107	−	0.578128i
$403$	1.83498	+	5.04156i	0.0914068	+	0.251138i
$404$	−1.35711	−	0.493947i	−0.0675186	−	0.0245748i
$405$		0			0
$406$	6.56691	−	11.3742i	0.325910	−	0.564493i
$407$	7.64456	−	4.41359i	0.378927	−	0.218774i
$408$	−5.48934	−	0.967919i	−0.271763	−	0.0479191i
$409$	2.99828	−	17.0041i	0.148255	−	0.840797i	−0.816440	−	0.577430i	$-0.804056\pi$
$409$	2.99828	−	17.0041i	0.148255	−	0.840797i	0.964696	−	0.263367i	$-0.0848332\pi$
$410$		0			0
$411$	1.38517	−	2.39918i	0.0683253	−	0.118343i
$412$	2.86770	−	3.41759i	0.141282	−	0.168373i
$413$	−23.6926	+	65.0950i	−1.16584	+	3.20312i
$414$	−1.70703	+	0.621309i	−0.0838961	+	0.0305357i
$415$		0			0
$416$	−0.458418	−	2.59982i	−0.0224758	−	0.127466i
$417$		−	13.1238i		−	0.642677i
$418$	−15.7203	−	11.0721i	−0.768903	−	0.541556i
$419$	−18.2962			−0.893827			−0.446914	−	0.894577i	$-0.647477\pi$
$419$	−18.2962			−0.893827			−0.446914	+	0.894577i	$0.647477\pi$
$420$		0			0
$421$	21.4711	−	18.0164i	1.04644	−	0.878067i	0.0537246	−	0.998556i	$-0.482891\pi$
$421$	21.4711	−	18.0164i	1.04644	−	0.878067i	0.992715	+	0.120489i	$0.0384462\pi$
$422$	4.66941	+	12.8291i	0.227303	+	0.624510i
$423$	1.08368	−	2.97740i	0.0526905	−	0.144766i
$424$	4.30802	+	3.61486i	0.209216	+	0.175553i
$425$		0			0
$426$	8.65052	+	14.9831i	0.419119	+	0.725935i
$427$	−70.4403	−	12.4205i	−3.40885	−	0.601072i
$428$	7.74349	+	1.36539i	0.374296	+	0.0659984i
$429$	−6.45831	−	11.1861i	−0.311810	−	0.540071i
$430$		0			0
$431$	11.8489	+	9.94239i	0.570740	+	0.478908i	0.881892	−	0.471452i	$-0.156270\pi$
$431$	11.8489	+	9.94239i	0.570740	+	0.478908i	−0.311151	+	0.950360i	$0.600715\pi$
$432$	1.80944	−	4.97141i	0.0870569	−	0.239187i
$433$	4.81630	+	13.2327i	0.231457	+	0.635922i	0.999992	−	0.00388467i	$-0.00123653\pi$
$433$	4.81630	+	13.2327i	0.231457	+	0.635922i	−0.768536	+	0.639807i	$0.779014\pi$
$434$	7.67383	−	6.43911i	0.368356	−	0.309087i
$435$		0			0
$436$	−2.52230			−0.120796
$437$	−2.55624	−	3.67219i	−0.122282	−	0.175665i
$438$			13.9892i			0.668430i
$439$	−1.61433	−	9.15534i	−0.0770479	−	0.436961i	−0.998791	−	0.0491593i	$-0.984346\pi$
$439$	−1.61433	−	9.15534i	−0.0770479	−	0.436961i	0.921743	−	0.387801i	$-0.126765\pi$
$440$		0			0
$441$	28.7639	−	10.4692i	1.36971	−	0.498533i
$442$	−4.53746	+	12.4666i	−0.215825	+	0.592974i
$443$	−7.64795	+	9.11448i	−0.363365	+	0.433042i	−0.916491	−	0.400056i	$-0.868991\pi$
$443$	−7.64795	+	9.11448i	−0.363365	+	0.433042i	0.553125	+	0.833098i	$0.313435\pi$
$444$	−1.10977	+	1.92218i	−0.0526673	+	0.0912225i
$445$		0			0
$446$	4.02533	−	22.8288i	0.190605	−	1.08097i
$447$	22.0019	+	3.87952i	1.04065	+	0.183495i
$448$	−4.26875	+	2.46456i	−0.201680	+	0.116440i
$449$	−9.95157	+	17.2366i	−0.469644	+	0.813446i	−0.999398	−	0.0347048i	$-0.988951\pi$
$449$	−9.95157	+	17.2366i	−0.469644	+	0.813446i	0.529754	+	0.848151i	$0.322284\pi$
$450$		0			0
$451$	−8.92871	−	3.24978i	−0.420436	−	0.153026i
$452$	−0.888617	−	2.44146i	−0.0417970	−	0.114836i
$453$	−5.47464	−	6.52442i	−0.257221	−	0.306544i
$454$	−1.28134	−	7.26682i	−0.0601361	−	0.341049i
$455$		0			0
