LMFDB - Embedded newform 770.2.o.b.549.3

Newspace parameters

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.3
Character	$\chi$	$=$	770.549
Dual form			770.2.o.b.439.3

$q$-expansion

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.44024 + 2.49457i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16254 + 0.568686i) q^{5} -2.88048 q^{6} +(0.391243 - 2.61666i) q^{7} -1.00000 q^{8} +(-2.64857 - 4.58746i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.44024 + 2.49457i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16254 + 0.568686i) q^{5} -2.88048 q^{6} +(0.391243 - 2.61666i) q^{7} -1.00000 q^{8} +(-2.64857 - 4.58746i) q^{9} +(-1.57377 - 1.58848i) q^{10} +(0.914142 + 3.18816i) q^{11} +(-1.44024 - 2.49457i) q^{12} -6.76312i q^{13} +(2.46172 - 0.969505i) q^{14} +(1.69596 - 6.21365i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.33823 - 0.772629i) q^{17} +(2.64857 - 4.58746i) q^{18} +(-0.445529 - 0.771679i) q^{19} +(0.588776 - 2.15716i) q^{20} +(5.96396 + 4.74460i) q^{21} +(-2.30395 + 2.38575i) q^{22} +(-6.17407 + 3.56460i) q^{23} +(1.44024 - 2.49457i) q^{24} +(4.35319 - 2.45962i) q^{25} +(5.85703 - 3.38156i) q^{26} +6.61688 q^{27} +(2.07048 + 1.64716i) q^{28} +2.79982i q^{29} +(6.22916 - 1.63809i) q^{30} +(0.849237 + 0.490307i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-9.26965 - 2.31132i) q^{33} -1.54526i q^{34} +(0.641979 + 5.88114i) q^{35} +5.29715 q^{36} +(8.14224 - 4.70093i) q^{37} +(0.445529 - 0.771679i) q^{38} +(16.8710 + 9.74050i) q^{39} +(2.16254 - 0.568686i) q^{40} -8.03479 q^{41} +(-1.12697 + 7.53724i) q^{42} -0.302038 q^{43} +(-3.21810 - 0.802409i) q^{44} +(8.33648 + 8.41439i) q^{45} +(-6.17407 - 3.56460i) q^{46} +(-5.24754 - 9.08901i) q^{47} +2.88048 q^{48} +(-6.69386 - 2.04750i) q^{49} +(4.30669 + 2.54017i) q^{50} +(3.85475 - 2.22554i) q^{51} +(5.85703 + 3.38156i) q^{52} +(-4.89115 - 2.82391i) q^{53} +(3.30844 + 5.73039i) q^{54} +(-3.78993 - 6.37467i) q^{55} +(-0.391243 + 2.61666i) q^{56} +2.56667 q^{57} +(-2.42472 + 1.39991i) q^{58} +(3.61218 + 2.08549i) q^{59} +(4.53320 + 4.57557i) q^{60} +(-0.226973 - 0.393129i) q^{61} +0.980614i q^{62} +(-13.0401 + 5.13561i) q^{63} +1.00000 q^{64} +(3.84609 + 14.6255i) q^{65} +(-2.63316 - 9.18341i) q^{66} +(8.39321 + 4.84582i) q^{67} +(1.33823 - 0.772629i) q^{68} -20.5355i q^{69} +(-4.77223 + 3.49654i) q^{70} -4.72658 q^{71} +(2.64857 + 4.58746i) q^{72} +(-2.80161 - 1.61751i) q^{73} +(8.14224 + 4.70093i) q^{74} +(-0.133963 + 14.4018i) q^{75} +0.891058 q^{76} +(8.69999 - 1.14466i) q^{77} +19.4810i q^{78} +(7.09357 - 4.09547i) q^{79} +(1.57377 + 1.58848i) q^{80} +(-1.58417 + 2.74386i) q^{81} +(-4.01739 - 6.95833i) q^{82} -4.01538i q^{83} +(-7.09092 + 2.79264i) q^{84} +(3.33337 + 0.909810i) q^{85} +(-0.151019 - 0.261573i) q^{86} +(-6.98434 - 4.03241i) q^{87} +(-0.914142 - 3.18816i) q^{88} +(6.83580 - 3.94665i) q^{89} +(-3.11883 + 11.4268i) q^{90} +(-17.6968 - 2.64602i) q^{91} -7.12921i q^{92} +(-2.44621 + 1.41232i) q^{93} +(5.24754 - 9.08901i) q^{94} +(1.40232 + 1.41542i) q^{95} +(1.44024 + 2.49457i) q^{96} -19.1494 q^{97} +(-1.57374 - 6.82080i) q^{98} +(12.2044 - 12.6377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.44024	+	2.49457i	−0.831522	+	1.44024i	0.0653088	+	0.997865i	$0.479197\pi$
$3$	−1.44024	+	2.49457i	−0.831522	+	1.44024i	−0.896831	+	0.442373i	$0.854137\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.16254	+	0.568686i	−0.967119	+	0.254324i
$5$	−2.16254	+	0.568686i	−0.967119	+	0.254324i
$6$	−2.88048			−1.17595
$7$	0.391243	−	2.61666i	0.147876	−	0.989006i
$7$	0.391243	−	2.61666i	0.147876	−	0.989006i
$8$	−1.00000			−0.353553
$9$	−2.64857	−	4.58746i	−0.882858	−	1.52915i
$10$	−1.57377	−	1.58848i	−0.497669	−	0.502320i
$11$	0.914142	+	3.18816i	0.275624	+	0.961266i
$11$	0.914142	+	3.18816i	0.275624	+	0.961266i
$12$	−1.44024	−	2.49457i	−0.415761	−	0.720119i
$13$		−	6.76312i		−	1.87575i	−0.346972	−	0.937875i	$-0.612790\pi$
$13$		−	6.76312i		−	1.87575i	0.346972	−	0.937875i	$-0.387210\pi$
$14$	2.46172	−	0.969505i	0.657922	−	0.259111i
$15$	1.69596	−	6.21365i	0.437894	−	1.60436i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.33823	−	0.772629i	−0.324569	−	0.187390i	0.328858	−	0.944379i	$-0.393336\pi$
$17$	−1.33823	−	0.772629i	−0.324569	−	0.187390i	−0.653427	+	0.756989i	$0.726669\pi$
$18$	2.64857	−	4.58746i	0.624275	−	1.08128i
$19$	−0.445529	−	0.771679i	−0.102211	−	0.177035i	0.810384	−	0.585899i	$-0.199258\pi$
$19$	−0.445529	−	0.771679i	−0.102211	−	0.177035i	−0.912595	+	0.408864i	$0.865925\pi$
$20$	0.588776	−	2.15716i	0.131654	−	0.482356i
$21$	5.96396	+	4.74460i	1.30144	+	1.03536i
$22$	−2.30395	+	2.38575i	−0.491205	+	0.508643i
$23$	−6.17407	+	3.56460i	−1.28738	+	0.743271i	−0.978187	−	0.207727i	$-0.933393\pi$
$23$	−6.17407	+	3.56460i	−1.28738	+	0.743271i	−0.309197	+	0.950998i	$0.600060\pi$
$24$	1.44024	−	2.49457i	0.293987	−	0.509201i
$25$	4.35319	−	2.45962i	0.870639	−	0.491923i
$26$	5.85703	−	3.38156i	1.14866	−	0.663178i
$27$	6.61688			1.27342
$28$	2.07048	+	1.64716i	0.391283	+	0.311284i
$29$			2.79982i			0.519914i	0.965620	+	0.259957i	$0.0837084\pi$
$29$			2.79982i			0.519914i	−0.965620	+	0.259957i	$0.916292\pi$
$30$	6.22916	−	1.63809i	1.13728	−	0.299072i
$31$	0.849237	+	0.490307i	0.152527	+	0.0880618i	0.574321	−	0.818630i	$-0.305266\pi$
$31$	0.849237	+	0.490307i	0.152527	+	0.0880618i	−0.421794	+	0.906692i	$0.638599\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−9.26965	−	2.31132i	−1.61364	−	0.402349i
$34$		−	1.54526i		−	0.265009i
$35$	0.641979	+	5.88114i	0.108514	+	0.994095i
$36$	5.29715			0.882858
$37$	8.14224	−	4.70093i	1.33858	−	0.772828i	0.351980	−	0.936007i	$-0.385508\pi$
$37$	8.14224	−	4.70093i	1.33858	−	0.772828i	0.986596	+	0.163180i	$0.0521751\pi$
$38$	0.445529	−	0.771679i	0.0722743	−	0.125183i
$39$	16.8710	+	9.74050i	2.70153	+	1.55973i
$40$	2.16254	−	0.568686i	0.341928	−	0.0899171i
$41$	−8.03479			−1.25482			−0.627412	−	0.778688i	$-0.715886\pi$
$41$	−8.03479			−1.25482			−0.627412	+	0.778688i	$0.715886\pi$
$42$	−1.12697	+	7.53724i	−0.173895	+	1.16302i
$43$	−0.302038			−0.0460604			−0.0230302	−	0.999735i	$-0.507331\pi$
$43$	−0.302038			−0.0460604			−0.0230302	+	0.999735i	$0.507331\pi$
$44$	−3.21810	−	0.802409i	−0.485146	−	0.120968i
$45$	8.33648	+	8.41439i	1.24273	+	1.25434i
$46$	−6.17407	−	3.56460i	−0.910317	−	0.525572i
$47$	−5.24754	−	9.08901i	−0.765433	−	1.32577i	−0.940017	−	0.341127i	$-0.889191\pi$
$47$	−5.24754	−	9.08901i	−0.765433	−	1.32577i	0.174584	−	0.984642i	$-0.444142\pi$
$48$	2.88048			0.415761
$49$	−6.69386	−	2.04750i	−0.956265	−	0.292500i
$50$	4.30669	+	2.54017i	0.609057	+	0.359234i
$51$	3.85475	−	2.22554i	0.539773	−	0.311638i
$52$	5.85703	+	3.38156i	0.812224	+	0.468938i
$53$	−4.89115	−	2.82391i	−0.671851	−	0.387893i	0.124927	−	0.992166i	$-0.460130\pi$
$53$	−4.89115	−	2.82391i	−0.671851	−	0.387893i	−0.796778	+	0.604273i	$0.793464\pi$
$54$	3.30844	+	5.73039i	0.450222	+	0.779807i
