LMFDB - Embedded newform 304.2.k.b.77.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.30
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28614 - 0.588093i) q^{2} +(1.00943 + 1.00943i) q^{3} +(1.30829 - 1.51273i) q^{4} +(1.26480 - 1.26480i) q^{5} +(1.89189 + 0.704623i) q^{6} +4.00933i q^{7} +(0.793017 - 2.71498i) q^{8} -0.962122i q^{9} +O(q^{10})$	\(q+(1.28614 - 0.588093i) q^{2} +(1.00943 + 1.00943i) q^{3} +(1.30829 - 1.51273i) q^{4} +(1.26480 - 1.26480i) q^{5} +(1.89189 + 0.704623i) q^{6} +4.00933i q^{7} +(0.793017 - 2.71498i) q^{8} -0.962122i q^{9} +(0.882889 - 2.37053i) q^{10} +(-3.73158 + 3.73158i) q^{11} +(2.84762 - 0.206367i) q^{12} +(-3.04804 - 3.04804i) q^{13} +(2.35786 + 5.15655i) q^{14} +2.55345 q^{15} +(-0.576732 - 3.95820i) q^{16} -0.118672 q^{17} +(-0.565817 - 1.23742i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-0.258577 - 3.56805i) q^{20} +(-4.04712 + 4.04712i) q^{21} +(-2.60481 + 6.99383i) q^{22} -4.63056i q^{23} +(3.54106 - 1.94008i) q^{24} +1.80054i q^{25} +(-5.71272 - 2.12766i) q^{26} +(3.99947 - 3.99947i) q^{27} +(6.06505 + 5.24538i) q^{28} +(3.30655 + 3.30655i) q^{29} +(3.28409 - 1.50167i) q^{30} -2.18760 q^{31} +(-3.06955 - 4.75162i) q^{32} -7.53350 q^{33} +(-0.152628 + 0.0697900i) q^{34} +(5.07102 + 5.07102i) q^{35} +(-1.45544 - 1.25874i) q^{36} +(2.54825 - 2.54825i) q^{37} +(-1.32528 - 0.493592i) q^{38} -6.15353i q^{39} +(-2.43091 - 4.43693i) q^{40} +4.76027i q^{41} +(-2.82507 + 7.58523i) q^{42} +(-8.31602 + 8.31602i) q^{43} +(0.762885 + 10.5269i) q^{44} +(-1.21690 - 1.21690i) q^{45} +(-2.72320 - 5.95553i) q^{46} +3.11908 q^{47} +(3.41334 - 4.57768i) q^{48} -9.07473 q^{49} +(1.05888 + 2.31574i) q^{50} +(-0.119790 - 0.119790i) q^{51} +(-8.59860 + 0.623142i) q^{52} +(1.97800 - 1.97800i) q^{53} +(2.79180 - 7.49591i) q^{54} +9.43944i q^{55} +(10.8853 + 3.17947i) q^{56} -1.42754i q^{57} +(6.19722 + 2.30811i) q^{58} +(1.94820 - 1.94820i) q^{59} +(3.34067 - 3.86269i) q^{60} +(-6.64200 - 6.64200i) q^{61} +(-2.81356 + 1.28651i) q^{62} +3.85746 q^{63} +(-6.74225 - 4.30605i) q^{64} -7.71034 q^{65} +(-9.68911 + 4.43039i) q^{66} +(-8.53000 - 8.53000i) q^{67} +(-0.155258 + 0.179519i) q^{68} +(4.67420 - 4.67420i) q^{69} +(9.50425 + 3.53980i) q^{70} -6.60033i q^{71} +(-2.61214 - 0.762979i) q^{72} +7.37248i q^{73} +(1.77879 - 4.77601i) q^{74} +(-1.81751 + 1.81751i) q^{75} +(-1.99477 + 0.144561i) q^{76} +(-14.9611 - 14.9611i) q^{77} +(-3.61885 - 7.91428i) q^{78} +12.3751 q^{79} +(-5.73581 - 4.27690i) q^{80} +5.18796 q^{81} +(2.79948 + 6.12236i) q^{82} +(8.11833 + 8.11833i) q^{83} +(0.827394 + 11.4170i) q^{84} +(-0.150097 + 0.150097i) q^{85} +(-5.80495 + 15.5861i) q^{86} +6.67542i q^{87} +(7.17196 + 13.0904i) q^{88} +17.7973i q^{89} +(-2.28074 - 0.849447i) q^{90} +(12.2206 - 12.2206i) q^{91} +(-7.00481 - 6.05813i) q^{92} +(-2.20822 - 2.20822i) q^{93} +(4.01157 - 1.83431i) q^{94} -1.78870 q^{95} +(1.69793 - 7.89488i) q^{96} +7.17865 q^{97} +(-11.6713 + 5.33678i) q^{98} +(3.59023 + 3.59023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.28614	−	0.588093i	0.909436	−	0.415844i
$2$	1.28614	−	0.588093i	0.909436	−	0.415844i
$3$	1.00943	+	1.00943i	0.582792	+	0.582792i	0.935669	−	0.352878i	$-0.114797\pi$
$3$	1.00943	+	1.00943i	0.582792	+	0.582792i	−0.352878	+	0.935669i	$0.614797\pi$
$4$	1.30829	−	1.51273i	0.654147	−	0.756367i
$5$	1.26480	−	1.26480i	0.565638	−	0.565638i	−0.365266	−	0.930903i	$-0.619022\pi$
$5$	1.26480	−	1.26480i	0.565638	−	0.565638i	0.930903	+	0.365266i	$0.119022\pi$
$6$	1.89189	+	0.704623i	0.772362	+	0.287661i
$7$			4.00933i			1.51538i	0.652612	+	0.757692i	$0.273673\pi$
$7$			4.00933i			1.51538i	−0.652612	+	0.757692i	$0.726327\pi$
$8$	0.793017	−	2.71498i	0.280374	−	0.959891i
$9$		−	0.962122i		−	0.320707i
$10$	0.882889	−	2.37053i	0.279194	−	0.749629i
$11$	−3.73158	+	3.73158i	−1.12511	+	1.12511i	−0.134153	+	0.990961i	$0.542831\pi$
$11$	−3.73158	+	3.73158i	−1.12511	+	1.12511i	−0.990961	+	0.134153i	$0.957169\pi$
$12$	2.84762	−	0.206367i	0.822036	−	0.0595731i
$13$	−3.04804	−	3.04804i	−0.845374	−	0.845374i	0.144178	−	0.989552i	$-0.453946\pi$
$13$	−3.04804	−	3.04804i	−0.845374	−	0.845374i	−0.989552	+	0.144178i	$0.953946\pi$
$14$	2.35786	+	5.15655i	0.630164	+	1.37815i
$15$	2.55345			0.659298
$16$	−0.576732	−	3.95820i	−0.144183	−	0.989551i
$17$	−0.118672			−0.0287821			−0.0143911	−	0.999896i	$-0.504581\pi$
$17$	−0.118672			−0.0287821			−0.0143911	+	0.999896i	$0.504581\pi$
$18$	−0.565817	−	1.23742i	−0.133364	−	0.291663i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	−0.258577	−	3.56805i	−0.0578196	−	0.797840i
$21$	−4.04712	+	4.04712i	−0.883154	+	0.883154i
$22$	−2.60481	+	6.99383i	−0.555346	+	1.49109i
$23$		−	4.63056i		−	0.965538i	−0.875748	−	0.482769i	$-0.839631\pi$
$23$		−	4.63056i		−	0.965538i	0.875748	−	0.482769i	$-0.160369\pi$
$24$	3.54106	−	1.94008i	0.722816	−	0.396017i
$25$			1.80054i			0.360108i
$26$	−5.71272	−	2.12766i	−1.12036	−	0.417269i
$27$	3.99947	−	3.99947i	0.769697	−	0.769697i
$28$	6.06505	+	5.24538i	1.14619	+	0.991285i
$29$	3.30655	+	3.30655i	0.614010	+	0.614010i	0.943989	−	0.329978i	$-0.107041\pi$
$29$	3.30655	+	3.30655i	0.614010	+	0.614010i	−0.329978	+	0.943989i	$0.607041\pi$
$30$	3.28409	−	1.50167i	0.599589	−	0.274165i
$31$	−2.18760			−0.392905			−0.196453	−	0.980513i	$-0.562942\pi$
$31$	−2.18760			−0.392905			−0.196453	+	0.980513i	$0.562942\pi$
$32$	−3.06955	−	4.75162i	−0.542624	−	0.839976i
$33$	−7.53350			−1.31141
$34$	−0.152628	+	0.0697900i	−0.0261755	+	0.0119689i
$35$	5.07102	+	5.07102i	0.857159	+	0.857159i
$36$	−1.45544	−	1.25874i	−0.242573	−	0.209790i
$37$	2.54825	−	2.54825i	0.418930	−	0.418930i	−0.465905	−	0.884835i	$-0.654271\pi$
$37$	2.54825	−	2.54825i	0.418930	−	0.418930i	0.884835	+	0.465905i	$0.154271\pi$
$38$	−1.32528	−	0.493592i	−0.214989	−	0.0800711i
$39$		−	6.15353i		−	0.985354i
$40$	−2.43091	−	4.43693i	−0.384360	−	0.701541i
$41$			4.76027i			0.743430i	0.928347	+	0.371715i	$0.121230\pi$
$41$			4.76027i			0.743430i	−0.928347	+	0.371715i	$0.878770\pi$
$42$	−2.82507	+	7.58523i	−0.435917	+	1.17043i
$43$	−8.31602	+	8.31602i	−1.26818	+	1.26818i	−0.321154	+	0.947027i	$0.604071\pi$
$43$	−8.31602	+	8.31602i	−1.26818	+	1.26818i	−0.947027	+	0.321154i	$0.895929\pi$
$44$	0.762885	+	10.5269i	0.115009	+	1.58699i
$45$	−1.21690	−	1.21690i	−0.181404	−	0.181404i
$46$	−2.72320	−	5.95553i	−0.401514	−	0.878095i
$47$	3.11908			0.454965			0.227482	−	0.973782i	$-0.426951\pi$
$47$	3.11908			0.454965			0.227482	+	0.973782i	$0.426951\pi$
$48$	3.41334	−	4.57768i	0.492674	−	0.660731i
$49$	−9.07473			−1.29639
$50$	1.05888	+	2.31574i	0.149749	+	0.327495i
$51$	−0.119790	−	0.119790i	−0.0167740	−	0.0167740i
$52$	−8.59860	+	0.623142i	−1.19241	+	0.0864142i
$53$	1.97800	−	1.97800i	0.271700	−	0.271700i	−0.558084	−	0.829784i	$-0.688463\pi$