$456$	4.81520	+	0.434651i	0.225492	+	0.0203544i
$457$		−	36.8095i		−	1.72188i	−0.508708	−	0.860939i	$-0.669877\pi$
$457$		−	36.8095i		−	1.72188i	0.508708	−	0.860939i	$-0.330123\pi$
$458$	13.0428	−	2.29980i	0.609449	−	0.107462i
$459$	−20.3665	+	17.0896i	−0.950628	+	0.797672i
$460$		0			0
$461$	−28.6287	−	10.4200i	−1.33337	−	0.485308i	−0.425653	−	0.904886i	$-0.639956\pi$
$461$	−28.6287	−	10.4200i	−1.33337	−	0.485308i	−0.907719	+	0.419578i	$0.862178\pi$
$462$	−15.5023	+	18.4749i	−0.721232	+	0.859530i
$463$	−19.3969	−	11.1988i	−0.901452	−	0.520454i	−0.0237813	−	0.999717i	$-0.507571\pi$
$463$	−19.3969	−	11.1988i	−0.901452	−	0.520454i	−0.877671	+	0.479263i	$0.840904\pi$
$464$	1.33227	+	2.30755i	0.0618489	+	0.107125i
$465$		0			0
$466$	−2.62905	+	14.9101i	−0.121789	+	0.690697i
$467$	−12.8027	+	7.39165i	−0.592439	+	0.342045i	−0.766061	−	0.642768i	$-0.777786\pi$
$467$	−12.8027	+	7.39165i	−0.592439	+	0.342045i	0.173623	+	0.984812i	$0.444453\pi$
$468$	−4.04604	−	2.33598i	−0.187028	−	0.107981i
$469$	51.5119	+	43.2236i	2.37860	+	1.99588i
$470$		0			0
$471$	−6.04597	+	2.20055i	−0.278583	+	0.101396i
$472$	−9.03357	−	10.7658i	−0.415804	−	0.495535i
$473$	6.56137	−	1.15695i	0.301692	−	0.0531965i
$474$	3.14407			0.144412
$475$		0			0
$476$	24.7708			1.13537
$477$	9.80130	−	1.72823i	0.448770	−	0.0791303i
$478$	7.51186	+	8.95228i	0.343584	+	0.409468i
$479$	−25.2882	+	9.20416i	−1.15545	+	0.420549i	−0.847469	−	0.530844i	$-0.821875\pi$
$479$	−25.2882	+	9.20416i	−1.15545	+	0.420549i	−0.307979	+	0.951393i	$0.599653\pi$
$480$		0			0
$481$	4.04677	+	3.39564i	0.184517	+	0.154828i
$482$	11.0485	+	6.37885i	0.503245	+	0.290549i
$483$	−4.86013	+	2.80600i	−0.221144	+	0.127677i
$484$	−1.46887	+	8.33035i	−0.0667667	+	0.378652i
$485$		0			0
$486$	−7.62577	−	13.2082i	−0.345912	−	0.599137i
$487$	12.2827	+	7.09140i	0.556581	+	0.321342i	0.751772	−	0.659423i	$-0.229199\pi$
$487$	12.2827	+	7.09140i	0.556581	+	0.321342i	−0.195191	+	0.980765i	$0.562533\pi$
$488$	9.32754	−	11.1161i	0.422238	−	0.503204i
$489$	11.1779	+	4.06843i	0.505483	+	0.183981i
$490$		0			0
$491$	7.44701	−	6.24878i	0.336079	−	0.282004i	−0.459092	−	0.888389i	$-0.651825\pi$
$491$	7.44701	−	6.24878i	0.336079	−	0.282004i	0.795171	+	0.606385i	$0.207381\pi$
$492$	2.35285	−	0.414871i	0.106075	−	0.0187039i
$493$		−	13.3903i		−	0.603069i
$494$	3.00889	−	11.1068i	0.135376	−	0.499719i
$495$		0			0
$496$	0.352906	+	2.00143i	0.0158459	+	0.0898667i
$497$	−49.4209	−	58.8975i	−2.21683	−	2.64191i
$498$	−2.76290	−	7.59100i	−0.123808	−	0.340161i
$499$	−11.5577	−	4.20666i	−0.517394	−	0.188316i	0.0701069	−	0.997539i	$-0.477666\pi$
$499$	−11.5577	−	4.20666i	−0.517394	−	0.188316i	−0.587501	+	0.809223i	$0.699888\pi$
$500$		0			0
$501$	5.48663	−	9.50312i	0.245124	−	0.424568i
$502$	−23.2583	+	13.4282i	−1.03807	+	0.599329i
$503$	24.5454	+	4.32801i	1.09442	+	0.192976i	0.691586	−	0.722295i	$-0.256913\pi$
$503$	24.5454	+	4.32801i	1.09442	+	0.192976i	0.402839	+	0.915271i	$0.368024\pi$
$504$	−1.51478	+	8.59073i	−0.0674735	+	0.382661i
$505$		0			0
$506$	−2.26400	+	3.92136i	−0.100647	+	0.174326i