$55$	−3.78993	−	6.37467i	−0.511034	−	0.859560i
$56$	−0.391243	+	2.61666i	−0.0522820	+	0.349666i
$57$	2.56667			0.339964
$58$	−2.42472	+	1.39991i	−0.318381	+	0.183817i
$59$	3.61218	+	2.08549i	0.470266	+	0.271508i	0.716351	−	0.697740i	$-0.245811\pi$
$59$	3.61218	+	2.08549i	0.470266	+	0.271508i	−0.246085	+	0.969248i	$0.579144\pi$
$60$	4.53320	+	4.57557i	0.585234	+	0.590703i
$61$	−0.226973	−	0.393129i	−0.0290609	−	0.0503350i	0.851129	−	0.524956i	$-0.175918\pi$
$61$	−0.226973	−	0.393129i	−0.0290609	−	0.0503350i	−0.880190	+	0.474621i	$0.842585\pi$
$62$			0.980614i			0.124538i
$63$	−13.0401	+	5.13561i	−1.64290	+	0.647027i
$64$	1.00000			0.125000
$65$	3.84609	+	14.6255i	0.477048	+	1.81407i
$66$	−2.63316	−	9.18341i	−0.324120	−	1.13040i
$67$	8.39321	+	4.84582i	1.02539	+	0.592012i	0.915662	−	0.401950i	$-0.131667\pi$
$67$	8.39321	+	4.84582i	1.02539	+	0.592012i	0.109732	+	0.993961i	$0.465001\pi$
$68$	1.33823	−	0.772629i	0.162285	−	0.0936950i
$69$		−	20.5355i		−	2.47219i
$70$	−4.77223	+	3.49654i	−0.570391	+	0.417917i
$71$	−4.72658			−0.560942			−0.280471	−	0.959863i	$-0.590491\pi$
$71$	−4.72658			−0.560942			−0.280471	+	0.959863i	$0.590491\pi$
$72$	2.64857	+	4.58746i	0.312137	+	0.540638i
$73$	−2.80161	−	1.61751i	−0.327904	−	0.189316i	0.327006	−	0.945022i	$-0.393960\pi$
$73$	−2.80161	−	1.61751i	−0.327904	−	0.189316i	−0.654910	+	0.755707i	$0.727294\pi$
$74$	8.14224	+	4.70093i	0.946517	+	0.546472i
$75$	−0.133963	+	14.4018i	−0.0154688	+	1.66297i
$76$	0.891058			0.102211
$77$	8.69999	−	1.14466i	0.991455	−	0.130446i
$78$			19.4810i			2.20579i
$79$	7.09357	−	4.09547i	0.798089	−	0.460777i	−0.0447138	−	0.999000i	$-0.514238\pi$
$79$	7.09357	−	4.09547i	0.798089	−	0.460777i	0.842802	+	0.538223i	$0.180904\pi$
$80$	1.57377	+	1.58848i	0.175953	+	0.177597i
$81$	−1.58417	+	2.74386i	−0.176019	+	0.304873i
$82$	−4.01739	−	6.95833i	−0.443647	−	0.768419i
$83$		−	4.01538i		−	0.440745i	−0.975416	−	0.220373i	$-0.929273\pi$
$83$		−	4.01538i		−	0.440745i	0.975416	−	0.220373i	$-0.0707274\pi$
$84$	−7.09092	+	2.79264i	−0.773683	+	0.304702i
$85$	3.33337	+	0.909810i	0.361555	+	0.0986828i
$86$	−0.151019	−	0.261573i	−0.0162848	−	0.0282061i
$87$	−6.98434	−	4.03241i	−0.748800	−	0.432320i
$88$	−0.914142	−	3.18816i	−0.0974478	−	0.339859i
$89$	6.83580	−	3.94665i	0.724594	−	0.418344i	−0.0918474	−	0.995773i	$-0.529277\pi$
$89$	6.83580	−	3.94665i	0.724594	−	0.418344i	0.816441	+	0.577429i	$0.195944\pi$
$90$	−3.11883	+	11.4268i	−0.328754	+	1.20449i
$91$	−17.6968	−	2.64602i	−1.85513	−	0.277378i
$92$		−	7.12921i		−	0.743271i
$93$	−2.44621	+	1.41232i	−0.253660	+	0.146451i
$94$	5.24754	−	9.08901i	0.541243	−	0.937460i
$95$	1.40232	+	1.41542i	0.143875	+	0.145219i
$96$	1.44024	+	2.49457i	0.146994	+	0.254601i
$97$	−19.1494			−1.94432			−0.972162	−	0.234312i	$-0.924716\pi$
$97$	−19.1494			−1.94432			−0.972162	+	0.234312i	$0.924716\pi$
$98$	−1.57374	−	6.82080i	−0.158972	−	0.689005i
$99$	12.2044	−	12.6377i	1.22659	−	1.27013i
$100$	−0.0465074	+	4.99978i	−0.00465074	+	0.499978i
$101$	5.11669	−	8.86237i	0.509130	−	0.881839i	−0.490814	−	0.871264i	$-0.663301\pi$
$101$	5.11669	−	8.86237i	0.509130	−	0.881839i	0.999944	−	0.0105746i	$-0.00336606\pi$
$102$	3.85475	+	2.22554i	0.381677	+	0.220361i
$103$	−1.03582	−	1.79408i	−0.102062	−	0.176776i	0.810472	−	0.585777i	$-0.199211\pi$
$103$	−1.03582	−	1.79408i	−0.102062	−	0.176776i	−0.912534	+	0.409001i	$0.865877\pi$
$104$			6.76312i			0.663178i
$105$	−15.5955	−	6.86879i	−1.52197	−	0.670326i
$106$		−	5.64781i		−	0.548564i
$107$	−8.13821	−	14.0958i	−0.786750	−	1.36269i	−0.927948	−	0.372710i	$-0.878429\pi$
$107$	−8.13821	−	14.0958i	−0.786750	−	1.36269i	0.141198	−	0.989981i	$-0.454905\pi$
$108$	−3.30844	+	5.73039i	−0.318355	+	0.551407i
$109$	−12.3584	−	7.13512i	−1.18372	−	0.683421i	−0.226847	−	0.973930i	$-0.572842\pi$
$109$	−12.3584	−	7.13512i	−1.18372	−	0.683421i	−0.956872	+	0.290510i	$0.906175\pi$
$110$	3.62566	−	6.46951i	0.345693	−	0.616844i
$111$			27.0818i			2.57049i
$112$	−2.46172	+	0.969505i	−0.232611	+	0.0916097i
$113$			2.93230i			0.275848i	0.990443	+	0.137924i	$0.0440429\pi$
$113$			2.93230i			0.275848i	−0.990443	+	0.137924i	$0.955957\pi$
$114$	1.28334	+	2.22280i	0.120195	+	0.208185i
$115$	11.3246	−	11.2197i	1.05602	−	1.04624i
$116$	−2.42472	−	1.39991i	−0.225129	−	0.129978i
$117$	−31.0256	+	17.9126i	−2.86831	+	1.65602i
$118$			4.17099i			0.383970i
$119$	−2.54528	+	3.19942i	−0.233326	+	0.293290i
$120$	−1.69596	+	6.21365i	−0.154819	+	0.567226i
$121$	−9.32869	+	5.82885i	−0.848063	+	0.529896i
$122$	0.226973	−	0.393129i	0.0205492	−	0.0355922i
$123$	11.5720	−	20.0433i	1.04341	−	1.80724i
$124$	−0.849237	+	0.490307i	−0.0762637	+	0.0440309i
$125$	−8.01522	+	7.79462i	−0.716903	+	0.697172i
$126$	−10.9676	−	8.72524i	−0.977073	−	0.777306i
$127$	11.9466			1.06009			0.530044	−	0.847970i	$-0.322175\pi$
$127$	11.9466			1.06009			0.530044	+	0.847970i	$0.322175\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.435007	−	0.753454i	0.0383002	−	0.0663379i
$130$	−10.7430	+	10.6436i	−0.942227	+	0.933503i
$131$	−2.49012	−	4.31301i	−0.217563	−	0.376830i	0.736500	−	0.676438i	$-0.236477\pi$
$131$	−2.49012	−	4.31301i	−0.217563	−	0.376830i	−0.954062	+	0.299608i	$0.903144\pi$
$132$	6.63649	−	6.87209i	0.577632	−	0.598139i
$133$	−2.19353	+	0.863885i	−0.190203	+	0.0749083i
$134$			9.69165i			0.837231i
$135$	−14.3093	+	3.76293i	−1.23155	+	0.323861i
$136$	1.33823	+	0.772629i	0.114752	+	0.0662524i
$137$	−9.98924	−	5.76729i	−0.853439	−	0.492733i	0.00837103	−	0.999965i	$-0.497335\pi$
$137$	−9.98924	−	5.76729i	−0.853439	−	0.492733i	−0.861810	+	0.507232i	$0.830669\pi$
$138$	17.7843	−	10.2678i	1.51390	−	0.874050i
$139$	−0.172337			−0.0146175			−0.00730873	−	0.999973i	$-0.502326\pi$
$139$	−0.172337			−0.0146175			−0.00730873	+	0.999973i	$0.502326\pi$
$140$	−5.41421	−	2.38460i	−0.457584	−	0.201536i
$141$	30.2309			2.54590
$142$	−2.36329	−	4.09334i	−0.198323	−	0.343505i
$143$	21.5619	−	6.18244i	1.80309	−	0.517002i
$144$	−2.64857	+	4.58746i	−0.220715	+	0.382289i
$145$	−1.59222	−	6.05474i	−0.132227	−	0.502819i
$146$		−	3.23503i		−	0.267733i
$147$	14.7484	−	13.7494i	1.21643	−	1.13403i
$148$			9.40185i			0.772828i
$149$	−0.339030	+	0.195739i	−0.0277744	+	0.0160356i	−0.513823	−	0.857896i	$-0.671771\pi$
$149$	−0.339030	+	0.195739i	−0.0277744	+	0.0160356i	0.486049	+	0.873932i	$0.338438\pi$
$150$	−12.5393	+	7.08487i	−1.02383	+	0.578477i
$151$	−2.34480	−	1.35377i	−0.190818	−	0.110169i	0.401548	−	0.915838i	$-0.368472\pi$
$151$	−2.34480	−	1.35377i	−0.190818	−	0.110169i	−0.592365	+	0.805670i	$0.701806\pi$
$152$	0.445529	+	0.771679i	0.0361372	+	0.0625914i
$153$			8.18546i			0.661755i
$154$	5.34129	+	6.96208i	0.430414	+	0.561020i
$155$	−2.11534	−	0.577362i	−0.169908	−	0.0463748i
$156$	−16.8710	+	9.74050i	−1.35076	+	0.779864i
$157$	−3.34433	+	5.79255i	−0.266907	+	0.462296i	−0.968061	−	0.250713i	$-0.919335\pi$
$157$	−3.34433	+	5.79255i	−0.266907	+	0.462296i	0.701155	+	0.713009i	$0.252668\pi$