$53$	1.97800	−	1.97800i	0.271700	−	0.271700i	0.829784	+	0.558084i	$0.188463\pi$
$54$	2.79180	−	7.49591i	0.379916	−	1.02006i
$55$			9.43944i			1.27281i
$56$	10.8853	+	3.17947i	1.45460	+	0.424874i
$57$		−	1.42754i		−	0.189083i
$58$	6.19722	+	2.30811i	0.813735	+	0.303070i
$59$	1.94820	−	1.94820i	0.253634	−	0.253634i	−0.568825	−	0.822459i	$-0.692602\pi$
$59$	1.94820	−	1.94820i	0.253634	−	0.253634i	0.822459	+	0.568825i	$0.192602\pi$
$60$	3.34067	−	3.86269i	0.431278	−	0.498672i
$61$	−6.64200	−	6.64200i	−0.850421	−	0.850421i	0.139764	−	0.990185i	$-0.455366\pi$
$61$	−6.64200	−	6.64200i	−0.850421	−	0.850421i	−0.990185	+	0.139764i	$0.955366\pi$
$62$	−2.81356	+	1.28651i	−0.357322	+	0.163387i
$63$	3.85746			0.485995
$64$	−6.74225	−	4.30605i	−0.842781	−	0.538257i
$65$	−7.71034			−0.956351
$66$	−9.68911	+	4.43039i	−1.19265	+	0.545344i
$67$	−8.53000	−	8.53000i	−1.04211	−	1.04211i	−0.999074	−	0.0430315i	$-0.986298\pi$
$67$	−8.53000	−	8.53000i	−1.04211	−	1.04211i	−0.0430315	−	0.999074i	$-0.513702\pi$
$68$	−0.155258	+	0.179519i	−0.0188278	+	0.0217699i
$69$	4.67420	−	4.67420i	0.562708	−	0.562708i
$70$	9.50425	+	3.53980i	1.13598	+	0.423086i
$71$		−	6.60033i		−	0.783315i	−0.920111	−	0.391658i	$-0.871902\pi$
$71$		−	6.60033i		−	0.783315i	0.920111	−	0.391658i	$-0.128098\pi$
$72$	−2.61214	−	0.762979i	−0.307844	−	0.0899180i
$73$			7.37248i			0.862884i	0.902141	+	0.431442i	$0.141995\pi$
$73$			7.37248i			0.862884i	−0.902141	+	0.431442i	$0.858005\pi$
$74$	1.77879	−	4.77601i	0.206780	−	0.555200i
$75$	−1.81751	+	1.81751i	−0.209868	+	0.209868i
$76$	−1.99477	+	0.144561i	−0.228816	+	0.0165823i
$77$	−14.9611	−	14.9611i	−1.70498	−	1.70498i
$78$	−3.61885	−	7.91428i	−0.409754	−	0.896116i
$79$	12.3751			1.39230			0.696151	−	0.717895i	$-0.254894\pi$
$79$	12.3751			1.39230			0.696151	+	0.717895i	$0.254894\pi$
$80$	−5.73581	−	4.27690i	−0.641283	−	0.478172i
$81$	5.18796			0.576440
$82$	2.79948	+	6.12236i	0.309151	+	0.676101i
$83$	8.11833	+	8.11833i	0.891103	+	0.891103i	0.994627	−	0.103524i	$-0.0330119\pi$
$83$	8.11833	+	8.11833i	0.891103	+	0.891103i	−0.103524	+	0.994627i	$0.533012\pi$
$84$	0.827394	+	11.4170i	0.0902761	+	1.24570i
$85$	−0.150097	+	0.150097i	−0.0162803	+	0.0162803i
$86$	−5.80495	+	15.5861i	−0.625964	+	1.68070i
$87$			6.67542i			0.715680i
$88$	7.17196	+	13.0904i	0.764533	+	1.39544i
$89$			17.7973i			1.88651i	0.332064	+	0.943257i	$0.392255\pi$
$89$			17.7973i			1.88651i	−0.332064	+	0.943257i	$0.607745\pi$
$90$	−2.28074	−	0.849447i	−0.240411	−	0.0895396i
$91$	12.2206	−	12.2206i	1.28107	−	1.28107i
$92$	−7.00481	−	6.05813i	−0.730302	−	0.631604i
$93$	−2.20822	−	2.20822i	−0.228982	−	0.228982i
$94$	4.01157	−	1.83431i	0.413761	−	0.189195i
$95$	−1.78870			−0.183517
$96$	1.69793	−	7.89488i	0.173294	−	0.805768i
$97$	7.17865			0.728882			0.364441	−	0.931227i	$-0.381260\pi$
$97$	7.17865			0.728882			0.364441	+	0.931227i	$0.381260\pi$
$98$	−11.6713	+	5.33678i	−1.17898	+	0.539097i
$99$	3.59023	+	3.59023i	0.360832	+	0.360832i
$100$	2.72374	+	2.35563i	0.272374	+	0.235563i
$101$	6.67243	−	6.67243i	0.663932	−	0.663932i	−0.292373	−	0.956304i	$-0.594445\pi$
$101$	6.67243	−	6.67243i	0.663932	−	0.663932i	0.956304	+	0.292373i	$0.0944448\pi$
$102$	−0.224515	−	0.0836189i	−0.0222303	−	0.00827951i
$103$			10.8947i			1.07348i	0.843746	+	0.536742i	$0.180345\pi$
$103$			10.8947i			1.07348i	−0.843746	+	0.536742i	$0.819655\pi$
$104$	−10.6925	+	5.85822i	−1.04849	+	0.574446i
$105$			10.2376i			0.999090i
$106$	1.38073	−	3.70723i	0.134109	−	0.360078i
$107$	−10.0439	+	10.0439i	−0.970983	+	0.970983i	−0.999591	−	0.0286081i	$-0.990893\pi$
$107$	−10.0439	+	10.0439i	−0.970983	+	0.970983i	0.0286081	+	0.999591i	$0.490893\pi$
$108$	−0.817652	−	11.2826i	−0.0786786	−	1.08567i
$109$	−1.40843	−	1.40843i	−0.134903	−	0.134903i	0.636431	−	0.771334i	$-0.280410\pi$
$109$	−1.40843	−	1.40843i	−0.134903	−	0.134903i	−0.771334	+	0.636431i	$0.780410\pi$
$110$	5.55126	+	12.1404i	0.529292	+	1.15754i
$111$	5.14454			0.488298
$112$	15.8698	−	2.31231i	1.49955	−	0.218493i
$113$	8.73527			0.821745			0.410872	−	0.911693i	$-0.365224\pi$
$113$	8.73527			0.821745			0.410872	+	0.911693i	$0.365224\pi$
$114$	−0.839527	−	1.83601i	−0.0786289	−	0.171959i
$115$	−5.85675	−	5.85675i	−0.546145	−	0.546145i
$116$	9.32786	−	0.675991i	0.866070	−	0.0627642i
$117$	−2.93258	+	2.93258i	−0.271117	+	0.271117i
$118$	1.35993	−	3.65137i	0.125192	−	0.336136i
$119$		−	0.475795i		−	0.0436160i
$120$	2.02493	−	6.93257i	0.184850	−	0.632854i
$121$		−	16.8494i		−	1.53176i
$122$	−12.4486	−	4.63641i	−1.12705	−	0.419761i
$123$	−4.80514	+	4.80514i	−0.433265	+	0.433265i
$124$	−2.86203	+	3.30926i	−0.257018	+	0.297181i
$125$	8.60135	+	8.60135i	0.769328	+	0.769328i
$126$	4.96123	−	2.26855i	0.441981	−	0.202098i
$127$	9.65187			0.856465			0.428232	−	0.903669i	$-0.359136\pi$
$127$	9.65187			0.856465			0.428232	+	0.903669i	$0.359136\pi$
$128$	−11.2038	−	1.57311i	−0.990286	−	0.139044i
$129$	−16.7888			−1.47817
$130$	−9.91656	+	4.53440i	−0.869739	+	0.397693i
$131$	−3.74786	−	3.74786i	−0.327452	−	0.327452i	0.524165	−	0.851617i	$-0.324378\pi$
$131$	−3.74786	−	3.74786i	−0.327452	−	0.327452i	−0.851617	+	0.524165i	$0.824378\pi$
$132$	−9.85603	+	11.3962i	−0.857858	+	0.991910i
$133$	2.83503	−	2.83503i	0.245828	−	0.245828i
$134$	−15.9872	−	5.95431i	−1.38108	−	0.514374i
$135$		−	10.1171i		−	0.870740i
$136$	−0.0941088	+	0.322192i	−0.00806976	+	0.0276277i
$137$		−	5.06626i		−	0.432840i	−0.976300	−	0.216420i	$-0.930562\pi$
$137$		−	5.06626i		−	0.432840i	0.976300	−	0.216420i	$-0.0694380\pi$
$138$	3.26280	−	8.76053i	0.277748	−	0.745746i
$139$	14.4929	−	14.4929i	1.22927	−	1.22927i	0.265035	−	0.964239i	$-0.414616\pi$
$139$	14.4929	−	14.4929i	1.22927	−	1.22927i	0.964239	−	0.265035i	$-0.0853836\pi$
$140$	14.3055	−	1.03672i	1.20903	−	0.0876189i
$141$	3.14848	+	3.14848i	0.265150	+	0.265150i
$142$	−3.88161	−	8.48893i	−0.325737	−	0.712375i
$143$	22.7480			1.90228
$144$	−3.80827	+	0.554886i	−0.317356	+	0.0462405i
$145$	8.36427			0.694615
$146$	4.33570	+	9.48202i	0.358825	+	0.784738i
$147$	−9.16026	−	9.16026i	−0.755526	−	0.755526i
$148$	−0.520966	−	7.18870i	−0.0428231	−	0.590907i
$149$	16.5960	−	16.5960i	1.35960	−	1.35960i	0.485189	−	0.874409i	$-0.338751\pi$
$149$	16.5960	−	16.5960i	1.35960	−	1.35960i	0.874409	−	0.485189i	$-0.161249\pi$
$150$	−1.26870	+	3.40643i	−0.103589	+	0.278134i
$151$			3.33681i			0.271546i	0.990740	+	0.135773i	$0.0433518\pi$
$151$			3.33681i			0.271546i	−0.990740	+	0.135773i	$0.956648\pi$
$152$	−2.48053	+	1.35903i	−0.201198	+	0.110232i
$153$			0.114177i			0.00923065i
$154$	−28.0406	−	10.4435i	−2.25958	−	0.841564i
$155$	−2.76689	+	2.76689i	−0.222242	+	0.222242i
$156$	−9.30866	−	8.05063i	−0.745289	−	0.644566i
$157$	−8.60291	−	8.60291i	−0.686587	−	0.686587i	0.274889	−	0.961476i	$-0.411359\pi$
$157$	−8.60291	−	8.60291i	−0.686587	−	0.686587i	−0.961476	+	0.274889i	$0.911359\pi$