$507$	−4.29974	+	5.12424i	−0.190958	+	0.227575i
$508$	7.08788	−	19.4738i	0.314474	−	0.864010i
$509$	−12.5923	+	4.58321i	−0.558142	+	0.203147i	−0.605660	−	0.795723i	$-0.707091\pi$
$509$	−12.5923	+	4.58321i	−0.558142	+	0.203147i	0.0475184	+	0.998870i	$0.484869\pi$
$510$		0			0
$511$	−10.7953	−	61.2231i	−0.477555	−	2.70835i
$512$		−	1.00000i		−	0.0441942i
$513$	16.3512	−	16.2613i	0.721922	−	0.717954i
$514$	−0.159696			−0.00704389
$515$		0			0
$516$	−1.28333	+	1.07684i	−0.0564954	+	0.0474053i
$517$	−2.70118	−	7.42143i	−0.118798	−	0.326394i
$518$	3.37353	−	9.26871i	0.148225	−	0.407244i
$519$	−13.3416	−	11.1949i	−0.585630	−	0.491402i
$520$		0			0
$521$	−0.583692	−	1.01098i	−0.0255720	−	0.0442920i	0.852956	−	0.521983i	$-0.174807\pi$
$521$	−0.583692	−	1.01098i	−0.0255720	−	0.0442920i	−0.878528	+	0.477690i	$0.841474\pi$
$522$	4.64388	+	0.818841i	0.203257	+	0.0358397i
$523$	9.28028	+	1.63636i	0.405798	+	0.0715532i	0.372822	−	0.927903i	$-0.378390\pi$
$523$	9.28028	+	1.63636i	0.405798	+	0.0715532i	0.0329765	+	0.999456i	$0.489501\pi$
$524$	−0.868533	−	1.50434i	−0.0379420	−	0.0657175i
$525$		0			0
$526$	−7.09280	−	5.95157i	−0.309261	−	0.259501i
$527$	3.49309	−	9.59718i	0.152161	−	0.418060i
$528$	−1.67344	−	4.59773i	−0.0728271	−	0.200091i
$529$	16.8119	−	14.1068i	0.730951	−	0.613341i
$530$		0			0
$531$	−24.8714			−1.07933
$532$	−21.4089	+	1.81359i	−0.928193	+	0.0786293i
$533$		−	5.68637i		−	0.246304i
$534$	−1.94353	−	11.0223i	−0.0841050	−	0.476983i
$535$		0			0
$536$	−12.8194	+	4.66590i	−0.553716	+	0.201536i
$537$	−3.83640	+	10.5404i	−0.165553	+	0.454853i
$538$	−8.02092	+	9.55896i	−0.345807	+	0.412116i
$539$	38.1489	−	66.0759i	1.64319	−	2.84609i
$540$		0			0
$541$	−7.26524	+	41.2032i	−0.312357	+	1.77147i	0.274314	+	0.961640i	$0.411549\pi$
$541$	−7.26524	+	41.2032i	−0.312357	+	1.77147i	−0.586671	+	0.809825i	$0.699562\pi$
$542$	27.7806	+	4.89846i	1.19328	+	0.210407i
$543$	2.57308	−	1.48557i	0.110422	−	0.0637520i
$544$	−2.51269	+	4.35211i	−0.107731	+	0.186595i
$545$		0			0
$546$	−13.5627	−	4.93642i	−0.580430	−	0.211259i
$547$	−9.61418	−	26.4147i	−0.411073	−	1.12941i	−0.956622	−	0.291334i	$-0.905901\pi$
$547$	−9.61418	−	26.4147i	−0.411073	−	1.12941i	0.545549	−	0.838079i	$-0.316321\pi$
$548$	−1.60546	−	1.91332i	−0.0685820	−	0.0817328i
$549$	−4.45942	−	25.2906i	−0.190323	−	1.07938i
$550$		0			0
$551$	0.980372	+	11.5730i	0.0417653	+	0.493025i
$552$		−	1.13854i		−	0.0484594i
$553$	−13.7599	+	2.42623i	−0.585129	+	0.103174i
$554$	6.44384	−	5.40702i	0.273772	−	0.229722i
$555$		0			0
$556$	−11.1185	−	4.04681i	−0.471530	−	0.171623i
$557$	−7.93117	+	9.45200i	−0.336055	+	0.400494i	−0.907436	−	0.420190i	$-0.861963\pi$
$557$	−7.93117	+	9.45200i	−0.336055	+	0.400494i	0.571381	+	0.820685i	$0.306408\pi$
$558$	3.11478	+	1.79832i	0.131859	+	0.0761289i
$559$	1.99364	+	3.45308i	0.0843218	+	0.146050i
$560$		0			0
$561$	−4.26971	+	24.2147i	−0.180267	+	1.02235i
$562$	−19.3507	+	11.1721i	−0.816259	+	0.471268i
$563$	−12.5114	−	7.22347i	−0.527293	−	0.304433i	0.212620	−	0.977135i	$-0.431800\pi$
$563$	−12.5114	−	7.22347i	−0.527293	−	0.304433i	−0.739914	+	0.672702i	$0.765134\pi$