$158$	7.09357	+	4.09547i	0.564334	+	0.325818i
$159$	14.0888	−	8.13419i	1.11732	−	0.645084i
$160$	−0.588776	+	2.15716i	−0.0465468	+	0.170539i
$161$	6.91180	+	17.5501i	0.544726	+	1.38314i
$162$	−3.16833			−0.248928
$163$	−13.3290	+	7.69553i	−1.04401	+	0.602760i	−0.920967	−	0.389641i	$-0.872599\pi$
$163$	−13.3290	+	7.69553i	−1.04401	+	0.602760i	−0.123044	+	0.992401i	$0.539266\pi$
$164$	4.01739	−	6.95833i	0.313706	−	0.543354i
$165$	21.3604	−	0.273186i	1.66291	−	0.0212675i
$166$	3.47742	−	2.00769i	0.269900	−	0.155827i
$167$			2.67400i			0.206920i	0.994634	+	0.103460i	$0.0329914\pi$
$167$			2.67400i			0.206920i	−0.994634	+	0.103460i	$0.967009\pi$
$168$	−5.96396	−	4.74460i	−0.460129	−	0.366054i
$169$	−32.7397			−2.51844
$170$	0.878766	+	3.34169i	0.0673983	+	0.256296i
$171$	−2.36003	+	4.08770i	−0.180476	+	0.312594i
$172$	0.151019	−	0.261573i	0.0115151	−	0.0199447i
$173$	−18.2861	+	10.5575i	−1.39027	+	0.802671i	−0.993344	−	0.115181i	$-0.963255\pi$
$173$	−18.2861	+	10.5575i	−1.39027	+	0.802671i	−0.396922	+	0.917852i	$0.629922\pi$
$174$		−	8.06482i		−	0.611393i
$175$	−4.73283	−	12.3532i	−0.357768	−	0.933810i
$176$	2.30395	−	2.38575i	0.173667	−	0.179833i
$177$	−10.4048	+	6.00721i	−0.782073	+	0.451530i
$178$	6.83580	+	3.94665i	0.512365	+	0.295814i
$179$	4.39977	−	7.62063i	0.328854	−	0.569592i	−0.653431	−	0.756986i	$-0.726671\pi$
$179$	4.39977	−	7.62063i	0.328854	−	0.569592i	0.982285	+	0.187394i	$0.0600042\pi$
$180$	−11.4553	+	3.01241i	−0.853829	+	0.224532i
$181$			5.30776i			0.394523i	0.980351	+	0.197261i	$0.0632048\pi$
$181$			5.30776i			0.394523i	−0.980351	+	0.197261i	$0.936795\pi$
$182$	−6.55688	−	16.6489i	−0.486028	−	1.23410i
$183$	1.30758			0.0966592
$184$	6.17407	−	3.56460i	0.455159	−	0.262786i
$185$	−14.9346	+	14.7963i	−1.09801	+	1.08785i
$186$	−2.44621	−	1.41232i	−0.179365	−	0.103556i
$187$	1.23993	−	4.97279i	0.0906725	−	0.363646i
$188$	10.4951			0.765433
$189$	2.58881	−	17.3142i	0.188308	−	1.25942i
$190$	−0.524633	+	1.92215i	−0.0380609	+	0.139448i
$191$	−3.95152	−	6.84423i	−0.285922	−	0.495231i	0.686910	−	0.726742i	$-0.258966\pi$
$191$	−3.95152	−	6.84423i	−0.285922	−	0.495231i	−0.972832	+	0.231511i	$0.925633\pi$
$192$	−1.44024	+	2.49457i	−0.103940	+	0.180030i
$193$	−7.13707	+	12.3618i	−0.513738	+	0.889820i	0.486135	+	0.873884i	$0.338406\pi$
$193$	−7.13707	+	12.3618i	−0.513738	+	0.889820i	−0.999873	+	0.0159362i	$0.994927\pi$
$194$	−9.57468	−	16.5838i	−0.687422	−	1.19065i
$195$	−42.0236	−	11.4699i	−3.00938	−	0.821380i
$196$	5.12012	−	4.77330i	0.365723	−	0.340950i
$197$	24.2556			1.72814			0.864071	−	0.503369i	$-0.167907\pi$
$197$	24.2556			1.72814			0.864071	+	0.503369i	$0.167907\pi$
$198$	17.0467	+	4.25048i	1.21146	+	0.302068i
$199$	9.10776	+	5.25837i	0.645632	+	0.372756i	0.786781	−	0.617233i	$-0.211746\pi$
$199$	9.10776	+	5.25837i	0.645632	+	0.372756i	−0.141149	+	0.989988i	$0.545080\pi$
$200$	−4.35319	+	2.45962i	−0.307817	+	0.173921i
$201$	−24.1765	+	13.9583i	−1.70528	+	0.984541i
$202$	10.2334			0.720018
$203$	7.32619	+	1.09541i	0.514198	+	0.0768828i
$204$			4.45108i			0.311638i
$205$	17.3756	−	4.56927i	1.21356	−	0.319132i
$206$	1.03582	−	1.79408i	0.0721687	−	0.125000i
$207$	32.7050	+	18.8822i	2.27315	+	1.31241i
$208$	−5.85703	+	3.38156i	−0.406112	+	0.234469i
$209$	2.05296	−	2.12584i	0.142006	−	0.147047i
$210$	−1.84920	−	16.9405i	−0.127607	−	1.16901i
$211$			7.05248i			0.485513i	0.970087	+	0.242756i	$0.0780516\pi$
$211$			7.05248i			0.485513i	−0.970087	+	0.242756i	$0.921948\pi$
$212$	4.89115	−	2.82391i	0.335925	−	0.193947i
$213$	6.80740	−	11.7908i	0.466435	−	0.807890i
$214$	8.13821	−	14.0958i	0.556316	−	0.963568i
$215$	0.653171	−	0.171765i	0.0445459	−	0.0117143i
$216$	−6.61688			−0.450222
$217$	1.61523	−	2.03034i	0.109649	−	0.137828i
$218$		−	14.2702i		−	0.966503i
$219$	8.06998	−	4.65921i	0.545319	−	0.314840i
$220$	7.41559	−	0.0948404i	0.499959	−	0.00639414i
$221$	−5.22538	+	9.05062i	−0.351497	+	0.608811i
$222$	−23.4535	+	13.5409i	−1.57410	+	0.908807i
$223$	14.8664			0.995529			0.497765	−	0.867312i	$-0.334154\pi$
$223$	14.8664			0.995529			0.497765	+	0.867312i	$0.334154\pi$
$224$	−2.07048	−	1.64716i	−0.138339	−	0.110055i
$225$	−22.8132	−	13.4556i	−1.52088	−	0.897043i
$226$	−2.53945	+	1.46615i	−0.168922	+	0.0975269i
$227$	−6.23204	−	3.59807i	−0.413635	−	0.238812i	0.278715	−	0.960374i	$-0.410091\pi$
$227$	−6.23204	−	3.59807i	−0.413635	−	0.238812i	−0.692350	+	0.721562i	$0.743425\pi$
$228$	−1.28334	+	2.22280i	−0.0849910	+	0.147209i
$229$	−6.72483	+	3.88258i	−0.444390	+	0.256568i	−0.705458	−	0.708752i	$-0.749259\pi$
$229$	−6.72483	+	3.88258i	−0.444390	+	0.256568i	0.261068	+	0.965320i	$0.415925\pi$
$230$	15.3788	+	4.19750i	1.01405	+	0.276775i
$231$	−9.67463	+	23.3513i	−0.636544	+	1.53640i
$232$		−	2.79982i		−	0.183817i
$233$	−1.44473	−	2.50235i	−0.0946474	−	0.163934i	0.814814	−	0.579723i	$-0.196839\pi$
$233$	−1.44473	−	2.50235i	−0.0946474	−	0.163934i	−0.909461	+	0.415788i	$0.863506\pi$
$234$	−31.0256	−	17.9126i	−2.02820	−	1.17098i
$235$	16.5168	+	16.6712i	1.07744	+	1.08751i
$236$	−3.61218	+	2.08549i	−0.235133	+	0.135754i
$237$			23.5938i			1.53258i
$238$	−4.04342	−	0.604571i	−0.262096	−	0.0391885i
$239$			21.5057i			1.39109i	0.718484	+	0.695544i	$0.244836\pi$
$239$			21.5057i			1.39109i	−0.718484	+	0.695544i	$0.755164\pi$
$240$	−6.22916	+	1.63809i	−0.402090	+	0.105738i
$241$	−10.4728	+	18.1393i	−0.674609	+	1.16846i	0.301973	+	0.953316i	$0.402355\pi$
$241$	−10.4728	+	18.1393i	−0.674609	+	1.16846i	−0.976583	+	0.215142i	$0.930979\pi$
$242$	−9.71228	−	5.16446i	−0.624329	−	0.331984i
$243$	5.36217	+	9.28755i	0.343983	+	0.595796i
$244$	0.453946			0.0290609
$245$	15.6401	+	0.621115i	0.999212	+	0.0396816i
$246$	23.1440			1.47561
$247$	−5.21895	+	3.01316i	−0.332074	+	0.191723i
$248$	−0.849237	−	0.490307i	−0.0539266	−	0.0311345i
$249$	10.0166	+	5.78311i	0.634779	+	0.366490i
$250$	−10.7580	−	3.04408i	−0.680393	−	0.192524i
$251$			11.5989i			0.732115i	0.930592	+	0.366057i	$0.119293\pi$
$251$			11.5989i			0.732115i	−0.930592	+	0.366057i	$0.880707\pi$
$252$	2.07247	−	13.8609i	0.130553	−	0.873152i
$253$	−17.0085	−	16.4254i	−1.06931	−	1.03265i
$254$	5.97330	+	10.3461i	0.374798	+	0.649169i
$255$	−7.07043	+	7.00497i	−0.442767	+	0.438668i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.24197	−	9.07936i	−0.326985	−	0.566355i	0.654927	−	0.755692i	$-0.272699\pi$
$257$	−5.24197	−	9.07936i	−0.326985	−	0.566355i	−0.981912	+	0.189337i	$0.939366\pi$
$258$	0.870014			0.0541647
$259$	−9.11515	−	23.1447i	−0.566388	−	1.43814i
$260$	−14.5891	−	3.98196i	−0.904779	−	0.246951i
$261$	12.8441	−	7.41554i	0.795029	−	0.459010i
$262$	2.49012	−	4.31301i	0.153840	−	0.266459i
$263$	−8.33780	+	14.4415i	−0.514131	+	0.890500i	0.485735	+	0.874106i	$0.338552\pi$
$263$	−8.33780	+	14.4415i	−0.514131	+	0.890500i	−0.999866	+	0.0163943i	$0.994781\pi$
$264$	9.26965	+	2.31132i	0.570508	+	0.142252i
$265$	12.1832	+	3.32529i	0.748410	+	0.204271i
$266$	−1.84491	−	1.46771i	−0.113119	−	0.0899913i