$158$	15.9160	−	7.27768i	1.26621	−	0.578981i
$159$	3.99329			0.316689
$160$	−9.89225	−	2.12749i	−0.782051	−	0.168193i
$161$	18.5654			1.46316
$162$	6.67242	−	3.05100i	0.524235	−	0.239709i
$163$	−12.6781	−	12.6781i	−0.993022	−	0.993022i	0.00695390	−	0.999976i	$-0.497786\pi$
$163$	−12.6781	−	12.6781i	−0.993022	−	0.993022i	−0.999976	+	0.00695390i	$0.997786\pi$
$164$	7.20103	+	6.22784i	0.562306	+	0.486312i
$165$	−9.52840	+	9.52840i	−0.741785	+	0.741785i
$166$	15.2156	+	5.66695i	1.18096	+	0.439841i
$167$			13.3531i			1.03329i	0.856200	+	0.516645i	$0.172819\pi$
$167$			13.3531i			1.03329i	−0.856200	+	0.516645i	$0.827181\pi$
$168$	7.77842	+	14.1973i	0.600118	+	1.09534i
$169$			5.58107i			0.429313i
$170$	−0.104774	+	0.281316i	−0.00803581	+	0.0215759i
$171$	−0.680323	+	0.680323i	−0.0520256	+	0.0520256i
$172$	1.70013	+	23.4597i	0.129634	+	1.78879i
$173$	−2.13641	−	2.13641i	−0.162428	−	0.162428i	0.621213	−	0.783641i	$-0.286640\pi$
$173$	−2.13641	−	2.13641i	−0.162428	−	0.162428i	−0.783641	+	0.621213i	$0.786640\pi$
$174$	3.92577	+	8.58550i	0.297612	+	0.650865i
$175$	−7.21895			−0.545702
$176$	16.9225	+	12.6182i	1.27558	+	0.951135i
$177$	3.93313			0.295632
$178$	10.4665	+	22.8898i	0.784496	+	1.71566i
$179$	3.34910	+	3.34910i	0.250323	+	0.250323i	0.821103	−	0.570780i	$-0.193359\pi$
$179$	3.34910	+	3.34910i	0.250323	+	0.250323i	−0.570780	+	0.821103i	$0.693359\pi$
$180$	−3.43290	+	0.248783i	−0.255873	+	0.0185432i
$181$	2.93587	−	2.93587i	0.218222	−	0.218222i	−0.589527	−	0.807749i	$-0.700686\pi$
$181$	2.93587	−	2.93587i	0.218222	−	0.218222i	0.807749	+	0.589527i	$0.200686\pi$
$182$	8.53051	−	22.9042i	0.632324	−	1.69777i
$183$		−	13.4092i		−	0.991237i
$184$	−12.5719	−	3.67211i	−0.926811	−	0.270712i
$185$		−	6.44609i		−	0.473926i
$186$	−4.13871	−	1.54144i	−0.303465	−	0.113024i
$187$	0.442833	−	0.442833i	0.0323832	−	0.0323832i
$188$	4.08068	−	4.71834i	0.297614	−	0.344121i
$189$	16.0352	+	16.0352i	1.16639	+	1.16639i
$190$	−2.30052	+	1.05192i	−0.166897	+	0.0763145i
$191$	7.29550			0.527884			0.263942	−	0.964539i	$-0.414977\pi$
$191$	7.29550			0.527884			0.263942	+	0.964539i	$0.414977\pi$
$192$	−2.45915	−	11.1524i	−0.177474	−	0.804858i
$193$	−12.7784			−0.919812			−0.459906	−	0.887968i	$-0.652117\pi$
$193$	−12.7784			−0.919812			−0.459906	+	0.887968i	$0.652117\pi$
$194$	9.23273	−	4.22171i	0.662871	−	0.303101i
$195$	−7.78302	−	7.78302i	−0.557353	−	0.557353i
$196$	−11.8724	+	13.7277i	−0.848030	+	0.980547i
$197$	−7.64451	+	7.64451i	−0.544649	+	0.544649i	−0.924888	−	0.380239i	$-0.875842\pi$
$197$	−7.64451	+	7.64451i	−0.544649	+	0.544649i	0.380239	+	0.924888i	$0.375842\pi$
$198$	6.72892	+	2.50614i	0.478203	+	0.178104i
$199$		−	18.2527i		−	1.29390i	−0.762532	−	0.646951i	$-0.776044\pi$
$199$		−	18.2527i		−	1.29390i	0.762532	−	0.646951i	$-0.223956\pi$
$200$	4.88843	+	1.42786i	0.345664	+	0.100965i
$201$		−	17.2208i		−	1.21466i
$202$	4.65765	−	12.5057i	0.327711	−	0.879896i
$203$	−13.2570	+	13.2570i	−0.930462	+	0.930462i
$204$	−0.337932	+	0.0244900i	−0.0236600	+	0.00171464i
$205$	6.02081	+	6.02081i	0.420512	+	0.420512i
$206$	6.40708	+	14.0120i	0.446402	+	0.976265i
$207$	−4.45516			−0.309655
$208$	−10.3069	+	13.8227i	−0.714652	+	0.958429i
$209$	5.27725			0.365035
$210$	6.02067	+	13.1670i	0.415466	+	0.908609i
$211$	−17.9545	−	17.9545i	−1.23604	−	1.23604i	−0.961607	−	0.274429i	$-0.911511\pi$
$211$	−17.9545	−	17.9545i	−1.23604	−	1.23604i	−0.274429	−	0.961607i	$-0.588489\pi$
$212$	−0.404384	−	5.58001i	−0.0277732	−	0.383236i
$213$	6.66254	−	6.66254i	0.456510	−	0.456510i
$214$	−7.01110	+	18.8246i	−0.479269	+	1.28682i
$215$			21.0363i			1.43466i
$216$	−7.68683	−	14.0301i	−0.523022	−	0.954629i
$217$		−	8.77083i		−	0.595402i
$218$	−2.63973	−	0.983149i	−0.178785	−	0.0665872i
$219$	−7.44197	+	7.44197i	−0.502882	+	0.502882i
$220$	14.2794	+	12.3496i	0.962714	+	0.832607i
$221$	0.361716	+	0.361716i	0.0243317	+	0.0243317i
$222$	6.61658	−	3.02547i	0.444076	−	0.203056i
$223$	4.76909			0.319362			0.159681	−	0.987169i	$-0.448953\pi$
$223$	4.76909			0.319362			0.159681	+	0.987169i	$0.448953\pi$
$224$	19.0508	−	12.3068i	1.27289	−	0.822284i
$225$	1.73234			0.115489
$226$	11.2347	−	5.13714i	0.747324	−	0.341718i
$227$	10.4633	+	10.4633i	0.694472	+	0.694472i	0.963213	−	0.268740i	$-0.0866074\pi$
$227$	10.4633	+	10.4633i	0.694472	+	0.694472i	−0.268740	+	0.963213i	$0.586607\pi$
$228$	−2.15949	−	1.86765i	−0.143016	−	0.123688i
$229$	−12.6095	+	12.6095i	−0.833261	+	0.833261i	−0.987961	−	0.154700i	$-0.950559\pi$
$229$	−12.6095	+	12.6095i	−0.833261	+	0.833261i	0.154700	+	0.987961i	$0.450559\pi$
$230$	−10.9769	−	4.08827i	−0.723795	−	0.269573i
$231$		−	30.2043i		−	1.98730i
$232$	11.5994	−	6.35506i	0.761535	−	0.417230i
$233$			0.447025i			0.0292856i	0.999893	+	0.0146428i	$0.00466111\pi$
$233$			0.447025i			0.0292856i	−0.999893	+	0.0146428i	$0.995339\pi$
$234$	−2.04707	+	5.49633i	−0.133821	+	0.359307i
$235$	3.94503	−	3.94503i	0.257345	−	0.257345i
$236$	−0.398291	−	5.49593i	−0.0259265	−	0.357755i
$237$	12.4917	+	12.4917i	0.811422	+	0.811422i
$238$	−0.279811	−	0.611937i	−0.0181375	−	0.0396660i
$239$	−20.5775			−1.33105			−0.665523	−	0.746377i	$-0.731792\pi$
$239$	−20.5775			−1.33105			−0.665523	+	0.746377i	$0.731792\pi$
$240$	−1.47266	−	10.1071i	−0.0950596	−	0.652409i
$241$	20.1353			1.29703			0.648513	−	0.761203i	$-0.275391\pi$
$241$	20.1353			1.29703			0.648513	+	0.761203i	$0.275391\pi$
$242$	−9.90898	−	21.6706i	−0.636973	−	1.39304i
$243$	−6.76154	−	6.76154i	−0.433753	−	0.433753i
$244$	−18.7373	+	1.35789i	−1.19953	+	0.0869302i
$245$	−11.4778	+	11.4778i	−0.733288	+	0.733288i
$246$	−3.35420	+	9.00593i	−0.213856	+	0.574197i
$247$			4.31058i			0.274275i
$248$	−1.73481	+	5.93930i	−0.110160	+	0.377146i
$249$			16.3897i			1.03866i
$250$	16.1209	+	6.00412i	1.01958	+	0.379734i
$251$	−6.88187	+	6.88187i	−0.434380	+	0.434380i	−0.890115	−	0.455735i	$-0.849376\pi$
$251$	−6.88187	+	6.88187i	−0.434380	+	0.434380i	0.455735	+	0.890115i	$0.349376\pi$
$252$	5.04670	−	5.83532i	0.317912	−	0.367591i
$253$	17.2793	+	17.2793i	1.08634	+	1.08634i
$254$	12.4136	−	5.67619i	0.778900	−	0.356156i
$255$	−0.303023			−0.0189760
$256$	−15.3348	+	4.56564i	−0.958423	+	0.285353i
$257$	27.9591			1.74404			0.872021	−	0.489468i	$-0.162809\pi$
$257$	27.9591			1.74404			0.872021	+	0.489468i	$0.162809\pi$
$258$	−21.5927	+	9.87337i	−1.34430	+	0.614689i
$259$	10.2168	+	10.2168i	0.634840	+	0.634840i
$260$	−10.0874	+	11.6637i	−0.625594	+	0.723352i
$261$	3.18130	−	3.18130i	0.196918	−	0.196918i
$262$	−7.02435	−	2.61617i	−0.433966	−	0.161628i
$263$			16.8374i			1.03824i	0.854701	+	0.519120i	$0.173740\pi$
$263$			16.8374i			1.03824i	−0.854701	+	0.519120i	$0.826260\pi$
$264$	−5.97419	+	20.4533i	−0.367686	+	1.25881i
$265$		−	5.00358i		−	0.307367i