$564$	1.52123	+	1.27647i	0.0640555	+	0.0537490i
$565$		0			0
$566$	11.9965	−	4.36638i	0.504252	−	0.183533i
$567$	−1.77060	−	2.11012i	−0.0743581	−	0.0886166i
$568$	15.3612	−	2.70859i	0.644540	−	0.113650i
$569$	−31.8303			−1.33439			−0.667197	−	0.744881i	$-0.732506\pi$
$569$	−31.8303			−1.33439			−0.667197	+	0.744881i	$0.732506\pi$
$570$		0			0
$571$	−9.10909			−0.381204			−0.190602	−	0.981667i	$-0.561044\pi$
$571$	−9.10909			−0.381204			−0.190602	+	0.981667i	$0.561044\pi$
$572$	−11.4684	+	2.02218i	−0.479516	+	0.0845516i
$573$	2.67432	+	3.18714i	0.111722	+	0.133145i
$574$	−9.97700	+	3.63133i	−0.416432	+	0.151569i
$575$		0			0
$576$	−1.35570	−	1.13756i	−0.0564873	−	0.0473985i
$577$	−10.1300	−	5.84857i	−0.421718	−	0.243479i	0.274094	−	0.961703i	$-0.411622\pi$
$577$	−10.1300	−	5.84857i	−0.421718	−	0.243479i	−0.695812	+	0.718224i	$0.744955\pi$
$578$	7.14863	−	4.12726i	0.297344	−	0.171671i
$579$	−2.77978	+	15.7649i	−0.115524	+	0.655167i
$580$		0			0
$581$	17.9496	+	31.0896i	0.744674	+	1.28981i
$582$	−11.4380	−	6.60375i	−0.474122	−	0.273734i
$583$	15.9459	−	19.0036i	0.660413	−	0.787050i
$584$	11.8517	+	4.31365i	0.490425	+	0.178500i
$585$		0			0
$586$	22.1470	−	18.5836i	0.914885	−	0.767680i
$587$	30.2839	−	5.33986i	1.24995	−	0.220400i	0.490774	−	0.871287i	$-0.336714\pi$
$587$	30.2839	−	5.33986i	1.24995	−	0.220400i	0.759175	+	0.650887i	$0.225603\pi$
$588$			19.1846i			0.791160i
$589$	−2.31635	+	8.55040i	−0.0954435	+	0.352313i
$590$		0			0
$591$	3.81359	+	21.6280i	0.156870	+	0.889655i
$592$	1.28627	+	1.53291i	0.0528652	+	0.0630023i
$593$	2.12039	+	5.82573i	0.0870741	+	0.239234i	0.975585	−	0.219621i	$-0.0704820\pi$
$593$	2.12039	+	5.82573i	0.0870741	+	0.239234i	−0.888511	+	0.458855i	$0.848260\pi$
$594$	−21.9300	−	7.98186i	−0.899798	−	0.327500i
$595$		0			0
$596$	10.0711	−	17.4437i	0.412530	−	0.714523i
$597$	−19.1924	+	11.0807i	−0.785491	+	0.453503i
$598$	−2.66864	−	0.470554i	−0.109129	−	0.0192424i
$599$	5.09116	−	28.8734i	0.208019	−	1.17973i	−0.684599	−	0.728920i	$-0.740022\pi$
$599$	5.09116	−	28.8734i	0.208019	−	1.17973i	0.892618	−	0.450815i	$-0.148866\pi$
$600$		0			0
$601$	23.1718	−	40.1348i	0.945199	−	1.63713i	0.189846	−	0.981814i	$-0.439201\pi$
$601$	23.1718	−	40.1348i	0.945199	−	1.63713i	0.755353	−	0.655318i	$-0.227466\pi$
$602$	4.78544	−	5.70307i	0.195040	−	0.232440i
$603$	−8.25740	+	22.6870i	−0.336267	+	0.923887i
$604$	−7.21563	+	2.62627i	−0.293600	+	0.106862i
$605$		0			0
$606$	−0.278162	−	1.57754i	−0.0112996	−	0.0640830i
$607$			25.4409i			1.03262i	0.856403	+	0.516308i	$0.172694\pi$
$607$			25.4409i			1.03262i	−0.856403	+	0.516308i	$0.827306\pi$
$608$	1.85303	−	3.94541i	0.0751503	−	0.160008i
$609$	14.5677			0.590312
$610$		0			0
$611$	3.62066	−	3.03810i	0.146476	−	0.122908i
$612$	3.04179	+	8.35725i	0.122957	+	0.337822i
$613$	10.4412	−	28.6870i	0.421717	−	1.15866i	−0.529006	−	0.848618i	$-0.677435\pi$
$613$	10.4412	−	28.6870i	0.421717	−	1.15866i	0.950723	−	0.310041i	$-0.100343\pi$
$614$	17.9758	+	15.0835i	0.725444	+	0.608720i
$615$		0			0