$267$			22.7365i			1.39145i
$268$	−8.39321	+	4.84582i	−0.512697	+	0.296006i
$269$	3.39881	+	1.96231i	0.207229	+	0.119644i	0.600023	−	0.799983i	$-0.295158\pi$
$269$	3.39881	+	1.96231i	0.207229	+	0.119644i	−0.392794	+	0.919627i	$0.628491\pi$
$270$	−10.4134	−	10.5108i	−0.633742	−	0.639664i
$271$	−4.29650	−	7.44176i	−0.260994	−	0.452055i	0.705512	−	0.708698i	$-0.250717\pi$
$271$	−4.29650	−	7.44176i	−0.260994	−	0.452055i	−0.966506	+	0.256643i	$0.917384\pi$
$272$			1.54526i			0.0936950i
$273$	32.0883	−	40.3349i	1.94207	−	2.44118i
$274$		−	11.5346i		−	0.696830i
$275$	11.8211	+	11.6302i	0.712838	+	0.701329i
$276$	17.7843	+	10.2678i	1.07049	+	0.618046i
$277$	14.4256	−	24.9858i	0.866748	−	1.50125i	0.00144636	−	0.999999i	$-0.499540\pi$
$277$	14.4256	−	24.9858i	0.866748	−	1.50125i	0.865301	−	0.501252i	$-0.167127\pi$
$278$	−0.0861686	−	0.149248i	−0.00516805	−	0.00895133i
$279$		−	5.19446i		−	0.310984i
$280$	−0.641979	−	5.88114i	−0.0383656	−	0.351466i
$281$		−	19.7917i		−	1.18068i	−0.807156	−	0.590338i	$-0.798994\pi$
$281$		−	19.7917i		−	1.18068i	0.807156	−	0.590338i	$-0.201006\pi$
$282$	15.1154	+	26.1807i	0.900111	+	1.55904i
$283$	26.0932	+	15.0649i	1.55108	+	0.895518i	0.998054	+	0.0623554i	$0.0198612\pi$
$283$	26.0932	+	15.0649i	1.55108	+	0.895518i	0.553028	+	0.833162i	$0.313472\pi$
$284$	2.36329	−	4.09334i	0.140235	−	0.242895i
$285$	−5.55054	+	1.45963i	−0.328786	+	0.0864610i
$286$	16.1351	+	15.5819i	0.954088	+	0.921378i
$287$	−3.14356	+	21.0243i	−0.185558	+	1.24103i
$288$	−5.29715			−0.312137
$289$	−7.30609	−	12.6545i	−0.429770	−	0.744383i
$290$	4.44745	−	4.40627i	0.261163	−	0.258745i
$291$	27.5796	−	47.7694i	1.61675	−	2.80029i
$292$	2.80161	−	1.61751i	0.163952	−	0.0946578i
$293$		−	2.94700i		−	0.172165i	−0.996288	−	0.0860827i	$-0.972565\pi$
$293$		−	2.94700i		−	0.172165i	0.996288	−	0.0860827i	$-0.0274349\pi$
$294$	19.2815	+	5.89779i	1.12452	+	0.343966i
$295$	−8.99749	−	2.45578i	−0.523854	−	0.142981i
$296$	−8.14224	+	4.70093i	−0.473258	+	0.273236i
$297$	6.04877	+	21.0957i	0.350985	+	1.22409i
$298$	−0.339030	−	0.195739i	−0.0196395	−	0.0113388i
$299$	24.1078	+	41.7560i	1.39419	+	2.41481i
$300$	−12.4053	−	7.31690i	−0.716221	−	0.422441i
$301$	−0.118170	+	0.790332i	−0.00681122	+	0.0455540i
$302$		−	2.70755i		−	0.155802i
$303$	14.7385	+	25.5279i	0.846706	+	1.46654i
$304$	−0.445529	+	0.771679i	−0.0255528	+	0.0442588i
$305$	0.714406	+	0.721082i	0.0409067	+	0.0412890i
$306$	−7.08881	+	4.09273i	−0.405241	+	0.233966i
$307$		−	27.4659i		−	1.56756i	−0.621039	−	0.783780i	$-0.713289\pi$
$307$		−	27.4659i		−	1.56756i	0.621039	−	0.783780i	$-0.286711\pi$
$308$	−3.35869	+	8.10674i	−0.191379	+	0.461924i
$309$	5.96728			0.339467
$310$	−0.557661	−	2.12062i	−0.0316730	−	0.120443i
$311$	−11.5613	−	6.67494i	−0.655584	−	0.378501i	0.135009	−	0.990844i	$-0.456894\pi$
$311$	−11.5613	−	6.67494i	−0.655584	−	0.378501i	−0.790592	+	0.612343i	$0.790227\pi$
$312$	−16.8710	−	9.74050i	−0.955135	−	0.551447i
$313$	14.1347	+	24.4821i	0.798942	+	1.38381i	0.920306	+	0.391200i	$0.127940\pi$
$313$	14.1347	+	24.4821i	0.798942	+	1.38381i	−0.121364	+	0.992608i	$0.538727\pi$
$314$	−6.68866			−0.377463
$315$	25.2792	−	18.5217i	1.42432	−	1.04358i
$316$			8.19094i			0.460777i
$317$	−20.4874	+	11.8284i	−1.15069	+	0.664349i	−0.949054	−	0.315112i	$-0.897958\pi$
$317$	−20.4874	+	11.8284i	−1.15069	+	0.664349i	−0.201632	+	0.979461i	$0.564624\pi$
$318$	14.0888	+	8.13419i	0.790063	+	0.456143i
$319$	−8.92627	+	2.55943i	−0.499775	+	0.143301i
$320$	−2.16254	+	0.568686i	−0.120890	+	0.0317905i
$321$	46.8838			2.61680
$322$	−11.7429	+	14.7608i	−0.654408	+	0.822590i
$323$			1.37691i			0.0766135i
$324$	−1.58417	−	2.74386i	−0.0880093	−	0.152437i
$325$	−16.6347	−	29.4411i	−0.922725	−	1.63310i
$326$	−13.3290	−	7.69553i	−0.738227	−	0.426216i
$327$	35.5981	−	20.5525i	1.96858	−	1.13656i
$328$	8.03479			0.443647
$329$	−25.8360	+	10.1750i	−1.42438	+	0.560968i
$330$	10.9168	+	18.3621i	0.600950	+	1.01080i
$331$	−7.28149	−	12.6119i	−0.400227	−	0.693213i	0.593526	−	0.804815i	$-0.297735\pi$
$331$	−7.28149	−	12.6119i	−0.400227	−	0.693213i	−0.993753	+	0.111602i	$0.964402\pi$
$332$	3.47742	+	2.00769i	0.190848	+	0.110186i
$333$	−43.1307	−	24.9015i	−2.36355	−	1.36459i
$334$	−2.31575	+	1.33700i	−0.126712	+	0.0731573i
$335$	−20.9064	−	5.70621i	−1.14224	−	0.311763i
$336$	1.12697	−	7.53724i	0.0614811	−	0.411190i
$337$	−19.9023			−1.08415			−0.542074	−	0.840331i	$-0.682361\pi$
$337$	−19.9023			−1.08415			−0.542074	+	0.840331i	$0.682361\pi$
$338$	−16.3699	−	28.3534i	−0.890403	−	1.54222i
$339$	−7.31482	−	4.22321i	−0.397286	−	0.229373i
$340$	−2.45460	+	2.43188i	−0.133120	+	0.131887i
$341$	−0.786854	+	3.15571i	−0.0426105	+	0.170891i
$342$	−4.72006			−0.255232
$343$	−7.97655	+	16.7145i	−0.430693	+	0.902498i
$344$	0.302038			0.0162848
$345$	11.6783	+	44.4090i	0.628736	+	2.39090i
$346$	−18.2861	−	10.5575i	−0.983067	−	0.567574i
$347$	−8.44426	+	14.6259i	−0.453312	+	0.785159i	−0.998589	−	0.0530967i	$-0.983091\pi$
$347$	−8.44426	+	14.6259i	−0.453312	+	0.785159i	0.545278	+	0.838255i	$0.316424\pi$
$348$	6.98434	−	4.03241i	0.374400	−	0.216160i
$349$	29.0093			1.55283			0.776417	−	0.630219i	$-0.217035\pi$
$349$	29.0093			1.55283			0.776417	+	0.630219i	$0.217035\pi$
$350$	8.33173	−	10.2753i	0.445350	−	0.549239i
$351$		−	44.7507i		−	2.38862i
$352$	3.21810	+	0.802409i	0.171525	+	0.0427685i
$353$	−6.99148	+	12.1096i	−0.372119	+	0.644528i	−0.989891	−	0.141828i	$-0.954702\pi$
$353$	−6.99148	+	12.1096i	−0.372119	+	0.644528i	0.617773	+	0.786357i	$0.288035\pi$
$354$	−10.4048	−	6.00721i	−0.553009	−	0.319280i
$355$	10.2214	−	2.68794i	0.542497	−	0.142661i
$356$			7.89331i			0.418344i
$357$	−4.31535	−	10.9573i	−0.228392	−	0.579922i
$358$	8.79954			0.465070
$359$	22.9522	−	13.2514i	1.21137	−	0.699384i	0.248311	−	0.968680i	$-0.420124\pi$
$359$	22.9522	−	13.2514i	1.21137	−	0.699384i	0.963057	+	0.269296i	$0.0867911\pi$
$360$	−8.33648	−	8.41439i	−0.439371	−	0.443477i
$361$	9.10301	−	15.7669i	0.479106	−	0.829835i
$362$	−4.59666	+	2.65388i	−0.241595	+	0.139485i
$363$	−1.10492	−	31.6660i	−0.0579933	−	1.66203i
$364$	11.1399	−	14.0029i	0.583891	−	0.733950i
$365$	6.97847	+	1.90470i	0.365270	+	0.0996968i
$366$	0.653790	+	1.13240i	0.0341742	+	0.0591914i
$367$	−14.0582	+	24.3495i	−0.733832	+	1.27103i	0.221402	+	0.975183i	$0.428937\pi$
$367$	−14.0582	+	24.3495i	−0.733832	+	1.27103i	−0.955234	+	0.295851i	$0.904397\pi$
$368$	6.17407	+	3.56460i	0.321846	+	0.185818i
$369$	21.2807	+	36.8593i	1.10783	+	1.91882i
$370$	−20.2813	−	5.53558i	−1.05438	−	0.287781i
$371$	−9.30284	+	11.6937i	−0.482979	+	0.607104i
$372$		−	2.82464i		−	0.146451i
$373$	7.76959	+	13.4573i	0.402294	+	0.696793i	0.994002	−	0.109359i	$-0.0348797\pi$
$373$	7.76959	+	13.4573i	0.402294	+	0.696793i	−0.591708	+	0.806152i	$0.701546\pi$
$374$	4.92652	−	1.41258i	0.254744	−	0.0730430i
$375$	−7.90037	−	31.2206i	−0.407973	−	1.61223i
$376$	5.24754	+	9.08901i	0.270621	+	0.468730i
$377$	18.9355			0.975229