$266$	1.97897	−	5.31349i	0.121339	−	0.325791i
$267$	−17.9651	+	17.9651i	−1.09945	+	1.09945i
$268$	−24.0634	+	1.74387i	−1.46990	+	0.106524i
$269$	−0.580143	−	0.580143i	−0.0353720	−	0.0353720i	0.689200	−	0.724572i	$-0.257962\pi$
$269$	−0.580143	−	0.580143i	−0.0353720	−	0.0353720i	−0.724572	+	0.689200i	$0.757962\pi$
$270$	−5.94978	−	13.0120i	−0.362092	−	0.791882i
$271$	−32.1665			−1.95398			−0.976989	−	0.213288i	$-0.931583\pi$
$271$	−32.1665			−1.95398			−0.976989	+	0.213288i	$0.931583\pi$
$272$	0.0684418	+	0.469727i	0.00414990	+	0.0284814i
$273$	24.6715			1.49319
$274$	−2.97943	−	6.51590i	−0.179994	−	0.393640i
$275$	−6.71885	−	6.71885i	−0.405162	−	0.405162i
$276$	−0.955595	−	13.1861i	−0.0575201	−	0.793708i
$277$	8.40053	−	8.40053i	0.504739	−	0.504739i	−0.408168	−	0.912907i	$-0.633832\pi$
$277$	8.40053	−	8.40053i	0.504739	−	0.504739i	0.912907	+	0.408168i	$0.133832\pi$
$278$	10.1167	−	27.1631i	0.606759	−	1.62913i
$279$			2.10474i			0.126008i
$280$	17.7891	−	9.74632i	1.06310	−	0.582454i
$281$			15.1655i			0.904699i	0.891841	+	0.452349i	$0.149414\pi$
$281$			15.1655i			0.904699i	−0.891841	+	0.452349i	$0.850586\pi$
$282$	5.90097	+	2.19778i	0.351398	+	0.130876i
$283$	10.0270	−	10.0270i	0.596045	−	0.596045i	−0.343213	−	0.939258i	$-0.611515\pi$
$283$	10.0270	−	10.0270i	0.596045	−	0.596045i	0.939258	+	0.343213i	$0.111515\pi$
$284$	−9.98455	−	8.63518i	−0.592474	−	0.512404i
$285$	−1.80556	−	1.80556i	−0.106952	−	0.106952i
$286$	29.2570	−	13.3779i	1.73000	−	0.791053i
$287$	−19.0855			−1.12658
$288$	−4.57164	+	2.95328i	−0.269386	+	0.174024i
$289$	−16.9859			−0.999172
$290$	10.7576	−	4.91896i	0.631708	−	0.288852i
$291$	7.24631	+	7.24631i	0.424786	+	0.424786i
$292$	11.1526	+	9.64538i	0.652657	+	0.564453i
$293$	−4.42160	+	4.42160i	−0.258313	+	0.258313i	−0.824368	−	0.566055i	$-0.808469\pi$
$293$	−4.42160	+	4.42160i	−0.258313	+	0.258313i	0.566055	+	0.824368i	$0.308469\pi$
$294$	−17.1684	−	6.39427i	−1.00128	−	0.372921i
$295$		−	4.92819i		−	0.286930i
$296$	−4.89765	−	8.93927i	−0.284670	−	0.519584i
$297$			29.8486i			1.73199i
$298$	11.5847	−	31.1047i	0.671086	−	1.80185i
$299$	−14.1141	+	14.1141i	−0.816241	+	0.816241i
$300$	0.371572	+	5.12724i	0.0214527	+	0.296022i
$301$	−33.3417	−	33.3417i	−1.92178	−	1.92178i
$302$	1.96235	+	4.29160i	0.112921	+	0.246954i
$303$	13.4706			0.773868
$304$	−2.39106	+	3.20668i	−0.137137	+	0.183916i
$305$	−16.8017			−0.962061
$306$	0.0671465	+	0.146847i	0.00383851	+	0.00839468i
$307$	9.99121	+	9.99121i	0.570228	+	0.570228i	0.932192	−	0.361964i	$-0.117894\pi$
$307$	9.99121	+	9.99121i	0.570228	+	0.570228i	−0.361964	+	0.932192i	$0.617894\pi$
$308$	−42.2058	+	3.05866i	−2.40490	+	0.174283i
$309$	−10.9974	+	10.9974i	−0.625618	+	0.625618i
$310$	−1.93141	+	5.18579i	−0.109697	+	0.294533i
$311$			5.33290i			0.302401i	0.988503	+	0.151201i	$0.0483139\pi$
$311$			5.33290i			0.302401i	−0.988503	+	0.151201i	$0.951686\pi$
$312$	−16.7067	−	4.87986i	−0.945832	−	0.276267i
$313$			5.42834i			0.306828i	0.988162	+	0.153414i	$0.0490268\pi$
$313$			5.42834i			0.306828i	−0.988162	+	0.153414i	$0.950973\pi$
$314$	−16.1238	−	6.00521i	−0.909920	−	0.338893i
$315$	4.87894	−	4.87894i	0.274897	−	0.274897i
$316$	16.1902	−	18.7202i	0.910770	−	1.05309i
$317$	−24.7189	−	24.7189i	−1.38835	−	1.38835i	−0.828783	−	0.559570i	$-0.810966\pi$
$317$	−24.7189	−	24.7189i	−1.38835	−	1.38835i	−0.559570	−	0.828783i	$-0.689034\pi$
$318$	5.13592	−	2.34843i	0.288008	−	0.131693i
$319$	−24.6773			−1.38166
$320$	−13.9739	+	3.08131i	−0.781167	+	0.172250i
$321$	−20.2772			−1.13176
$322$	23.8777	−	10.9182i	1.33065	−	0.608447i
$323$	0.0839137	+	0.0839137i	0.00466908	+	0.00466908i
$324$	6.78737	−	7.84800i	0.377076	−	0.436000i
$325$	5.48811	−	5.48811i	0.304426	−	0.304426i
$326$	−23.7616	−	8.84984i	−1.31603	−	0.490147i
$327$		−	2.84342i		−	0.157241i
$328$	12.9240	+	3.77498i	0.713611	+	0.208438i
$329$			12.5054i			0.689447i
$330$	−6.65124	+	17.8584i	−0.366139	+	0.983073i
$331$	6.72087	−	6.72087i	0.369413	−	0.369413i	−0.497850	−	0.867263i	$-0.665877\pi$
$331$	6.72087	−	6.72087i	0.369413	−	0.369413i	0.867263	+	0.497850i	$0.165877\pi$
$332$	22.9021	−	1.65971i	1.25691	−	0.0910886i
$333$	−2.45173	−	2.45173i	−0.134354	−	0.134354i
$334$	7.85283	+	17.1739i	0.429688	+	0.939712i
$335$	−21.5776			−1.17891
$336$	18.3534	+	13.6852i	1.00126	+	0.746590i
$337$	−19.3969			−1.05662			−0.528308	−	0.849053i	$-0.677173\pi$
$337$	−19.3969			−1.05662			−0.528308	+	0.849053i	$0.677173\pi$
$338$	3.28218	+	7.17801i	0.178527	+	0.390433i
$339$	8.81760	+	8.81760i	0.478906	+	0.478906i
$340$	0.0306858	+	0.423427i	0.00166417	+	0.0229636i
$341$	8.16321	−	8.16321i	0.442063	−	0.442063i
$342$	−0.474895	+	1.27508i	−0.0256794	+	0.0689485i
$343$		−	8.31829i		−	0.449146i
$344$	15.9831	+	29.1726i	0.861751	+	1.57288i
$345$		−	11.8239i		−	0.636578i
$346$	−4.00412	−	1.49131i	−0.215263	−	0.0801732i
$347$	7.86897	−	7.86897i	0.422429	−	0.422429i	−0.463610	−	0.886039i	$-0.653446\pi$
$347$	7.86897	−	7.86897i	0.422429	−	0.422429i	0.886039	+	0.463610i	$0.153446\pi$
$348$	10.0981	+	8.73342i	0.541317	+	0.468160i
$349$	8.73092	+	8.73092i	0.467356	+	0.467356i	0.901057	−	0.433701i	$-0.142793\pi$
$349$	8.73092	+	8.73092i	0.467356	+	0.467356i	−0.433701	+	0.901057i	$0.642793\pi$
$350$	−9.28456	+	4.24541i	−0.496281	+	0.226927i
$351$	−24.3810			−1.30136
$352$	29.1853	+	6.27679i	1.55558	+	0.334554i
$353$	−14.6825			−0.781471			−0.390735	−	0.920503i	$-0.627779\pi$
$353$	−14.6825			−0.781471			−0.390735	+	0.920503i	$0.627779\pi$
$354$	5.05854	−	2.31304i	0.268858	−	0.122937i
$355$	−8.34813	−	8.34813i	−0.443073	−	0.443073i
$356$	26.9226	+	23.2842i	1.42690	+	1.23406i
$357$	0.480279	−	0.480279i	0.0254191	−	0.0254191i
$358$	6.27697	+	2.33782i	0.331748	+	0.123557i
$359$		−	5.49869i		−	0.290210i	−0.989416	−	0.145105i	$-0.953648\pi$
$359$		−	5.49869i		−	0.290210i	0.989416	−	0.145105i	$-0.0463520\pi$
$360$	−4.26887	+	2.33883i	−0.224989	+	0.123267i
$361$			1.00000i			0.0526316i
$362$	2.04937	−	5.50250i	0.107712	−	0.289205i
$363$	17.0082	−	17.0082i	0.892697	−	0.892697i
$364$	−2.49838	−	34.4746i	−0.130951	−	1.80696i
$365$	9.32475	+	9.32475i	0.488080	+	0.488080i
$366$	−7.88585	−	17.2461i	−0.412200	−	0.901467i
$367$	−29.2177			−1.52515			−0.762577	−	0.646898i	$-0.776066\pi$
$367$	−29.2177			−1.52515			−0.762577	+	0.646898i	$0.776066\pi$
$368$	−18.3287	+	2.67059i	−0.955449	+	0.139214i
$369$	4.57996			0.238423
$370$	−3.79089	−	8.29055i	−0.197079	−	0.431005i
$371$	7.93047	+	7.93047i	0.411730	+	0.411730i
$372$	−6.22946	+	0.451449i	−0.322982	+	0.0234066i
$373$	−15.5789	+	15.5789i	−0.806646	+	0.806646i	−0.984125	−	0.177478i	$-0.943206\pi$
$373$	−15.5789	+	15.5789i	−0.806646	+	0.806646i	0.177478	+	0.984125i	$0.443206\pi$
$374$	0.309117	−	0.829971i	0.0159841	−	0.0429168i
$375$			17.3648i			0.896717i
$376$	2.47349	−	8.46825i	0.127560	−	0.436717i