$616$	10.8717	+	18.8304i	0.438035	+	0.758698i
$617$	6.00494	+	1.05883i	0.241750	+	0.0426270i	0.293210	−	0.956048i	$-0.405276\pi$
$617$	6.00494	+	1.05883i	0.241750	+	0.0426270i	−0.0514603	+	0.998675i	$0.516388\pi$
$618$	4.87323	+	0.859283i	0.196030	+	0.0345654i
$619$	9.07568	+	15.7195i	0.364782	+	0.631821i	0.988741	−	0.149636i	$-0.0478101\pi$
$619$	9.07568	+	15.7195i	0.364782	+	0.631821i	−0.623959	+	0.781457i	$0.714477\pi$
$620$		0			0
$621$	−4.16002	−	3.49067i	−0.166936	−	0.140076i
$622$	−1.45193	+	3.98914i	−0.0582171	+	0.159950i
$623$	17.0116	+	46.7389i	0.681554	+	1.87255i
$624$	2.24308	−	1.88217i	0.0897950	−	0.0753469i
$625$		0			0
$626$	11.6148			0.464221
$627$	1.91734	−	21.2409i	0.0765712	−	0.848279i
$628$			5.80070i			0.231473i
$629$	−1.74624	−	9.90340i	−0.0696270	−	0.394874i
$630$		0			0
$631$	−14.9306	+	5.43428i	−0.594376	+	0.216335i	−0.621653	−	0.783293i	$-0.713539\pi$
$631$	−14.9306	+	5.43428i	−0.594376	+	0.216335i	0.0272768	+	0.999628i	$0.491316\pi$
$632$	0.969492	−	2.66366i	0.0385643	−	0.105955i
$633$	−9.73368	+	11.6001i	−0.386879	+	0.461064i
$634$	1.11812	−	1.93664i	0.0444061	−	0.0769137i
$635$		0			0
$636$	−1.08316	+	6.14292i	−0.0429502	+	0.243582i
$637$	44.9672	+	7.92893i	1.78167	+	0.314156i
$638$	10.1791	−	5.87692i	0.402995	−	0.232669i
$639$	13.8023	−	23.9063i	0.546010	−	0.945717i
$640$		0			0
$641$	33.1458	+	12.0641i	1.30918	+	0.476503i	0.899976	−	0.435940i	$-0.143584\pi$
$641$	33.1458	+	12.0641i	1.30918	+	0.476503i	0.409205	+	0.912443i	$0.365806\pi$
$642$	2.98288	+	8.19540i	0.117725	+	0.323447i
$643$	5.36891	+	6.39841i	0.211729	+	0.252329i	0.861448	−	0.507846i	$-0.169558\pi$
$643$	5.36891	+	6.39841i	0.211729	+	0.252329i	−0.649719	+	0.760174i	$0.725113\pi$
$644$	0.878594	+	4.98275i	0.0346215	+	0.196348i
$645$		0			0
$646$	−17.9782	+	12.5148i	−0.707343	+	0.492387i
$647$		−	12.0057i		−	0.471991i	−0.971754	−	0.235995i	$-0.924165\pi$
$647$		−	12.0057i		−	0.471991i	0.971754	−	0.235995i	$-0.0758350\pi$
$648$	0.550344	−	0.0970404i	0.0216195	−	0.00381211i
$649$	−47.4903	+	39.8491i	−1.86416	+	1.56421i
$650$		0			0
$651$	10.4410	+	3.80023i	0.409216	+	0.148943i
$652$	6.89356	−	8.21542i	0.269973	−	0.321741i
$653$	−33.8062	−	19.5180i	−1.32294	−	0.763798i	−0.338741	−	0.940880i	$-0.610001\pi$
$653$	−33.8062	−	19.5180i	−1.32294	−	0.763798i	−0.984196	+	0.177081i	$0.943334\pi$
$654$	−1.39884	−	2.42285i	−0.0546988	−	0.0947411i
$655$		0			0
$656$	0.374037	−	2.12127i	0.0146037	−	0.0828216i
$657$	19.3300	−	11.1602i	0.754136	−	0.435401i
$658$	−7.64265	−	4.41248i	−0.297941	−	0.172017i
$659$	3.38617	+	2.84133i	0.131906	+	0.110683i	0.706354	−	0.707859i	$-0.250339\pi$
$659$	3.38617	+	2.84133i	0.131906	+	0.110683i	−0.574448	+	0.818541i	$0.694783\pi$
$660$		0			0
$661$	5.32012	−	1.93636i	0.206929	−	0.0753159i	−0.236476	−	0.971637i	$-0.575993\pi$
$661$	5.32012	−	1.93636i	0.206929	−	0.0753159i	0.443405	+	0.896321i	$0.353770\pi$
$662$	0.327351	+	0.390122i	0.0127229	+	0.0151625i
$663$	−14.4914	+	2.55523i	−0.562801	+	0.0992370i
$664$	−7.28306			−0.282638
$665$		0			0
$666$	3.54137			0.137225
$667$	2.69352	−	0.474940i	0.104294	−	0.0183898i