$378$	16.2889	−	6.41510i	0.837811	−	0.329957i
$379$	−22.9334			−1.17801			−0.589004	−	0.808130i	$-0.700480\pi$
$379$	−22.9334			−1.17801			−0.589004	+	0.808130i	$0.700480\pi$
$380$	−1.92695	+	0.506732i	−0.0988505	+	0.0259948i
$381$	−17.2059	+	29.8016i	−0.881487	+	1.52678i
$382$	3.95152	−	6.84423i	0.202177	−	0.350181i
$383$	−14.9019	−	25.8109i	−0.761452	−	1.31887i	−0.942102	−	0.335327i	$-0.891153\pi$
$383$	−14.9019	−	25.8109i	−0.761452	−	1.31887i	0.180649	−	0.983548i	$-0.442180\pi$
$384$	−2.88048			−0.146994
$385$	−18.1632	+	7.42293i	−0.925680	+	0.378307i
$386$	−14.2741			−0.726535
$387$	0.799970	+	1.38559i	0.0406648	+	0.0704334i
$388$	9.57468	−	16.5838i	0.486081	−	0.841917i
$389$	10.7426	−	18.6067i	0.544670	−	0.943396i	−0.453957	−	0.891023i	$-0.649988\pi$
$389$	10.7426	−	18.6067i	0.544670	−	0.943396i	0.998628	−	0.0523731i	$-0.0166785\pi$
$390$	−11.0786	−	42.1285i	−0.560985	−	2.13326i
$391$	11.0165			0.557126
$392$	6.69386	+	2.04750i	0.338091	+	0.103415i
$393$	14.3455			0.723633
$394$	12.1278	+	21.0060i	0.610991	+	1.05827i
$395$	−13.0111	+	12.8906i	−0.654660	+	0.648599i
$396$	4.84234	+	16.8881i	0.243337	+	0.848661i
$397$	−16.2517	−	28.1488i	−0.815652	−	1.41275i	−0.908859	−	0.417103i	$-0.863045\pi$
$397$	−16.2517	−	28.1488i	−0.815652	−	1.41275i	0.0932073	−	0.995647i	$-0.470288\pi$
$398$			10.5167i			0.527156i
$399$	1.00419	−	6.71611i	0.0502725	−	0.336226i
$400$	−4.30669	−	2.54017i	−0.215334	−	0.127008i
$401$	−11.1849	−	19.3728i	−0.558546	−	0.967430i	−0.997618	−	0.0689781i	$-0.978026\pi$
$401$	−11.1849	−	19.3728i	−0.558546	−	0.967430i	0.439072	−	0.898452i	$-0.355307\pi$
$402$	−24.1765	−	13.9583i	−1.20581	−	0.696176i
$403$	3.31600	−	5.74349i	0.165182	−	0.286104i
$404$	5.11669	+	8.86237i	0.254565	+	0.440919i
$405$	1.86544	−	6.83460i	0.0926944	−	0.339614i
$406$	2.71444	+	6.89238i	0.134716	+	0.342063i
$407$	22.4305	+	21.6614i	1.11184	+	1.07372i
$408$	−3.85475	+	2.22554i	−0.190838	+	0.110181i
$409$	−9.53760	+	16.5196i	−0.471604	+	0.816842i	−0.999472	−	0.0324840i	$-0.989658\pi$
$409$	−9.53760	+	16.5196i	−0.471604	+	0.816842i	0.527868	+	0.849326i	$0.322992\pi$
$410$	12.6449	+	12.7631i	0.624487	+	0.630323i
$411$	28.7738	−	16.6126i	1.41931	−	0.819437i
$412$	2.07163			0.102062
$413$	6.87027	−	8.63592i	0.338064	−	0.424946i
$414$			37.7645i			1.85602i
$415$	2.28349	+	8.68344i	0.112092	+	0.426253i
$416$	−5.85703	−	3.38156i	−0.287165	−	0.165795i
$417$	0.248207	−	0.429907i	0.0121547	−	0.0210526i
$418$	2.86751	+	0.714992i	0.140254	+	0.0349714i
$419$			19.4987i			0.952574i	0.879290	+	0.476287i	$0.158018\pi$
$419$			19.4987i			0.952574i	−0.879290	+	0.476287i	$0.841982\pi$
$420$	13.7463	−	10.0717i	0.670751	−	0.491449i
$421$	7.90039			0.385041			0.192521	−	0.981293i	$-0.438334\pi$
$421$	7.90039			0.385041			0.192521	+	0.981293i	$0.438334\pi$
$422$	−6.10763	+	3.52624i	−0.297315	+	0.171655i
$423$	−27.7970	+	48.1459i	−1.35154	+	2.34093i
$424$	4.89115	+	2.82391i	0.237535	+	0.137141i
$425$	−7.72595	−	0.0718659i	−0.374764	−	0.00348601i
$426$	13.6148			0.659639
$427$	−1.11749	+	0.440103i	−0.0540790	+	0.0212981i
$428$	16.2764			0.786750
$429$	−15.6317	+	62.6917i	−0.754707	+	3.02678i
$430$	0.475338	+	0.479780i	0.0229228	+	0.0231370i
$431$	−25.2940	−	14.6035i	−1.21837	−	0.703425i	−0.253800	−	0.967257i	$-0.581680\pi$
$431$	−25.2940	−	14.6035i	−1.21837	−	0.703425i	−0.964569	+	0.263831i	$0.915014\pi$
$432$	−3.30844	−	5.73039i	−0.159177	−	0.275703i
$433$	−17.6790			−0.849599			−0.424799	−	0.905287i	$-0.639655\pi$
$433$	−17.6790			−0.849599			−0.424799	+	0.905287i	$0.639655\pi$
$434$	2.56594	+	0.383659i	0.123169	+	0.0184162i
$435$	17.3971	+	4.74837i	0.834128	+	0.227667i
$436$	12.3584	−	7.13512i	0.591860	−	0.341710i
$437$	5.50146	+	3.17627i	0.263170	+	0.151941i
$438$	8.06998	+	4.65921i	0.385599	+	0.222626i
$439$	−3.88898	−	6.73591i	−0.185611	−	0.321488i	0.758171	−	0.652055i	$-0.226093\pi$
$439$	−3.88898	−	6.73591i	−0.185611	−	0.321488i	−0.943782	+	0.330568i	$0.892760\pi$
$440$	3.78993	+	6.37467i	0.180678	+	0.303901i
$441$	8.33633	+	36.1308i	0.396968	+	1.72051i
$442$	−10.4508			−0.497092
$443$	26.6196	−	15.3688i	1.26473	−	0.730195i	0.290747	−	0.956800i	$-0.406096\pi$
$443$	26.6196	−	15.3688i	1.26473	−	0.730195i	0.973987	+	0.226605i	$0.0727627\pi$
$444$	−23.4535	−	13.5409i	−1.11306	−	0.642623i
$445$	−12.5383	+	12.4222i	−0.594373	+	0.588870i
$446$	7.43321	+	12.8747i	0.351973	+	0.609635i
$447$		−	1.12764i		−	0.0533357i
$448$	0.391243	−	2.61666i	0.0184845	−	0.123626i
$449$	8.20812			0.387365			0.193682	−	0.981064i	$-0.437957\pi$
$449$	8.20812			0.387365			0.193682	+	0.981064i	$0.437957\pi$
$450$	0.246357	−	26.4846i	0.0116134	−	1.24850i
$451$	−7.34493	−	25.6162i	−0.345859	−	1.20622i
$452$	−2.53945	−	1.46615i	−0.119446	−	0.0689619i
$453$	6.75416	−	3.89951i	0.317338	−	0.183215i
$454$		−	7.19614i		−	0.337731i
$455$	39.7749	−	4.34178i	1.86467	−	0.203546i
$456$	−2.56667			−0.120195
$457$	8.43227	+	14.6051i	0.394445	+	0.683199i	0.993030	−	0.117861i	$-0.0376036\pi$
$457$	8.43227	+	14.6051i	0.394445	+	0.683199i	−0.598585	+	0.801059i	$0.704270\pi$
$458$	−6.72483	−	3.88258i	−0.314231	−	0.181421i
$459$	−8.85493	−	5.11239i	−0.413313	−	0.238626i
$460$	4.05428	+	15.4172i	0.189032	+	0.718832i
$461$	25.9736			1.20971			0.604856	−	0.796335i	$-0.293230\pi$
$461$	25.9736			1.20971			0.604856	+	0.796335i	$0.293230\pi$
$462$	−25.0601	+	3.29716i	−1.16590	+	0.153398i
$463$			6.66326i			0.309668i	0.987941	+	0.154834i	$0.0494842\pi$
$463$			6.66326i			0.309668i	−0.987941	+	0.154834i	$0.950516\pi$
$464$	2.42472	−	1.39991i	0.112565	−	0.0649892i
$465$	4.48687	−	4.44532i	0.208073	−	0.206147i
$466$	1.44473	−	2.50235i	0.0669259	−	0.115919i
$467$	−4.29559	−	7.44018i	−0.198776	−	0.344290i	0.749356	−	0.662168i	$-0.230363\pi$
$467$	−4.29559	−	7.44018i	−0.198776	−	0.344290i	−0.948132	+	0.317877i	$0.897030\pi$
$468$		−	35.8252i		−	1.65602i
$469$	15.9637	−	20.0663i	0.737134	−	0.926577i
$470$	−6.17926	+	22.6396i	−0.285028	+	1.04429i
$471$	−9.63327	−	16.6853i	−0.443877	−	0.768818i
$472$	−3.61218	−	2.08549i	−0.166264	−	0.0959926i
$473$	−0.276106	−	0.962945i	−0.0126953	−	0.0442762i
$474$	−20.4329	+	11.7969i	−0.938512	+	0.541850i
$475$	−3.83751	−	2.26344i	−0.176077	−	0.103854i
$476$	−1.49814	−	3.80399i	−0.0686669	−	0.174356i
$477$			29.9173i			1.36982i
$478$	−18.6245	+	10.7528i	−0.851864	+	0.491824i
$479$	9.15755	−	15.8613i	0.418419	−	0.724723i	−0.577362	−	0.816488i	$-0.695918\pi$
$479$	9.15755	−	15.8613i	0.418419	−	0.724723i	0.995781	+	0.0917657i	$0.0292511\pi$
$480$	−4.53320	−	4.57557i	−0.206911	−	0.208845i
$481$	−31.7929	−	55.0669i	−1.44963	−	2.51084i
$482$	−20.9455			−0.954042
$483$	−53.7345	−	8.03438i	−2.44501	−	0.365577i
$484$	−0.383590	−	10.9933i	−0.0174359	−	0.499696i
$485$	41.4113	−	10.8900i	1.88039	−	0.494488i
$486$	−5.36217	+	9.28755i	−0.243233	+	0.421292i
$487$	16.3775	+	9.45553i	0.742133	+	0.428471i	0.822844	−	0.568267i	$-0.192386\pi$