$377$		−	20.1570i		−	1.03814i
$378$	30.0536	+	11.1933i	1.54579	+	0.575719i
$379$	−1.76582	+	1.76582i	−0.0907043	+	0.0907043i	−0.751003	−	0.660299i	$-0.770430\pi$
$379$	−1.76582	+	1.76582i	−0.0907043	+	0.0907043i	0.660299	+	0.751003i	$0.270430\pi$
$380$	−2.34015	+	2.70583i	−0.120047	+	0.138806i
$381$	9.74284	+	9.74284i	0.499141	+	0.499141i
$382$	9.38301	−	4.29043i	0.480077	−	0.219517i
$383$	31.4757			1.60833			0.804167	−	0.594404i	$-0.202612\pi$
$383$	31.4757			1.60833			0.804167	+	0.594404i	$0.202612\pi$
$384$	−9.72147	−	12.8973i	−0.496097	−	0.658165i
$385$	−37.8458			−1.92880
$386$	−16.4348	+	7.51490i	−0.836510	+	0.382498i
$387$	8.00103	+	8.00103i	0.406715	+	0.406715i
$388$	9.39179	−	10.8594i	0.476796	−	0.551302i
$389$	−2.17442	+	2.17442i	−0.110248	+	0.110248i	−0.760079	−	0.649831i	$-0.774840\pi$
$389$	−2.17442	+	2.17442i	−0.110248	+	0.110248i	0.649831	+	0.760079i	$0.274840\pi$
$390$	−14.5872	−	5.43289i	−0.738649	−	0.275105i
$391$			0.549517i			0.0277903i
$392$	−7.19642	+	24.6377i	−0.363474	+	1.24439i
$393$		−	7.56637i		−	0.381673i
$394$	−5.33621	+	14.3276i	−0.268834	+	0.721812i
$395$	15.6520	−	15.6520i	0.787539	−	0.787539i
$396$	10.1282	−	0.733988i	0.508959	−	0.0368843i
$397$	8.89871	+	8.89871i	0.446613	+	0.446613i	0.894227	−	0.447614i	$-0.147726\pi$
$397$	8.89871	+	8.89871i	0.446613	+	0.446613i	−0.447614	+	0.894227i	$0.647726\pi$
$398$	−10.7343	−	23.4755i	−0.538062	−	1.17672i
$399$	5.72349			0.286533
$400$	7.12690	−	1.03843i	0.356345	−	0.0519214i
$401$	2.55419			0.127550			0.0637752	−	0.997964i	$-0.479686\pi$
$401$	2.55419			0.127550			0.0637752	+	0.997964i	$0.479686\pi$
$402$	−10.1274	−	22.1483i	−0.505110	−	1.10466i
$403$	6.66790	+	6.66790i	0.332152	+	0.332152i
$404$	−1.36411	−	18.8231i	−0.0678672	−	0.936485i
$405$	6.56175	−	6.56175i	0.326056	−	0.326056i
$406$	−9.25400	+	24.8467i	−0.459268	+	1.23312i
$407$			19.0180i			0.942688i
$408$	−0.420224	+	0.230233i	−0.0208042	+	0.0113982i
$409$			31.4467i			1.55494i	0.628921	+	0.777469i	$0.283497\pi$
$409$			31.4467i			1.55494i	−0.628921	+	0.777469i	$0.716503\pi$
$410$	11.2844	+	4.20279i	0.557296	+	0.207561i
$411$	5.11401	−	5.11401i	0.252255	−	0.252255i
$412$	16.4808	+	14.2534i	0.811949	+	0.702217i
$413$	7.81098	+	7.81098i	0.384353	+	0.384353i
$414$	−5.72995	+	2.62005i	−0.281612	+	0.128768i
$415$	20.5362			1.00808
$416$	−5.12702	+	23.8392i	−0.251373	+	1.16881i
$417$	29.2590			1.43282
$418$	6.78726	−	3.10351i	0.331976	−	0.151798i
$419$	5.52372	+	5.52372i	0.269851	+	0.269851i	0.829040	−	0.559189i	$-0.188887\pi$
$419$	5.52372	+	5.52372i	0.269851	+	0.269851i	−0.559189	+	0.829040i	$0.688887\pi$
$420$	15.4868	+	13.3938i	0.755679	+	0.653552i
$421$	−4.71177	+	4.71177i	−0.229638	+	0.229638i	−0.812541	−	0.582904i	$-0.801916\pi$
$421$	−4.71177	+	4.71177i	−0.229638	+	0.229638i	0.582904	+	0.812541i	$0.301916\pi$
$422$	−33.6508	−	12.5330i	−1.63809	−	0.610097i
$423$		−	3.00094i		−	0.145911i
$424$	−3.80165	−	6.93883i	−0.184625	−	0.336980i
$425$		−	0.213673i		−	0.0103647i
$426$	4.65075	−	12.4871i	0.225329	−	0.605003i
$427$	26.6300	−	26.6300i	1.28872	−	1.28872i
$428$	2.05338	+	28.3342i	0.0992540	+	1.36959i
$429$	22.9624	+	22.9624i	1.10863	+	1.10863i
$430$	12.3713	+	27.0555i	0.596596	+	1.30473i
$431$	−11.3698			−0.547664			−0.273832	−	0.961778i	$-0.588291\pi$
$431$	−11.3698			−0.547664			−0.273832	+	0.961778i	$0.588291\pi$
$432$	−18.1373	−	13.5241i	−0.872632	−	0.650678i
$433$	4.02337			0.193351			0.0966755	−	0.995316i	$-0.469179\pi$
$433$	4.02337			0.193351			0.0966755	+	0.995316i	$0.469179\pi$
$434$	−5.15806	−	11.2805i	−0.247595	−	0.541480i
$435$	8.44310	+	8.44310i	0.404816	+	0.404816i
$436$	−3.97323	+	0.287941i	−0.190283	+	0.0137898i
$437$	−3.27430	+	3.27430i	−0.156631	+	0.156631i
$438$	−5.19482	+	13.9480i	−0.248218	+	0.666459i
$439$		−	17.2840i		−	0.824921i	−0.910976	−	0.412460i	$-0.864670\pi$
$439$		−	17.2840i		−	0.824921i	0.910976	−	0.412460i	$-0.135330\pi$
$440$	25.6279	+	7.48564i	1.22176	+	0.356864i
$441$			8.73100i			0.415762i
$442$	0.677939	+	0.252494i	0.0322463	+	0.0120099i
$443$	−22.4350	+	22.4350i	−1.06592	+	1.06592i	−0.0682510	+	0.997668i	$0.521742\pi$
$443$	−22.4350	+	22.4350i	−1.06592	+	1.06592i	−0.997668	+	0.0682510i	$0.978258\pi$
$444$	6.73057	−	7.78233i	0.319419	−	0.369333i
$445$	22.5102	+	22.5102i	1.06708	+	1.06708i
$446$	6.13371	−	2.80467i	0.290439	−	0.132805i
$447$	33.5049			1.58473
$448$	17.2644	−	27.0319i	0.815666	−	1.27714i
$449$	4.93650			0.232968			0.116484	−	0.993193i	$-0.462838\pi$
$449$	4.93650			0.232968			0.116484	+	0.993193i	$0.462838\pi$
$450$	2.22802	−	1.01877i	0.105030	−	0.0480255i
$451$	−17.7633	−	17.7633i	−0.836442	−	0.836442i
$452$	11.4283	−	13.2141i	0.537542	−	0.621541i
$453$	−3.36826	+	3.36826i	−0.158255	+	0.158255i
$454$	19.6106	+	7.30383i	0.920370	+	0.342786i
$455$		−	30.9133i		−	1.44924i
$456$	−3.87575	−	1.13207i	−0.181499	−	0.0530138i
$457$		−	25.7479i		−	1.20443i	−0.798332	−	0.602217i	$-0.794284\pi$
$457$		−	25.7479i		−	1.20443i	0.798332	−	0.602217i	$-0.205716\pi$
$458$	−8.80201	+	23.6332i	−0.411291	+	1.10430i
$459$	−0.474624	+	0.474624i	−0.0221535	+	0.0221535i
$460$	−16.5221	+	1.19736i	−0.770345	+	0.0558270i
$461$	−15.5714	−	15.5714i	−0.725233	−	0.725233i	0.244433	−	0.969666i	$-0.421398\pi$
$461$	−15.5714	−	15.5714i	−0.725233	−	0.725233i	−0.969666	+	0.244433i	$0.921398\pi$
$462$	−17.7629	−	38.8468i	−0.826406	−	1.80732i
$463$	−3.05806			−0.142120			−0.0710600	−	0.997472i	$-0.522638\pi$
$463$	−3.05806			−0.142120			−0.0710600	+	0.997472i	$0.522638\pi$
$464$	11.1810	−	14.9950i	0.519065	−	0.696124i
$465$	−5.58594			−0.259042
$466$	0.262892	+	0.574935i	0.0121782	+	0.0266334i
$467$	−6.48955	−	6.48955i	−0.300301	−	0.300301i	0.540831	−	0.841131i	$-0.318110\pi$
$467$	−6.48955	−	6.48955i	−0.300301	−	0.300301i	−0.841131	+	0.540831i	$0.818110\pi$
$468$	0.599538	+	8.27290i	0.0277137	+	0.382415i
$469$	34.1996	−	34.1996i	1.57919	−	1.57919i
$470$	2.75380	−	7.39389i	0.127024	−	0.341055i
$471$		−	17.3680i		−	0.800274i
$472$	−3.74437	−	6.83429i	−0.172349	−	0.314573i
$473$		−	62.0638i		−	2.85370i
$474$	23.4123	+	8.71975i	1.07536	+	0.400511i
$475$	1.27317	−	1.27317i	0.0584172	−	0.0584172i
$476$	−0.719751	−	0.622479i	−0.0329897	−	0.0285313i
$477$	−1.90308	−	1.90308i	−0.0871361	−	0.0871361i
$478$	−26.4655	+	12.1015i	−1.21050	+	0.553508i
$479$	5.51269			0.251881			0.125941	−	0.992038i	$-0.459805\pi$
$479$	5.51269			0.251881			0.125941	+	0.992038i	$0.459805\pi$
$480$	−7.83794	−	12.1330i	−0.357751	−	0.553794i
$481$	−15.5343			−0.708305
$482$	25.8967	−	11.8414i	1.17956	−	0.539361i
$483$	18.7404	+	18.7404i	0.852719	+	0.852719i
$484$	−25.4886	−	22.0439i	−1.15857	−	1.00200i
$485$	9.07959	−	9.07959i	0.412283	−	0.412283i
$486$	−12.6727	−	4.71985i	−0.574844	−	0.214097i
$487$			11.5524i			0.523490i	0.965137	+	0.261745i	$0.0842980\pi$