$668$	−6.35922	−	7.57862i	−0.246046	−	0.293226i
$669$	24.1611	−	8.79392i	0.934122	−	0.339992i
$670$		0			0
$671$	−49.0357	−	41.1458i	−1.89300	−	1.58842i
$672$	−4.73478	−	2.73363i	−0.182648	−	0.105452i
$673$	−14.1761	+	8.18457i	−0.546448	+	0.315492i	−0.747688	−	0.664050i	$-0.768836\pi$
$673$	−14.1761	+	8.18457i	−0.546448	+	0.315492i	0.201240	+	0.979542i	$0.435503\pi$
$674$	−2.61882	+	14.8520i	−0.100873	+	0.572079i
$675$		0			0
$676$	3.01541	+	5.22284i	0.115977	+	0.200878i
$677$	16.2304	+	9.37064i	0.623786	+	0.360143i	0.778341	−	0.627841i	$-0.216061\pi$
$677$	16.2304	+	9.37064i	0.623786	+	0.360143i	−0.154556	+	0.987984i	$0.549395\pi$
$678$	1.85238	−	2.20758i	0.0711402	−	0.0847816i
$679$	55.1540	+	20.0744i	2.11662	+	0.770386i
$680$		0			0
$681$	6.26969	−	5.26089i	0.240255	−	0.201598i
$682$	8.82873	−	1.55674i	0.338070	−	0.0596108i
$683$		−	11.1202i		−	0.425501i	−0.977107	−	0.212751i	$-0.931758\pi$
$683$		−	11.1202i		−	0.425501i	0.977107	−	0.212751i	$-0.0682422\pi$
$684$	−3.24084	−	7.00030i	−0.123917	−	0.267663i
$685$		0			0
$686$	−8.81296	−	49.9808i	−0.336480	−	1.90828i
$687$	9.44247	+	11.2531i	0.360253	+	0.429333i
$688$	0.516578	+	1.41929i	0.0196944	+	0.0541098i
$689$	13.9509	+	5.07769i	0.531485	+	0.193445i
$690$		0			0
$691$	−5.97792	+	10.3541i	−0.227411	+	0.393887i	−0.957040	−	0.289956i	$-0.906359\pi$
$691$	−5.97792	+	10.3541i	−0.227411	+	0.393887i	0.729629	+	0.683843i	$0.239693\pi$
$692$	−13.5983	+	7.85098i	−0.516929	+	0.298449i
$693$	37.8956	+	6.68201i	1.43953	+	0.253829i
$694$	5.86560	−	33.2655i	0.222655	−	1.26274i
$695$		0			0
$696$	−1.47771	+	2.55947i	−0.0560126	+	0.0970166i
$697$	−6.95795	+	8.29216i	−0.263551	+	0.314088i
$698$	−0.0112278	+	0.0308480i	−0.000424977	+	0.00116761i
$699$	−15.7803	+	5.74355i	−0.596865	+	0.217241i
$700$		0			0
$701$	3.45791	+	19.6108i	0.130603	+	0.740689i	0.977821	+	0.209443i	$0.0671650\pi$
$701$	3.45791	+	19.6108i	0.130603	+	0.740689i	−0.847217	+	0.531246i	$0.821724\pi$
$702$		−	13.9664i		−	0.527128i
$703$	2.23432	+	8.43146i	0.0842688	+	0.317999i
$704$	−4.41122			−0.166254
$705$		0			0
$706$	0.215239	−	0.180607i	0.00810064	−	0.00679725i
$707$	2.43473	+	6.68935i	0.0915673	+	0.251579i
$708$	5.33142	−	14.6480i	0.200367	−	0.550504i
$709$	9.27123	+	7.77949i	0.348188	+	0.292165i	0.800062	−	0.599917i	$-0.204800\pi$
$709$	9.27123	+	7.77949i	0.348188	+	0.292165i	−0.451874	+	0.892082i	$0.649244\pi$
$710$		0			0
$711$	−2.50825	−	4.34442i	−0.0940667	−	0.162928i
$712$	−9.93743	−	1.75224i	−0.372421	−	0.0656679i
$713$	2.05441	+	0.362248i	0.0769383	+	0.0135663i
$714$	13.7375	+	23.7941i	0.514115	+	0.890473i
$715$		0			0
$716$	7.74689	+	6.50041i	0.289515	+	0.242932i
$717$	−4.43334	+	12.1805i	−0.165566	+	0.454889i
$718$	−4.51759	−	12.4120i	−0.168595	−	0.463211i
$719$	−22.9902	+	19.2911i	−0.857389	+	0.719435i	−0.961404	−	0.275141i	$-0.911275\pi$
$719$	−22.9902	+	19.2911i	−0.857389	+	0.719435i	0.104015	+	0.994576i	$0.466831\pi$
$720$		0			0
$721$	−21.9906			−0.818972
$722$	14.6219	−	12.1326i	0.544172	−	0.451527i
$723$			14.1505i			0.526263i