$487$	16.3775	+	9.45553i	0.742133	+	0.428471i	−0.0807111	+	0.996738i	$0.525719\pi$
$488$	0.226973	+	0.393129i	0.0102746	+	0.0177961i
$489$		−	44.3336i		−	2.00483i
$490$	7.28217	+	13.8553i	0.328975	+	0.625920i
$491$		−	2.08588i		−	0.0941345i	−0.998892	−	0.0470672i	$-0.985012\pi$
$491$		−	2.08588i		−	0.0941345i	0.998892	−	0.0470672i	$-0.0149875\pi$
$492$	11.5720	+	20.0433i	0.521707	+	0.903622i
$493$	2.16322	−	3.74681i	0.0974267	−	0.168748i
$494$	−5.21895	−	3.01316i	−0.234812	−	0.135569i
$495$	−19.2057	+	34.2700i	−0.863231	+	1.54032i
$496$		−	0.980614i		−	0.0440309i
$497$	−1.84924	+	12.3679i	−0.0829498	+	0.554775i
$498$			11.5662i			0.518295i
$499$	11.0473	+	19.1345i	0.494546	+	0.856580i	0.999980	−	0.00628578i	$-0.00200084\pi$
$499$	11.0473	+	19.1345i	0.494546	+	0.856580i	−0.505434	+	0.862865i	$0.668668\pi$
$500$	−2.74273	−	10.8387i	−0.122659	−	0.484721i
$501$	−6.67046	−	3.85119i	−0.298014	−	0.172059i
$502$	−10.0449	+	5.79944i	−0.448327	+	0.258842i
$503$		−	5.93021i		−	0.264415i	−0.991222	−	0.132208i	$-0.957793\pi$
$503$		−	5.93021i		−	0.264415i	0.991222	−	0.132208i	$-0.0422065\pi$
$504$	13.0401	−	5.13561i	0.580852	−	0.228758i
$505$	−6.02517	+	22.0751i	−0.268117	+	0.982327i
$506$	5.72054	−	22.9425i	0.254309	−	1.01992i
$507$	47.1530	−	81.6714i	2.09414	−	3.62716i
$508$	−5.97330	+	10.3461i	−0.265022	+	0.459032i
$509$	3.85268	−	2.22435i	0.170767	−	0.0985924i	−0.412180	−	0.911102i	$-0.635233\pi$
$509$	3.85268	−	2.22435i	0.170767	−	0.0985924i	0.582947	+	0.812510i	$0.301899\pi$
$510$	−9.60169	−	2.62069i	−0.425170	−	0.116046i
$511$	−5.32860	+	6.69804i	−0.235723	+	0.296304i
$512$	−1.00000			−0.0441942
$513$	−2.94801	−	5.10611i	−0.130158	−	0.225440i
$514$	5.24197	−	9.07936i	0.231213	−	0.400473i
$515$	3.26027	+	3.29073i	0.143665	+	0.145007i
$516$	0.435007	+	0.753454i	0.0191501	+	0.0331690i
$517$	24.1802	−	25.0386i	1.06344	−	1.10120i
$518$	15.4863	−	19.4663i	0.680431	−	0.855301i
$519$		−	60.8212i		−	2.66975i
$520$	−3.84609	−	14.6255i	−0.168662	−	0.641372i
$521$	36.9647	+	21.3416i	1.61945	+	0.934992i	0.987061	+	0.160345i	$0.0512607\pi$
$521$	36.9647	+	21.3416i	1.61945	+	0.934992i	0.632393	+	0.774647i	$0.282073\pi$
$522$	12.8441	+	7.41554i	0.562170	+	0.324569i
$523$	−24.1037	+	13.9163i	−1.05398	+	0.608517i	−0.923762	−	0.382968i	$-0.874902\pi$
$523$	−24.1037	+	13.9163i	−1.05398	+	0.608517i	−0.130221	+	0.991485i	$0.541569\pi$
$524$	4.98024			0.217563
$525$	37.6322	+	5.98513i	1.64240	+	0.261212i
$526$	−16.6756			−0.727091
$527$	−0.757651	−	1.31229i	−0.0330038	−	0.0571642i
$528$	2.63316	+	9.18341i	0.114594	+	0.399657i
$529$	13.9128	−	24.0977i	0.604904	−	1.04772i
$530$	3.21183	+	12.2136i	0.139513	+	0.530527i
$531$		−	22.0943i		−	0.958812i
$532$	0.348620	−	2.33160i	0.0151146	−	0.101088i
$533$			54.3402i			2.35374i
$534$	−19.6904	+	11.3682i	−0.852086	+	0.491952i
$535$	25.6153	+	25.8547i	1.10745	+	1.11780i
$536$	−8.39321	−	4.84582i	−0.362532	−	0.209308i
$537$	12.6734	+	21.9510i	0.546899	+	0.947257i
$538$			3.92461i			0.169202i
$539$	0.408628	−	23.2128i	0.0176008	−	0.999845i
$540$	3.89586	−	14.2737i	0.167651	−	0.614241i
$541$	−2.72711	+	1.57450i	−0.117248	+	0.0676930i	−0.557477	−	0.830192i	$-0.688231\pi$
$541$	−2.72711	+	1.57450i	−0.117248	+	0.0676930i	0.440229	+	0.897885i	$0.354897\pi$
$542$	4.29650	−	7.44176i	0.184550	−	0.319651i
$543$	−13.2406	−	7.64445i	−0.568207	−	0.328055i
$544$	−1.33823	+	0.772629i	−0.0573762	+	0.0331262i
$545$	30.7832	+	8.40197i	1.31861	+	0.359901i
$546$	50.9752	+	7.62181i	2.18154	+	0.326183i
$547$	−34.6612			−1.48201			−0.741003	−	0.671501i	$-0.765650\pi$
$547$	−34.6612			−1.48201			−0.741003	+	0.671501i	$0.765650\pi$
$548$	9.98924	−	5.76729i	0.426719	−	0.246366i
$549$	−1.20231	+	2.08246i	−0.0513133	+	0.0888773i
$550$	−4.16154	+	16.0525i	−0.177448	+	0.684479i
$551$	2.16056	−	1.24740i	0.0920431	−	0.0531411i
$552$			20.5355i			0.874050i
$553$	−7.94117	−	20.1638i	−0.337693	−	0.857452i
$554$	28.8511			1.22577
$555$	−15.4010	−	58.5656i	−0.653738	−	2.48597i
$556$	0.0861686	−	0.149248i	0.00365436	−	0.00632955i
$557$	−9.14129	+	15.8332i	−0.387329	+	0.670873i	−0.992089	−	0.125534i	$-0.959936\pi$
$557$	−9.14129	+	15.8332i	−0.387329	+	0.670873i	0.604760	+	0.796407i	$0.293269\pi$
$558$	4.49853	−	2.59723i	0.190438	−	0.109950i
$559$			2.04272i			0.0863978i
$560$	4.77223	−	3.49654i	0.201664	−	0.147756i
$561$	10.6192	+	10.2551i	0.448341	+	0.432970i
$562$	17.1401	−	9.89587i	0.723014	−	0.417432i
$563$	6.56375	+	3.78958i	0.276629	+	0.159712i	0.631896	−	0.775053i	$-0.282277\pi$
$563$	6.56375	+	3.78958i	0.276629	+	0.159712i	−0.355267	+	0.934765i	$0.615610\pi$
$564$	−15.1154	+	26.1807i	−0.636475	+	1.10241i
$565$	−1.66756	−	6.34123i	−0.0701547	−	0.266778i
$566$			30.1299i			1.26645i
$567$	6.55996	+	5.21875i	0.275492	+	0.219167i
$568$	4.72658			0.198323
$569$	12.8228	−	7.40323i	0.537558	−	0.310359i	−0.206530	−	0.978440i	$-0.566217\pi$
$569$	12.8228	−	7.40323i	0.537558	−	0.310359i	0.744089	+	0.668081i	$0.232884\pi$
$570$	−4.03935	−	4.07709i	−0.169190	−	0.170771i
$571$	37.1225	+	21.4327i	1.55353	+	0.896930i	0.997850	+	0.0655330i	$0.0208748\pi$
$571$	37.1225	+	21.4327i	1.55353	+	0.896930i	0.555678	+	0.831397i	$0.312459\pi$
$572$	−5.42678	+	21.7644i	−0.226905	+	0.910013i
$573$	22.7645			0.951002
$574$	−19.7794	+	7.78977i	−0.825576	+	0.325139i
$575$	−18.1094	+	30.7033i	−0.755214	+	1.28041i
$576$	−2.64857	−	4.58746i	−0.110357	−	0.191144i
$577$	−1.62463	+	2.81394i	−0.0676341	+	0.117146i	−0.897859	−	0.440282i	$-0.854878\pi$
$577$	−1.62463	+	2.81394i	−0.0676341	+	0.117146i	0.830225	+	0.557428i	$0.188212\pi$
$578$	7.30609	−	12.6545i	0.303893	−	0.526359i
$579$	−20.5582	−	35.6078i	−0.854368	−	1.47981i
$580$	6.03967	+	1.64847i	0.250784	+	0.0684489i
$581$	−10.5069	−	1.57099i	−0.435900	−	0.0651757i
$582$	55.1593			2.28643
$583$	4.53185	−	18.1752i	0.187690	−	0.752740i
$584$	2.80161	+	1.61751i	0.115932	+	0.0669331i
$585$	56.9075	−	56.3806i	2.35283	−	2.33105i
$586$	2.55217	−	1.47350i	0.105429	−	0.0608696i
$587$	−17.0225			−0.702593			−0.351296	−	0.936264i	$-0.614259\pi$
$587$	−17.0225			−0.702593			−0.351296	+	0.936264i	$0.614259\pi$
$588$	4.53312	+	19.6472i	0.186943	+	0.810235i
$589$		−	0.873784i		−	0.0360036i
$590$	−2.37198	−	9.01994i	−0.0976528	−	0.371345i
$591$	−34.9339	+	60.5073i	−1.43699	+	2.48894i
$592$	−8.14224	−	4.70093i	−0.334644	−	0.193207i
$593$	17.0074	−	9.81923i	0.698411	−	0.403228i	−0.108345	−	0.994113i	$-0.534555\pi$
$593$	17.0074	−	9.81923i	0.698411	−	0.403228i	0.806755	+	0.590886i	$0.201222\pi$
$594$	−15.2450	+	15.7862i	−0.625510	+	0.647716i
$595$	3.68483	−	8.36635i	0.151063	−	0.342987i
$596$		−	0.391478i		−	0.0160356i
$597$	−26.2347	+	15.1466i	−1.07371	+	0.619909i
$598$	−24.1078	+	41.7560i	−0.985842	+	1.70753i
$599$	−9.84488	+	17.0518i	−0.402251	+	0.696719i	−0.993997	−	0.109405i	$-0.965105\pi$
$599$	−9.84488	+	17.0518i	−0.402251	+	0.696719i	0.591746	+	0.806124i	$0.298439\pi$
$600$	0.133963	−	14.4018i	0.00546904	−	0.587949i
$601$	−12.1124			−0.494076			−0.247038	−	0.969006i	$-0.579457\pi$