$487$			11.5524i			0.523490i	−0.965137	+	0.261745i	$0.915702\pi$
$488$	−23.3001	+	12.7657i	−1.05475	+	0.577876i
$489$		−	25.5951i		−	1.15745i
$490$	−8.01199	+	21.5120i	−0.361945	+	0.971811i
$491$	0.922318	−	0.922318i	0.0416236	−	0.0416236i	−0.685989	−	0.727612i	$-0.740630\pi$
$491$	0.922318	−	0.922318i	0.0416236	−	0.0416236i	0.727612	+	0.685989i	$0.240630\pi$
$492$	0.982364	+	13.5554i	0.0442884	+	0.611126i
$493$	−0.392394	−	0.392394i	−0.0176725	−	0.0176725i
$494$	2.53502	+	5.54399i	0.114056	+	0.249436i
$495$	9.08189			0.408200
$496$	1.26166	+	8.65898i	0.0566502	+	0.388800i
$497$	26.4629			1.18702
$498$	9.63866	+	21.0794i	0.431919	+	0.944590i
$499$	6.83356	+	6.83356i	0.305912	+	0.305912i	0.843322	−	0.537409i	$-0.180597\pi$
$499$	6.83356	+	6.83356i	0.305912	+	0.305912i	−0.537409	+	0.843322i	$0.680597\pi$
$500$	24.2647	−	1.75846i	1.08515	−	0.0786408i
$501$	−13.4789	+	13.4789i	−0.602193	+	0.602193i
$502$	−4.80385	+	12.8982i	−0.214406	+	0.575675i
$503$		−	5.45915i		−	0.243411i	−0.992566	−	0.121706i	$-0.961164\pi$
$503$		−	5.45915i		−	0.243411i	0.992566	−	0.121706i	$-0.0388364\pi$
$504$	3.05904	−	10.4729i	0.136260	−	0.466502i
$505$		−	16.8786i		−	0.751090i
$506$	32.3854	+	12.0617i	1.43970	+	0.536208i
$507$	−5.63367	+	5.63367i	−0.250200	+	0.250200i
$508$	12.6275	−	14.6007i	0.560254	−	0.647802i
$509$	10.6834	+	10.6834i	0.473533	+	0.473533i	0.903056	−	0.429523i	$-0.141318\pi$
$509$	10.6834	+	10.6834i	0.473533	+	0.473533i	−0.429523	+	0.903056i	$0.641318\pi$
$510$	−0.389729	+	0.178205i	−0.0172575	+	0.00789107i
$511$	−29.5587			−1.30760
$512$	−17.0376	+	14.8903i	−0.752962	+	0.658065i
$513$	−5.65610			−0.249723
$514$	35.9593	−	16.4426i	1.58609	−	0.725250i
$515$	13.7796	+	13.7796i	0.607203	+	0.607203i
$516$	−21.9647	+	25.3970i	−0.966942	+	1.11804i
$517$	−11.6391	+	11.6391i	−0.511887	+	0.511887i
$518$	19.1486	+	7.13177i	0.841341	+	0.313352i
$519$		−	4.31309i		−	0.189324i
$520$	−6.11444	+	20.9334i	−0.268136	+	0.917992i
$521$		−	29.7689i		−	1.30420i	−0.758133	−	0.652100i	$-0.773888\pi$
$521$		−	29.7689i		−	1.30420i	0.758133	−	0.652100i	$-0.226112\pi$
$522$	2.22069	−	5.96249i	0.0971969	−	0.260971i
$523$	−10.2969	+	10.2969i	−0.450253	+	0.450253i	−0.895438	−	0.445186i	$-0.853138\pi$
$523$	−10.2969	+	10.2969i	−0.450253	+	0.450253i	0.445186	+	0.895438i	$0.353138\pi$
$524$	−10.5728	+	0.766214i	−0.461876	+	0.0334722i
$525$	−7.28699	−	7.28699i	−0.318030	−	0.318030i
$526$	9.90197	+	21.6552i	0.431746	+	0.944213i
$527$	0.259607			0.0113087
$528$	4.34481	+	29.8191i	0.189084	+	1.29771i
$529$	1.55792			0.0677358
$530$	−2.94257	−	6.43528i	−0.127817	−	0.279531i
$531$	−1.87441	−	1.87441i	−0.0813423	−	0.0813423i
$532$	−0.579593	−	7.99769i	−0.0251286	−	0.346744i
$533$	14.5095	−	14.5095i	0.628476	−	0.628476i
$534$	−12.5404	+	33.6707i	−0.542677	+	1.45707i
$535$			25.4072i			1.09845i
$536$	−29.9232	+	16.3944i	−1.29249	+	0.708128i
$537$			6.76132i			0.291773i
$538$	−1.08732	−	0.404966i	−0.0468778	−	0.0174593i
$539$	33.8631	−	33.8631i	1.45859	−	1.45859i
$540$	−15.3045	−	13.2361i	−0.658599	−	0.569592i
$541$	3.11671	+	3.11671i	0.133998	+	0.133998i	0.770924	−	0.636927i	$-0.219795\pi$
$541$	3.11671	+	3.11671i	0.133998	+	0.133998i	−0.636927	+	0.770924i	$0.719795\pi$
$542$	−41.3706	+	18.9169i	−1.77702	+	0.812551i
$543$	5.92709			0.254356
$544$	0.364269	+	0.563883i	0.0156179	+	0.0241763i
$545$	−3.56279			−0.152613
$546$	31.7310	−	14.5092i	1.35796	−	0.620934i
$547$	13.5785	+	13.5785i	0.580573	+	0.580573i	0.935061	−	0.354488i	$-0.115345\pi$
$547$	13.5785	+	13.5785i	0.580573	+	0.580573i	−0.354488	+	0.935061i	$0.615345\pi$
$548$	−7.66390	−	6.62816i	−0.327386	−	0.283141i
$549$	−6.39042	+	6.39042i	−0.272736	+	0.272736i
$550$	−12.5927	−	4.69005i	−0.536953	−	0.199985i
$551$		−	4.67616i		−	0.199211i
$552$	−8.98365	−	16.3971i	−0.382370	−	0.697907i
$553$			49.6157i			2.10987i
$554$	5.86394	−	15.7445i	0.249135	−	0.668921i
$555$	6.50684	−	6.50684i	0.276200	−	0.276200i
$556$	−2.96294	−	40.8850i	−0.125657	−	1.73391i
$557$	−22.9444	−	22.9444i	−0.972185	−	0.972185i	0.0274388	−	0.999623i	$-0.491265\pi$
$557$	−22.9444	−	22.9444i	−0.972185	−	0.972185i	−0.999623	+	0.0274388i	$0.991265\pi$
$558$	1.23778	+	2.70698i	0.0523995	+	0.114596i
$559$	50.6951			2.14417
$560$	17.1475	−	22.9968i	0.724615	−	0.971790i
$561$	0.894014			0.0377453
$562$	8.91873	+	19.5049i	0.376214	+	0.822766i
$563$	−1.70132	−	1.70132i	−0.0717021	−	0.0717021i	0.670346	−	0.742048i	$-0.266146\pi$
$563$	−1.70132	−	1.70132i	−0.0717021	−	0.0717021i	−0.742048	+	0.670346i	$0.766146\pi$
$564$	8.88195	−	0.643676i	0.373998	−	0.0271036i
$565$	11.0484	−	11.0484i	0.464810	−	0.464810i
$566$	6.99930	−	18.7929i	0.294203	−	0.789926i
$567$			20.8002i			0.873528i
$568$	−17.9198	−	5.23418i	−0.751897	−	0.219621i
$569$		−	14.6514i		−	0.614220i	−0.951674	−	0.307110i	$-0.900638\pi$
$569$		−	14.6514i		−	0.614220i	0.951674	−	0.307110i	$-0.0993620\pi$
$570$	−3.38404	−	1.26036i	−0.141742	−	0.0527908i
$571$	−22.4606	+	22.4606i	−0.939948	+	0.939948i	−0.998296	−	0.0583487i	$-0.981416\pi$
$571$	−22.4606	+	22.4606i	−0.939948	+	0.939948i	0.0583487	+	0.998296i	$0.481416\pi$
$572$	29.7611	−	34.4117i	1.24437	−	1.43882i
$573$	7.36426	+	7.36426i	0.307646	+	0.307646i
$574$	−24.5466	+	11.2240i	−1.02455	+	0.468482i
$575$	8.33750			0.347698
$576$	−4.14295	+	6.48686i	−0.172623	+	0.270286i
$577$	−29.4663			−1.22670			−0.613349	−	0.789812i	$-0.710178\pi$
$577$	−29.4663			−1.22670			−0.613349	+	0.789812i	$0.710178\pi$
$578$	−21.8462	+	9.98929i	−0.908682	+	0.415500i
$579$	−12.8989	−	12.8989i	−0.536059	−	0.536059i
$580$	10.9429	−	12.6529i	0.454380	−	0.525384i
$581$	−32.5491	+	32.5491i	−1.35036	+	1.35036i
$582$	13.5812	+	5.05824i	0.562961	+	0.209671i
$583$			14.7622i			0.611386i
$584$	20.0162	+	5.84651i	0.828274	+	0.241930i
$585$			7.41829i			0.306709i
$586$	−3.08647	+	8.28709i	−0.127501	+	0.342337i
$587$	−3.43573	+	3.43573i	−0.141808	+	0.141808i	−0.774447	−	0.632639i	$-0.781972\pi$
$587$	−3.43573	+	3.43573i	−0.141808	+	0.141808i	0.632639	+	0.774447i	$0.281972\pi$
$588$	−25.8414	+	1.87273i	−1.06568	+	0.0772299i
$589$	1.54687	+	1.54687i	0.0637376	+	0.0637376i
$590$	−2.89823	−	6.33832i	−0.119318	−	0.260945i
$591$	−15.4331			−0.634834
$592$	−11.5562	−	8.61685i	−0.474955	−	0.354150i
$593$	34.0014			1.39627			0.698136	−	0.715966i	$-0.254013\pi$
$593$	34.0014			1.39627			0.698136	+	0.715966i	$0.254013\pi$
$594$	17.5538	+	38.3894i	0.720240	+	1.57514i
$595$	−0.601787	−	0.601787i	−0.0246709	−	0.0246709i
$596$	−3.39289	−	46.8178i	−0.138978	−	1.91773i
$597$	18.4248	−	18.4248i	0.754075	−	0.754075i
$598$	−9.85228	+	26.4531i	−0.402890	+	1.08175i
$599$		−	36.7623i		−	1.50207i	−0.660265	−	0.751033i	$-0.729556\pi$
$599$		−	36.7623i		−	1.50207i	0.660265	−	0.751033i	$-0.270444\pi$
$600$	3.49319	+	6.37582i	0.142609	+	0.260292i