$724$	−0.465151	−	2.63800i	−0.0172872	−	0.0980407i
$725$		0			0
$726$	−8.81652	+	3.20895i	−0.327212	+	0.119095i
$727$	−14.4115	+	39.5954i	−0.534494	+	1.46851i	0.319175	+	0.947696i	$0.396594\pi$
$727$	−14.4115	+	39.5954i	−0.534494	+	1.46851i	−0.853669	+	0.520815i	$0.825628\pi$
$728$	−8.36428	+	9.96816i	−0.310001	+	0.369445i
$729$	9.29655	−	16.1021i	0.344317	−	0.596374i
$730$		0			0
$731$	1.31803	−	7.47490i	0.0487490	−	0.276469i
$732$	15.8508	+	2.79492i	0.585862	+	0.103303i
$733$	7.24116	−	4.18069i	0.267458	−	0.154417i	−0.360274	−	0.932847i	$-0.617317\pi$
$733$	7.24116	−	4.18069i	0.267458	−	0.154417i	0.627732	+	0.778429i	$0.283983\pi$
$734$	−5.15220	+	8.92387i	−0.190171	+	0.329386i
$735$		0			0
$736$	−0.964570	−	0.351075i	−0.0355545	−	0.0129408i
$737$	20.5823	+	56.5494i	0.758159	+	2.08302i
$738$	−2.45030	−	2.92016i	−0.0901969	−	0.107492i
$739$	3.03167	+	17.1935i	0.111522	+	0.632472i	0.988414	+	0.151784i	$0.0485019\pi$
$739$	3.03167	+	17.1935i	0.111522	+	0.632472i	−0.876892	+	0.480688i	$0.840387\pi$
$740$		0			0
$741$	12.3376	−	3.26943i	0.453232	−	0.120105i
$742$		−	27.7200i		−	1.01763i
$743$	−15.4396	+	2.72242i	−0.566424	+	0.0998758i	−0.449524	−	0.893268i	$-0.648407\pi$
$743$	−15.4396	+	2.72242i	−0.566424	+	0.0998758i	−0.116899	+	0.993144i	$0.537295\pi$
$744$	−1.72680	+	1.44896i	−0.0633075	+	0.0531213i
$745$		0			0
$746$	26.6774	+	9.70980i	0.976731	+	0.355501i
$747$	−8.28494	+	9.87361i	−0.303130	+	0.361257i
$748$	19.1981	+	11.0840i	0.701953	+	0.405273i
$749$	−19.3787	−	33.5649i	−0.708083	−	1.22644i
$750$		0			0
$751$	−0.425213	+	2.41150i	−0.0155162	+	0.0879970i	−0.991583	−	0.129476i	$-0.958670\pi$
$751$	−0.425213	+	2.41150i	−0.0155162	+	0.0879970i	0.976066	+	0.217473i	$0.0697815\pi$
$752$	1.55051	−	0.895185i	0.0565412	−	0.0326441i
$753$	−25.7975	−	14.8942i	−0.940111	−	0.542774i
$754$	5.38848	+	4.52147i	0.196237	+	0.164662i
$755$		0			0
$756$	−24.5047	+	8.91898i	−0.891228	+	0.324380i
$757$	17.7921	+	21.2038i	0.646664	+	0.770664i	0.985407	−	0.170215i	$-0.0544461\pi$
$757$	17.7921	+	21.2038i	0.646664	+	0.770664i	−0.338743	+	0.940879i	$0.610002\pi$
$758$	−18.9068	+	3.33377i	−0.686725	+	0.121088i
$759$	−5.02234			−0.182299
$760$		0			0
$761$	−34.7738			−1.26055			−0.630275	−	0.776372i	$-0.717058\pi$
$761$	−34.7738			−1.26055			−0.630275	+	0.776372i	$0.717058\pi$
$762$	22.6368	−	3.99148i	0.820046	−	0.144596i
$763$	7.99162	+	9.52404i	0.289316	+	0.344793i
$764$	3.52479	−	1.28292i	0.127522	−	0.0464143i
$765$		0			0
$766$	−15.9934	−	13.4201i	−0.577866	−	0.484887i
$767$	−32.1302	−	18.5504i	−1.16015	−	0.669815i
$768$	0.960572	−	0.554587i	0.0346617	−	0.0200119i
$769$	1.17313	−	6.65313i	0.0423040	−	0.239918i	−0.956322	−	0.292314i	$-0.905575\pi$
$769$	1.17313	−	6.65313i	0.0423040	−	0.239918i	0.998626	+	0.0523962i	$0.0166859\pi$
$770$		0			0
$771$	−0.0885653	−	0.153400i	−0.00318960	−	0.00552455i
$772$	12.4989	+	7.21623i	0.449844	+	0.259718i
$773$	7.77917	−	9.27086i	0.279797	−	0.333450i	−0.607782	−	0.794104i	$-0.707941\pi$
$773$	7.77917	−	9.27086i	0.279797	−	0.333450i	0.887580	+	0.460654i	$0.152385\pi$