$601$	−12.1124			−0.494076			−0.247038	+	0.969006i	$0.579457\pi$
$602$	−0.743533	+	0.292828i	−0.0303041	+	0.0119348i
$603$		−	51.3381i		−	2.09065i
$604$	2.34480	−	1.35377i	0.0954088	−	0.0550843i
$605$	16.8589	−	17.9102i	0.685413	−	0.728155i
$606$	−14.7385	+	25.5279i	−0.598711	+	1.03700i
$607$	24.9376	−	14.3977i	1.01219	−	0.584386i	0.100355	−	0.994952i	$-0.468002\pi$
$607$	24.9376	−	14.3977i	1.01219	−	0.584386i	0.911831	+	0.410566i	$0.134669\pi$
$608$	−0.891058			−0.0361372
$609$	−13.2840	+	16.6980i	−0.538297	+	0.676638i
$610$	−0.267272	+	0.979234i	−0.0108215	+	0.0396480i
$611$	−61.4701	+	35.4898i	−2.48681	+	1.43576i
$612$	−7.08881	−	4.09273i	−0.286548	−	0.165439i
$613$	−18.5998	+	32.2158i	−0.751240	+	1.30119i	0.195983	+	0.980607i	$0.437210\pi$
$613$	−18.5998	+	32.2158i	−0.751240	+	1.30119i	−0.947222	+	0.320578i	$0.896123\pi$
$614$	23.7861	−	13.7329i	0.959930	−	0.554216i
$615$	−13.6266	+	49.9254i	−0.549479	+	2.01319i
$616$	−8.69999	+	1.14466i	−0.350532	+	0.0461195i
$617$		−	3.41654i		−	0.137545i	−0.997632	−	0.0687724i	$-0.978092\pi$
$617$		−	3.41654i		−	0.137545i	0.997632	−	0.0687724i	$-0.0219082\pi$
$618$	2.98364	+	5.16782i	0.120020	+	0.207880i
$619$	−23.5560	−	13.6001i	−0.946796	−	0.546633i	−0.0547120	−	0.998502i	$-0.517424\pi$
$619$	−23.5560	−	13.6001i	−0.946796	−	0.546633i	−0.892084	+	0.451869i	$0.850757\pi$
$620$	1.55768	−	1.54326i	0.0625580	−	0.0619788i
$621$	−40.8531	+	23.5866i	−1.63938	+	0.946496i
$622$		−	13.3499i		−	0.535282i
$623$	−7.65260	−	19.4311i	−0.306595	−	0.778490i
$624$		−	19.4810i		−	0.779864i
$625$	12.9006	−	21.4144i	0.516023	−	0.856574i
$626$	−14.1347	+	24.4821i	−0.564937	+	0.978500i
$627$	2.34630	+	8.18295i	0.0937022	+	0.326796i
$628$	−3.34433	−	5.79255i	−0.133453	−	0.231148i
$629$	−14.5283			−0.579281
$630$	28.6799	+	12.6316i	1.14263	+	0.503255i
$631$	−7.01999			−0.279462			−0.139731	−	0.990190i	$-0.544624\pi$
$631$	−7.01999			−0.279462			−0.139731	+	0.990190i	$0.544624\pi$
$632$	−7.09357	+	4.09547i	−0.282167	+	0.162909i
$633$	−17.5929	−	10.1573i	−0.699254	−	0.403715i
$634$	−20.4874	−	11.8284i	−0.813658	−	0.469766i
$635$	−25.8350	+	6.79385i	−1.02523	+	0.269606i
$636$			16.2684i			0.645084i
$637$	−13.8475	+	45.2713i	−0.548658	+	1.79372i
$638$	−6.67967	−	6.45066i	−0.264451	−	0.255384i
$639$	12.5187	+	21.6830i	0.495232	+	0.857767i
$640$	−1.57377	−	1.58848i	−0.0622086	−	0.0627900i
$641$	15.7071	−	27.2055i	0.620393	−	1.07455i	−0.369020	−	0.929422i	$-0.620306\pi$
$641$	15.7071	−	27.2055i	0.620393	−	1.07455i	0.989413	−	0.145131i	$-0.0463602\pi$
$642$	23.4419	+	40.6026i	0.925179	+	1.60246i
$643$	−10.1418			−0.399953			−0.199976	−	0.979801i	$-0.564087\pi$
$643$	−10.1418			−0.399953			−0.199976	+	0.979801i	$0.564087\pi$
$644$	−18.6547	−	2.78925i	−0.735100	−	0.109912i
$645$	−0.512243	+	1.87676i	−0.0201696	+	0.0738973i
$646$	−1.19244	+	0.688457i	−0.0469160	+	0.0270870i
$647$	5.00464	−	8.66829i	0.196753	−	0.340786i	−0.750721	−	0.660619i	$-0.770294\pi$
$647$	5.00464	−	8.66829i	0.196753	−	0.340786i	0.947474	+	0.319834i	$0.103627\pi$
$648$	1.58417	−	2.74386i	0.0622319	−	0.107789i
$649$	−3.34683	+	13.4226i	−0.131375	+	0.526884i
$650$	17.1795	−	29.1266i	0.673834	−	1.14244i
$651$	2.73850	+	6.95346i	0.107330	+	0.272528i
$652$		−	15.3911i		−	0.602760i
$653$	8.60496	−	4.96807i	0.336738	−	0.194416i	−0.322091	−	0.946709i	$-0.604386\pi$
$653$	8.60496	−	4.96807i	0.336738	−	0.194416i	0.658829	+	0.752293i	$0.271052\pi$
$654$	35.5981	+	20.5525i	1.39199	+	0.803668i
$655$	7.83774	+	7.91099i	0.306246	+	0.309108i
$656$	4.01739	+	6.95833i	0.156853	+	0.271677i
$657$			17.1364i			0.668555i
$658$	−21.7298	−	17.2871i	−0.847117	−	0.673920i
$659$			16.9698i			0.661050i	0.943797	+	0.330525i	$0.107226\pi$
$659$			16.9698i			0.661050i	−0.943797	+	0.330525i	$0.892774\pi$
$660$	−10.4436	+	18.6353i	−0.406518	+	0.725377i
$661$	20.0753	+	11.5905i	0.780840	+	0.450818i	0.836728	−	0.547619i	$-0.184466\pi$
$661$	20.0753	+	11.5905i	0.780840	+	0.450818i	−0.0558878	+	0.998437i	$0.517799\pi$
$662$	7.28149	−	12.6119i	0.283003	−	0.490176i
$663$	−15.0516	−	26.0701i	−0.584555	−	1.01248i
$664$			4.01538i			0.155827i
$665$	4.25233	−	3.11562i	0.164898	−	0.120819i
$666$		−	49.8030i		−	1.92983i
$667$	−9.98026	−	17.2863i	−0.386437	−	0.669329i
$668$	−2.31575	−	1.33700i	−0.0895990	−	0.0517300i
$669$	−21.4112	+	37.0853i	−0.827805	+	1.43380i
$670$	−5.51150	−	20.9586i	−0.212928	−	0.809702i
$671$	1.04587	−	1.08300i	0.0403754	−	0.0418088i
$672$	7.09092	−	2.79264i	0.273538	−	0.107728i
$673$	−21.1462			−0.815127			−0.407564	−	0.913177i	$-0.633622\pi$
$673$	−21.1462			−0.815127			−0.407564	+	0.913177i	$0.633622\pi$
$674$	−9.95115	−	17.2359i	−0.383304	−	0.663902i
$675$	28.8046	−	16.2750i	1.10869	−	0.626424i
$676$	16.3699	−	28.3534i	0.629610	−	1.09052i
$677$	25.4368	−	14.6859i	0.977614	−	0.564426i	0.0760650	−	0.997103i	$-0.475764\pi$
$677$	25.4368	−	14.6859i	0.977614	−	0.564426i	0.901549	+	0.432677i	$0.142431\pi$
$678$		−	8.44643i		−	0.324383i
$679$	−7.49205	+	50.1074i	−0.287519	+	1.92295i
$680$	−3.33337	−	0.909810i	−0.127829	−	0.0348896i
$681$	17.9512	−	10.3642i	0.687893	−	0.397155i
$682$	−3.12635	+	0.896420i	−0.119714	+	0.0343257i
$683$	26.0105	+	15.0172i	0.995266	+	0.574617i	0.906844	−	0.421466i	$-0.138484\pi$
$683$	26.0105	+	15.0172i	0.995266	+	0.574617i	0.0884218	+	0.996083i	$0.471818\pi$
$684$	−2.36003	−	4.08770i	−0.0902381	−	0.156297i
$685$	24.8820	+	6.79128i	0.950690	+	0.259482i
$686$	−18.4635	+	1.44936i	−0.704938	+	0.0553366i
$687$		−	22.3674i		−	0.853369i
$688$	0.151019	+	0.261573i	0.00575755	+	0.00997236i
$689$	−19.0984	+	33.0794i	−0.727591	+	1.26022i
$690$	−32.6202	+	32.3181i	−1.24183	+	1.23033i
$691$	−1.98906	+	1.14838i	−0.0756673	+	0.0436865i	−0.537356	−	0.843355i	$-0.680577\pi$
$691$	−1.98906	+	1.14838i	−0.0756673	+	0.0436865i	0.461689	+	0.887042i	$0.347244\pi$
$692$		−	21.1150i		−	0.802671i
$693$	−28.2936	−	36.8792i	−1.07479	−	1.40092i
$694$	−16.8885			−0.641079
$695$	0.372687	−	0.0980057i	0.0141368	−	0.00371757i
$696$	6.98434	+	4.03241i	0.264741	+	0.152848i
$697$	10.7524	+	6.20791i	0.407277	+	0.235141i
$698$	14.5047	+	25.1228i	0.549010	+	0.950913i
$699$	8.32303			0.314806
$700$	13.0646	+	2.07782i	0.493794	+	0.0785344i
$701$		−	38.2267i		−	1.44380i	−0.691995	−	0.721902i	$-0.743268\pi$
$701$		−	38.2267i		−	1.44380i	0.691995	−	0.721902i	$-0.256732\pi$
$702$	38.7553	−	22.3754i	1.46272	−	0.844504i
$703$	−7.25521	−	4.18880i	−0.273635	−	0.157983i
$704$	0.914142	+	3.18816i	0.0344530	+	0.120158i
$705$	−65.3756	+	17.1919i	−2.46219	+	0.647483i
$706$	−13.9830			−0.526255
$707$	−21.1880	−	16.8560i	−0.796856	−	0.633935i
$708$		−	12.0144i		−	0.451530i
$709$	13.5481	+	23.4660i	0.508810	+	0.881285i	0.999948	+	0.0102029i	$0.00324772\pi$
$709$	13.5481	+	23.4660i	0.508810	+	0.881285i	−0.491138	+	0.871082i	$0.663419\pi$
$710$	7.43854	+	7.50805i	0.279163	+	0.281772i
$711$	−37.5757	−	21.6943i	−1.40920	−	0.813601i
$712$	−6.83580	+	3.94665i	−0.256183	+	0.147907i