$601$		−	34.9783i		−	1.42679i	−0.700761	−	0.713397i	$-0.747156\pi$
$601$		−	34.9783i		−	1.42679i	0.700761	−	0.713397i	$-0.252844\pi$
$602$	−62.4899	−	23.2740i	−2.54690	−	0.948576i
$603$	−8.20690	+	8.20690i	−0.334211	+	0.334211i
$604$	5.04771	+	4.36553i	0.205388	+	0.177631i
$605$	−21.3111	−	21.3111i	−0.866421	−	0.866421i
$606$	17.3251	−	7.92198i	0.703783	−	0.321809i
$607$	0.393296			0.0159634			0.00798169	−	0.999968i	$-0.497459\pi$
$607$	0.393296			0.0159634			0.00798169	+	0.999968i	$0.497459\pi$
$608$	−1.18941	+	5.53040i	−0.0482368	+	0.224287i
$609$	−26.7640			−1.08453
$610$	−21.6092	+	9.88094i	−0.874933	+	0.400067i
$611$	−9.50708	−	9.50708i	−0.384615	−	0.384615i
$612$	0.172719	+	0.149377i	0.00698176	+	0.00603820i
$613$	−27.8649	+	27.8649i	−1.12545	+	1.12545i	−0.134546	+	0.990907i	$0.542957\pi$
$613$	−27.8649	+	27.8649i	−1.12545	+	1.12545i	−0.990907	+	0.134546i	$0.957043\pi$
$614$	18.7258	+	6.97430i	0.755712	+	0.281460i
$615$			12.1551i			0.490142i
$616$	−52.4836	+	28.7548i	−2.11463	+	1.15856i
$617$			9.15303i			0.368487i	0.982881	+	0.184244i	$0.0589835\pi$
$617$			9.15303i			0.368487i	−0.982881	+	0.184244i	$0.941016\pi$
$618$	−7.67664	+	20.6116i	−0.308800	+	0.829119i
$619$	−0.431430	+	0.431430i	−0.0173406	+	0.0173406i	−0.715724	−	0.698383i	$-0.753903\pi$
$619$	−0.431430	+	0.431430i	−0.0173406	+	0.0173406i	0.698383	+	0.715724i	$0.253903\pi$
$620$	0.565664	+	7.80548i	0.0227176	+	0.313476i
$621$	−18.5198	−	18.5198i	−0.743172	−	0.743172i
$622$	3.13624	+	6.85884i	0.125752	+	0.275014i
$623$	−71.3554			−2.85879
$624$	−24.3569	+	3.54894i	−0.975058	+	0.142071i
$625$	12.7554			0.510215
$626$	3.19237	+	6.98158i	0.127593	+	0.279040i
$627$	5.32699	+	5.32699i	0.212739	+	0.212739i
$628$	−24.2690	+	1.75878i	−0.968440	+	0.0701830i
$629$	−0.302406	+	0.302406i	−0.0120577	+	0.0120577i
$630$	3.40571	−	9.14425i	0.135687	−	0.364316i
$631$		−	8.60394i		−	0.342517i	−0.985226	−	0.171259i	$-0.945217\pi$
$631$		−	8.60394i		−	0.342517i	0.985226	−	0.171259i	$-0.0547834\pi$
$632$	9.81363	−	33.5980i	0.390365	−	1.33646i
$633$		−	36.2474i		−	1.44070i
$634$	−46.3289	−	17.2549i	−1.83996	−	0.685280i
$635$	12.2077	−	12.2077i	0.484449	−	0.484449i
$636$	5.22440	−	6.04079i	0.207161	−	0.239533i
$637$	27.6601	+	27.6601i	1.09593	+	1.09593i
$638$	−31.7383	+	14.5125i	−1.25653	+	0.574556i
$639$	−6.35032			−0.251215
$640$	−16.1603	+	12.1810i	−0.638792	+	0.481495i
$641$	4.86245			0.192055			0.0960276	−	0.995379i	$-0.469386\pi$
$641$	4.86245			0.192055			0.0960276	+	0.995379i	$0.469386\pi$
$642$	−26.0792	+	11.9249i	−1.02926	+	0.470637i
$643$	31.9868	+	31.9868i	1.26144	+	1.26144i	0.950397	+	0.311039i	$0.100677\pi$
$643$	31.9868	+	31.9868i	1.26144	+	1.26144i	0.311039	+	0.950397i	$0.399323\pi$
$644$	24.2891	−	28.0846i	0.957123	−	1.10669i
$645$	−21.2346	+	21.2346i	−0.836110	+	0.836110i
$646$	0.157273	+	0.0585754i	0.00618784	+	0.00230462i
$647$			37.4759i			1.47333i	0.676259	+	0.736664i	$0.263600\pi$
$647$			37.4759i			1.47333i	−0.676259	+	0.736664i	$0.736400\pi$
$648$	4.11414	−	14.0852i	0.161619	−	0.553319i
$649$			14.5397i			0.570734i
$650$	3.83094	−	10.2860i	0.150262	−	0.403449i
$651$	8.85349	−	8.85349i	0.346996	−	0.346996i
$652$	−35.7652	+	2.59190i	−1.40067	+	0.101507i
$653$	30.6418	+	30.6418i	1.19911	+	1.19911i	0.974434	+	0.224673i	$0.0721315\pi$
$653$	30.6418	+	30.6418i	1.19911	+	1.19911i	0.224673	+	0.974434i	$0.427868\pi$
$654$	−1.67219	−	3.65702i	−0.0653879	−	0.143001i
$655$	−9.48063			−0.370439
$656$	18.8421	−	2.74540i	0.735661	−	0.107190i
$657$	7.09323			0.276733
$658$	7.35435	+	16.0837i	0.286702	+	0.627008i
$659$	−21.2793	−	21.2793i	−0.828925	−	0.828925i	0.158443	−	0.987368i	$-0.449353\pi$
$659$	−21.2793	−	21.2793i	−0.828925	−	0.828925i	−0.987368	+	0.158443i	$0.949353\pi$
$660$	1.94799	+	26.8799i	0.0758254	+	1.04630i
$661$	−12.6373	+	12.6373i	−0.491534	+	0.491534i	−0.908789	−	0.417255i	$-0.862992\pi$
$661$	−12.6373	+	12.6373i	−0.491534	+	0.491534i	0.417255	+	0.908789i	$0.362992\pi$
$662$	4.69147	−	12.5965i	0.182339	−	0.489575i
$663$			0.730251i			0.0283606i
$664$	28.4791	−	15.6031i	1.10520	−	0.605519i
$665$		−	7.17151i		−	0.278099i
$666$	−4.59510	−	1.71142i	−0.178057	−	0.0663160i
$667$	15.3112	−	15.3112i	0.592850	−	0.592850i
$668$	20.1996	+	17.4697i	0.781547	+	0.675924i
$669$	4.81404	+	4.81404i	0.186122	+	0.186122i
$670$	−27.7517	+	12.6896i	−1.07214	+	0.490242i
$671$	49.5703			1.91364
$672$	31.6532	+	6.80755i	1.22105	+	0.262607i
$673$	6.89552			0.265803			0.132901	−	0.991129i	$-0.457571\pi$
$673$	6.89552			0.265803			0.132901	+	0.991129i	$0.457571\pi$
$674$	−24.9471	+	11.4072i	−0.960925	+	0.439388i
$675$	7.20119	+	7.20119i	0.277174	+	0.277174i
$676$	8.44267	+	7.30168i	0.324718	+	0.280834i
$677$	1.60866	−	1.60866i	0.0618260	−	0.0618260i	−0.675518	−	0.737344i	$-0.736080\pi$
$677$	1.60866	−	1.60866i	0.0618260	−	0.0618260i	0.737344	+	0.675518i	$0.236080\pi$
$678$	16.5262	+	6.15507i	0.634685	+	0.236384i
$679$			28.7816i			1.10454i
$680$	0.288480	+	0.526539i	0.0110627	+	0.0201918i
$681$			21.1238i			0.809466i
$682$	5.69828	−	15.2997i	0.218199	−	0.585857i
$683$	−7.11301	+	7.11301i	−0.272172	+	0.272172i	−0.829974	−	0.557802i	$-0.811645\pi$
$683$	−7.11301	+	7.11301i	−0.272172	+	0.272172i	0.557802	+	0.829974i	$0.311645\pi$
$684$	0.139085	+	1.91921i	0.00531806	+	0.0733829i
$685$	−6.40783	−	6.40783i	−0.244830	−	0.244830i
$686$	−4.89193	−	10.6985i	−0.186775	−	0.408469i
$687$	−25.4568			−0.971236
$688$	37.7126	+	28.1204i	1.43778	+	1.07208i
$689$	−12.0581			−0.459375
$690$	−6.95355	−	15.2072i	−0.264717	−	0.578927i
$691$	1.44255	+	1.44255i	0.0548773	+	0.0548773i	0.734013	−	0.679136i	$-0.237645\pi$
$691$	1.44255	+	1.44255i	0.0548773	+	0.0548773i	−0.679136	+	0.734013i	$0.737645\pi$
$692$	−6.02687	+	0.436768i	−0.229107	+	0.0166034i
$693$	−14.3944	+	14.3944i	−0.546799	+	0.546799i
$694$	5.49289	−	14.7483i	0.208507	−	0.559836i
$695$		−	36.6614i		−	1.39065i
$696$	18.1236	+	5.29372i	0.686975	+	0.200658i
$697$		−	0.564910i		−	0.0213975i
$698$	16.3637	+	6.09457i	0.619377	+	0.230683i
$699$	−0.451238	+	0.451238i	−0.0170674	+	0.0170674i
$700$	−9.44452	+	10.9204i	−0.356969	+	0.412751i
$701$	−25.9615	−	25.9615i	−0.980554	−	0.980554i	0.0192607	−	0.999814i	$-0.493869\pi$
$701$	−25.9615	−	25.9615i	−0.980554	−	0.980554i	−0.999814	+	0.0192607i	$0.993869\pi$
$702$	−31.3573	+	14.3383i	−1.18351	+	0.541165i
$703$	−3.60377			−0.135919
$704$	41.2276	−	9.09085i	1.55382	−	0.342624i
$705$	7.96442			0.299958
$706$	−18.8837	+	8.63467i	−0.710697	+	0.324970i
$707$	26.7520	+	26.7520i	1.00611	+	1.00611i
$708$	5.14569	−	5.94977i	0.193387	−	0.223606i
$709$	17.5137	−	17.5137i	0.657739	−	0.657739i	−0.297106	−	0.954845i	$-0.596021\pi$
$709$	17.5137	−	17.5137i	0.657739	−	0.657739i	0.954845	+	0.297106i	$0.0960213\pi$
$710$	−15.6463	−	5.82736i	−0.587196	−	0.218697i
$711$		−	11.9063i		−	0.446521i