$774$	2.51176	+	0.914207i	0.0902834	+	0.0328605i
$775$		0			0
$776$	−9.12169	+	7.65401i	−0.327450	+	0.274763i
$777$	10.7742	−	1.89978i	0.386522	−	0.0681542i
$778$			15.5273i			0.556680i
$779$	5.40650	−	7.67617i	0.193708	−	0.275027i
$780$		0			0
$781$	−11.9482	−	67.7615i	−0.427540	−	2.42470i
$782$	3.31577	+	3.95159i	0.118572	+	0.141308i
$783$	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(0.712963 + 0.849676i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(-4.26875 - 2.46456i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.307311 - 1.74285i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(0.712963 + 0.849676i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(-4.26875 - 2.46456i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.307311 - 1.74285i) q^{9} +(-2.20561 - 3.82023i) q^{11} +(0.960572 + 0.554587i) q^{12} +(1.69691 - 2.02230i) q^{13} +(-4.63187 - 1.68586i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-4.94904 + 0.872649i) q^{17} -1.76973i q^{18} +(4.21347 - 1.11656i) q^{19} +(-0.949379 - 5.38420i) q^{21} +(-2.83548 - 3.37919i) q^{22} +(-0.351075 - 0.964570i) q^{23} +(1.04228 + 0.379360i) q^{24} +(1.31996 - 2.28624i) q^{26} +(4.58167 - 2.64523i) q^{27} +(-4.85424 - 0.855934i) q^{28} +(-0.462691 + 2.62405i) q^{29} +(-1.01615 + 1.76003i) q^{31} +(0.642788 - 0.766044i) q^{32} +(1.67344 - 4.59773i) q^{33} +(-4.72232 + 1.71878i) q^{34} +(-0.307311 - 1.74285i) q^{36} +2.00107i q^{37} +(3.95557 - 1.83126i) q^{38} +2.92813 q^{39} +(1.65005 - 1.38456i) q^{41} +(-1.86991 - 5.13754i) q^{42} +(-0.516578 + 1.41929i) q^{43} +(-3.37919 - 2.83548i) q^{44} +(-0.513237 - 0.888952i) q^{46} +(1.76317 + 0.310895i) q^{47} +(1.09232 + 0.192606i) q^{48} +(8.64815 + 14.9790i) q^{49} +(-4.26995 - 3.58291i) q^{51} +(0.902907 - 2.48072i) q^{52} +(1.92343 + 5.28457i) q^{53} +(4.05273 - 3.40064i) q^{54} -4.92913 q^{56} +(3.95276 + 2.78402i) q^{57} +2.66453i q^{58} +(-2.44041 - 13.8402i) q^{59} +(13.6360 - 4.96308i) q^{61} +(-0.695088 + 1.90974i) q^{62} +(-5.60720 + 6.68240i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.849627 - 4.81847i) q^{66} +(-13.4349 - 2.36894i) q^{67} +(-4.35211 + 2.51269i) q^{68} +(0.569269 - 0.986002i) q^{69} +(14.6575 + 5.33488i) q^{71} +(-0.605285 - 1.66301i) q^{72} +(8.10702 + 9.66157i) q^{73} +(0.347483 + 1.97067i) q^{74} +(3.57748 - 2.49031i) q^{76} +21.7435i q^{77} +(2.88365 - 0.508465i) q^{78} +(2.17143 - 1.82205i) q^{79} +(0.525132 + 0.191132i) q^{81} +(1.38456 - 1.65005i) q^{82} +(-6.30732 - 3.64153i) q^{83} +(-2.73363 - 4.73478i) q^{84} +(-0.262274 + 1.48743i) q^{86} +(-2.55947 + 1.47771i) q^{87} +(-3.82023 - 2.20561i) q^{88} +(-7.72995 - 6.48620i) q^{89} +(-12.2278 + 4.45054i) q^{91} +(-0.659805 - 0.786325i) q^{92} +(-2.21993 + 0.391433i) q^{93} +1.79037 q^{94} +1.10917 q^{96} +(-11.7266 + 2.06772i) q^{97} +(11.1179 + 13.2497i) q^{98} +(-7.33589 + 2.67005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36q + 36q^{9} + O(q^{10}) \)	\( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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