$713$	−6.99100			−0.261815
$714$	7.33163	−	9.21585i	0.274379	−	0.344895i
$715$	−43.1126	+	25.6317i	−1.61232	+	0.958573i
$716$	4.39977	+	7.62063i	0.164427	+	0.284796i
$717$	−53.6474	−	30.9733i	−2.00350	−	1.15672i
$718$	22.9522	+	13.2514i	0.856567	+	0.494539i
$719$	−16.7058	+	9.64509i	−0.623021	+	0.359701i	−0.778044	−	0.628210i	$-0.783788\pi$
$719$	−16.7058	+	9.64509i	−0.623021	+	0.359701i	0.155024	+	0.987911i	$0.450455\pi$
$720$	3.11883	−	11.4268i	0.116232	−	0.425852i
$721$	−5.09977	+	2.00846i	−0.189925	+	0.0747989i
$722$	18.2060			0.677558
$723$	−30.1665	−	52.2500i	−1.12191	−	1.94320i
$724$	−4.59666	−	2.65388i	−0.170833	−	0.0986307i
$725$	6.88649	+	12.1882i	0.255758	+	0.452657i
$726$	26.8711	−	16.7899i	0.997279	−	0.623131i
$727$	−2.36203			−0.0876029			−0.0438015	−	0.999040i	$-0.513947\pi$
$727$	−2.36203			−0.0876029			−0.0438015	+	0.999040i	$0.513947\pi$
$728$	17.6968	+	2.64602i	0.655887	+	0.0980681i
$729$	−40.3962			−1.49616
$730$	1.83971	+	6.99588i	0.0680908	+	0.258929i
$731$	0.404197	+	0.233363i	0.0149498	+	0.00863125i
$732$	−0.653790	+	1.13240i	−0.0241648	+	0.0418546i
$733$	−12.5500	+	7.24574i	−0.463544	+	0.267627i	−0.713533	−	0.700621i	$-0.752906\pi$
$733$	−12.5500	+	7.24574i	−0.463544	+	0.267627i	0.249989	+	0.968249i	$0.419573\pi$
$734$	−28.1164			−1.03779
$735$	−24.0750	+	38.1208i	−0.888018	+	1.40611i
$736$			7.12921i			0.262786i
$737$	−7.77666	+	31.1887i	−0.286457	+	1.14885i
$738$	−21.2807	+	36.8593i	−0.783355	+	1.35681i
$739$	4.01288	+	2.31684i	0.147616	+	0.0852262i	0.571989	−	0.820261i	$-0.306172\pi$
$739$	4.01288	+	2.31684i	0.147616	+	0.0852262i	−0.424373	+	0.905488i	$0.639505\pi$
$740$	−5.34670	−	20.3319i	−0.196549	−	0.747416i
$741$		−	17.3587i		−	0.637688i
$742$	−14.7784	−	2.20967i	−0.542533	−	0.0811194i
$743$	−30.3368			−1.11295			−0.556475	−	0.830864i	$-0.687847\pi$
$743$	−30.3368			−1.11295			−0.556475	+	0.830864i	$0.687847\pi$
$744$	2.44621	−	1.41232i	0.0896823	−	0.0517781i
$745$	0.621853	−	0.616095i	0.0227829	−	0.0225720i
$746$	−7.76959	+	13.4573i	−0.284465	+	0.492707i
$747$	−18.4204	+	10.6350i	−0.673968	+	0.389116i
$748$	3.68660	+	3.56020i	0.134795	+	0.130174i
$749$	−40.0680	+	15.7801i	−1.46405	+	0.576591i
$750$	23.0877	−	22.4522i	0.843043	−	0.819840i
$751$	10.1668	+	17.6094i	0.370992	+	0.642577i	0.989718	−	0.143030i	$-0.0456844\pi$
$751$	10.1668	+	17.6094i	0.370992	+	0.642577i	−0.618727	+	0.785606i	$0.712351\pi$
$752$	−5.24754	+	9.08901i	−0.191358	+	0.331442i
$753$	−28.9342	−	16.7052i	−1.05442	−	0.608770i
$754$	9.46776	+	16.3986i	0.344796	+	0.597203i
$755$	5.84062	+	1.59414i	0.212562	+	0.0580166i
$756$	13.7001	+	10.8991i	0.498268	+	0.396395i
$757$		−	30.7879i		−	1.11901i	−0.828828	−	0.559503i	$-0.810992\pi$
$757$		−	30.7879i		−	1.11901i	0.828828	−	0.559503i	$-0.189008\pi$
$758$	−11.4667	−	19.8609i	−0.416488	−	0.721379i
$759$	65.4704	−	18.7724i	2.37643	−	0.681394i
$760$	−1.40232	−	1.41542i	−0.0508674	−	0.0513428i
$761$	−19.2459	−	33.3348i	−0.697662	−	1.20839i	−0.969275	−	0.245979i	$-0.920891\pi$
$761$	−19.2459	−	33.3348i	−0.697662	−	1.20839i	0.271614	−	0.962406i	$-0.412443\pi$
$762$	−34.4119			−1.24661
$763$	−23.5053	+	29.5462i	−0.850951	+	1.06964i
$764$	7.90304			0.285922
$765$	−4.65495	−	17.7014i	−0.168300	−	0.639996i
$766$	14.9019	−	25.8109i	0.538428	−	0.932585i
$767$	14.1044	−	24.4296i	0.509281	−	0.882101i
$768$	−1.44024	−	2.49457i	−0.0519701	−	0.0900149i
$769$	−29.6119			−1.06783			−0.533916	−	0.845537i	$-0.679280\pi$
$769$	−29.6119			−1.06783			−0.533916	+	0.845537i	$0.679280\pi$
$770$	−15.5100	−	12.0183i	−0.558942	−	0.433109i
$771$	30.1988			1.08758
$772$	−7.13707	−	12.3618i	−0.256869	−	0.444910i
$773$	−18.4694	+	31.9899i	−0.664297	+	1.15060i	0.315179	+	0.949032i	$0.397936\pi$
$773$	−18.4694	+	31.9899i	−0.664297	+	1.15060i	−0.979475	+	0.201563i	$0.935398\pi$
$774$	−0.799970	+	1.38559i

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.44024 + 2.49457i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16254 + 0.568686i) q^{5} -2.88048 q^{6} +(0.391243 - 2.61666i) q^{7} -1.00000 q^{8} +(-2.64857 - 4.58746i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.44024 + 2.49457i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16254 + 0.568686i) q^{5} -2.88048 q^{6} +(0.391243 - 2.61666i) q^{7} -1.00000 q^{8} +(-2.64857 - 4.58746i) q^{9} +(-1.57377 - 1.58848i) q^{10} +(0.914142 + 3.18816i) q^{11} +(-1.44024 - 2.49457i) q^{12} -6.76312i q^{13} +(2.46172 - 0.969505i) q^{14} +(1.69596 - 6.21365i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.33823 - 0.772629i) q^{17} +(2.64857 - 4.58746i) q^{18} +(-0.445529 - 0.771679i) q^{19} +(0.588776 - 2.15716i) q^{20} +(5.96396 + 4.74460i) q^{21} +(-2.30395 + 2.38575i) q^{22} +(-6.17407 + 3.56460i) q^{23} +(1.44024 - 2.49457i) q^{24} +(4.35319 - 2.45962i) q^{25} +(5.85703 - 3.38156i) q^{26} +6.61688 q^{27} +(2.07048 + 1.64716i) q^{28} +2.79982i q^{29} +(6.22916 - 1.63809i) q^{30} +(0.849237 + 0.490307i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-9.26965 - 2.31132i) q^{33} -1.54526i q^{34} +(0.641979 + 5.88114i) q^{35} +5.29715 q^{36} +(8.14224 - 4.70093i) q^{37} +(0.445529 - 0.771679i) q^{38} +(16.8710 + 9.74050i) q^{39} +(2.16254 - 0.568686i) q^{40} -8.03479 q^{41} +(-1.12697 + 7.53724i) q^{42} -0.302038 q^{43} +(-3.21810 - 0.802409i) q^{44} +(8.33648 + 8.41439i) q^{45} +(-6.17407 - 3.56460i) q^{46} +(-5.24754 - 9.08901i) q^{47} +2.88048 q^{48} +(-6.69386 - 2.04750i) q^{49} +(4.30669 + 2.54017i) q^{50} +(3.85475 - 2.22554i) q^{51} +(5.85703 + 3.38156i) q^{52} +(-4.89115 - 2.82391i) q^{53} +(3.30844 + 5.73039i) q^{54} +(-3.78993 - 6.37467i) q^{55} +(-0.391243 + 2.61666i) q^{56} +2.56667 q^{57} +(-2.42472 + 1.39991i) q^{58} +(3.61218 + 2.08549i) q^{59} +(4.53320 + 4.57557i) q^{60} +(-0.226973 - 0.393129i) q^{61} +0.980614i q^{62} +(-13.0401 + 5.13561i) q^{63} +1.00000 q^{64} +(3.84609 + 14.6255i) q^{65} +(-2.63316 - 9.18341i) q^{66} +(8.39321 + 4.84582i) q^{67} +(1.33823 - 0.772629i) q^{68} -20.5355i q^{69} +(-4.77223 + 3.49654i) q^{70} -4.72658 q^{71} +(2.64857 + 4.58746i) q^{72} +(-2.80161 - 1.61751i) q^{73} +(8.14224 + 4.70093i) q^{74} +(-0.133963 + 14.4018i) q^{75} +0.891058 q^{76} +(8.69999 - 1.14466i) q^{77} +19.4810i q^{78} +(7.09357 - 4.09547i) q^{79} +(1.57377 + 1.58848i) q^{80} +(-1.58417 + 2.74386i) q^{81} +(-4.01739 - 6.95833i) q^{82} -4.01538i q^{83} +(-7.09092 + 2.79264i) q^{84} +(3.33337 + 0.909810i) q^{85} +(-0.151019 - 0.261573i) q^{86} +(-6.98434 - 4.03241i) q^{87} +(-0.914142 - 3.18816i) q^{88} +(6.83580 - 3.94665i) q^{89} +(-3.11883 + 11.4268i) q^{90} +(-17.6968 - 2.64602i) q^{91} -7.12921i q^{92} +(-2.44621 + 1.41232i) q^{93} +(5.24754 - 9.08901i) q^{94} +(1.40232 + 1.41542i) q^{95} +(1.44024 + 2.49457i) q^{96} -19.1494 q^{97} +(-1.57374 - 6.82080i) q^{98} +(12.2044 - 12.6377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

Introduction

L-functions

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