$712$	48.3194	+	14.1136i	1.81085	+	0.528929i
$713$			10.1298i			0.379365i
$714$	0.335256	−	0.900153i	0.0125466	−	0.0336874i
$715$	28.7718	−	28.7718i	1.07600	−	1.07600i
$716$	9.44790	−	0.684690i	0.353084	−	0.0255881i
$717$	−20.7714	−	20.7714i	−0.775723	−	0.775723i
$718$	−3.23374	−	7.07207i	−0.120682	−	0.263927i
$719$	−15.9343			−0.594250			−0.297125	−	0.954839i	$-0.596028\pi$
$719$	−15.9343			−0.594250			−0.297125	+	0.954839i	$0.596028\pi$
$720$	−4.11490	+	5.51855i	−0.153353	+	0.205664i
$721$	−43.6804			−1.62674
$722$	0.588093	+	1.28614i	0.0218865	+	0.0478650i
$723$	20.3250	+	20.3250i	0.755897	+	0.755897i
$724$	−0.600210	−	8.28218i	−0.0223066	−	0.307805i
$725$	−5.95356	+	5.95356i	−0.221110	+	0.221110i
$726$	11.8724	−	31.8772i	0.440628	−	1.18307i
$727$		−	41.4564i		−	1.53753i	−0.639530	−	0.768766i	$-0.720871\pi$
$727$		−	41.4564i		−	1.53753i	0.639530	−	0.768766i	$-0.279129\pi$
$728$	−23.4875	−	42.8698i	−0.870506	−	1.58886i
$729$		−	29.2144i		−	1.08202i
$730$	17.4767	+	6.50909i	0.646842	+	0.240912i
$731$	0.986877	−	0.986877i	0.0365010	−	0.0365010i
$732$	−20.2846	−	17.5432i	−0.749739	−	0.648415i
$733$	−1.24420	−	1.24420i	−0.0459555	−	0.0459555i	0.683756	−	0.729711i	$-0.260345\pi$
$733$	−1.24420	−	1.24420i	−0.0459555	−	0.0459555i	−0.729711	+	0.683756i	$0.760345\pi$
$734$	−37.5780	+	17.1827i	−1.38703	+	0.634226i
$735$	−23.1719			−0.854708
$736$	−22.0027	+	14.2137i	−0.811029	+	0.523924i
$737$	63.6607			2.34497
$738$	5.89046	−	2.69344i	0.216831	−	0.0991469i
$739$	−10.5071	−	10.5071i	−0.386511	−	0.386511i	0.486930	−	0.873441i	$-0.338117\pi$
$739$	−10.5071	−	10.5071i	−0.386511	−	0.386511i	−0.873441	+	0.486930i	$0.838117\pi$
$740$	−9.75122	−	8.43338i	−0.358462	−	0.310017i
$741$	−4.35120	+	4.35120i	−0.159845	+	0.159845i
$742$	14.8635	+	5.53582i	0.545657	+	0.203226i
$743$			30.3905i			1.11492i	0.830204	+	0.557460i	$0.188224\pi$
$743$			30.3905i			1.11492i	−0.830204	+	0.557460i	$0.811776\pi$
$744$	−7.74644	+	4.24412i	−0.283998	+	0.155597i
$745$		−	41.9814i		−	1.53808i
$746$	−10.8748	+	29.1985i	−0.398154	+	1.06903i
$747$	7.81083	−	7.81083i	0.285783	−	0.285783i
$748$	−0.0905329	−	1.24925i	−0.00331021	−	0.0456769i
$749$	−40.2694	−	40.2694i	−1.47141	−	1.47141i
$750$	10.2121	+	22.3336i	0.372894	+	0.815506i
$751$	19.0069			0.693571			0.346786	−	0.937944i	$-0.387273\pi$
$751$	19.0069			0.693571			0.346786	+	0.937944i	$0.387273\pi$
$752$	−1.79887	−	12.3460i	−0.0655982	−	0.450211i
$753$	−13.8935			−0.506306
$754$	−11.8542	−	25.9246i	−0.431703	−	0.944118i
$755$	4.22042	+	4.22042i	0.153597	+	0.153597i
$756$	45.2357	−	3.27824i	1.64521	−	0.119228i
$757$	−5.74185	+	5.74185i	−0.208691	+	0.208691i	−0.803711	−	0.595020i	$-0.797144\pi$
$757$	−5.74185	+	5.74185i	−0.208691	+	0.208691i	0.595020	+	0.803711i	$0.297144\pi$
$758$	−1.23262	+	3.30956i	−0.0447709	+	0.120209i
$759$			34.8843i			1.26622i
$760$	−1.41847	+	4.85630i	−0.0514534	+	0.176156i
$761$		−	38.1347i		−	1.38238i	−0.722673	−	0.691190i	$-0.757087\pi$
$761$		−	38.1347i		−	1.38238i	0.722673	−	0.691190i	$-0.242913\pi$
$762$	18.2603	+	6.80093i	0.661501	+	0.246372i
$763$	5.64688	−	5.64688i	0.204431	−	0.204431i
$764$	9.54466	−	11.0362i	0.345314	−	0.399274i
$765$	0.144411	+	0.144411i	0.00522120	+	0.00522120i
$766$	40.4821	−	18.5106i	1.46268	−	0.668816i
$767$	−11.8764			−0.428831
$768$	−20.0880	−	10.8706i	−0.724862	−	0.392260i
$769$	−6.52911			−0.235446			−0.117723	−	0.993046i	$-0.537559\pi$
$769$	−6.52911			−0.235446			−0.117723	+	0.993046i	$0.537559\pi$
$770$	−48.6749	+	22.2568i	−1.75412	+	0.802081i
$771$	28.2226	+	28.2226i	1.01641	+	1.01641i
$772$	−16.7180	+	19.3304i	−0.601692	+	0.695716i
$773$	6.67799	−	6.67799i	0.240191	−	0.240191i	−0.576738	−	0.816929i	$-0.695675\pi$
$773$	6.67799	−	6.67799i	0.240191	−	0.240191i	0.816929	+	0.576738i	$0.195675\pi$
$774$	14.9958	+	5.58507i	0.539011	+	0.200751i
$775$		−	3.93886i		−	0.141488i
$776$	5.69279	−	19.4899i	0.204359	−	0.699647i
$777$			20.6262i			0.739960i
$778$	−1.51784	+	4.07537i	−0.0544173	+	0.146109i
$779$	3.36602	−	3.36602i	0.120600	−	0.120600i
$780$	−21.9561	+	1.59116i	−0.786155	+	0.0569727i
$781$	24.6297	+	24.6297i	0.881318	+	0.881318i
$782$	0.323167	+	0.706754i	0.0115564	+	0.0252735i
$783$	26.4488			0.945204
$784$	5.23369	+	35.9196i	0.186917	+	1.28284i
$785$	−21.7620			−0.776719
$786$	−4.44973	−	9.73139i	−0.158717	−	0.347107i
$787$	2.23519	+	2.23519i	0.0796760	+	0.0796760i	0.745822	−	0.666146i	$-0.232057\pi$
$787$	2.23519	+	2.23519i	0.0796760	+	0.0796760i	−0.666146	+	0.745822i	$0.732057\pi$
$788$	1.56285	+	21.5654i	0.0556741	+	0.768235i
$789$	−16.9961	+	16.9961i	−0.605078	+	0.605078i
$790$	10.9258	−	29.3355i	0.388723	−	1.04371i
$791$			35.0226i			1.24526i
$792$	12.5945	−	6.90030i	0.447527	−	0.245191i
$793$			40.4901i			1.43785i
$794$	16.6782	+	6.21169i	0.591888	+	0.220445i
$795$	5.05074	−	5.05074i	0.179131	−	0.179131i
$796$	−27.6115	−	23.8799i	−0.978665	−	0.846402i
$797$	38.2981	+	38.2981i	1.35659	+	1.35659i	0.878087	+	0.478501i	$0.158820\pi$
$797$	38.2981	+	38.2981i	1.35659	+	1.35659i	0.478501	+	0.878087i	$0.341180\pi$
$798$	7.36119	−	3.36594i	0.260583	−	0.119153i
$799$	−0.370147			−0.0130949
$800$	8.55547	−	5.52684i	0.302482	−	0.195403i
$801$	17.1232			0.605019
$802$	3.28504	−	1.50210i	0.115999	−	0.0530411i
$803$	−27.5110	−	27.5110i	−0.970842	−	0.970842i
$804$	−26.0505	−	22.5299i	−0.918730	−	0.794567i
$805$	23.4817	−	23.4817i	0.827620	−	0.827620i
$806$	12.4972	+	4.65449i	0.440194	+	0.163947i
$807$		−	1.17122i		−	0.0412290i
$808$	−12.8242	−	23.4069i	−0.451153	−	0.823451i
$809$			19.5807i			0.688422i	0.938892	+	0.344211i	$0.111854\pi$
$809$			19.5807i			0.688422i	−0.938892	+	0.344211i	$0.888146\pi$
$810$	4.58039	−	12.2982i	0.160939	−	0.432116i
$811$	31.8185	−	31.8185i	1.11730	−	1.11730i	0.125163	−	0.992136i	$-0.460055\pi$
$811$	31.8185	−	31.8185i	1.11730	−	1.11730i	0.992136	−	0.125163i	$-0.0399453\pi$
$812$	2.71027	+	37.3985i	0.0951119	+	1.31243i
$813$	−32.4697	−	32.4697i	−1.13876	−	1.13876i
$814$	11.1844	+	24.4598i	0.392011	+	0.857314i
$815$	−32.0705			−1.12338
$816$	−0.405068	+	0.543242i	−0.0141802	+	0.0190173i
$817$	11.7606			0.411452
$818$	18.4936	+	40.4447i	0.646612	+	1.41412i
$819$	−11.7577	−	11.7577i	−0.410847	−	0.410847i
$820$	16.9849	−	1.23090i	0.593138	−	0.0429848i
$821$	37.5530	−	37.5530i	1.31061	−	1.31061i	0.389640	−	0.920967i	$-0.372600\pi$
$821$	37.5530	−	37.5530i	1.31061	−	1.31061i	0.920967	−	0.389640i	$-0.127400\pi$
$822$	3.56980	−	9.58482i	0.124511	−	0.334309i
$823$		−	41.6379i		−	1.45140i	−0.688009	−	0.725702i	$-0.741515\pi$
$823$		−	41.6379i		−	1.45140i	0.688009	−	0.725702i	$-0.258485\pi$
$824$	29.5788	+	8.63967i	1.03043	+	0.300977i
$825$		−	13.5644i		−	0.472250i
$826$	14.6396	+	5.45241i	0.509376	+	0.189714i
$827$	0.638479	−	0.638479i	0.0222021	−	0.0222021i	−0.695919	−	0.718121i	$-0.745003\pi$
$827$	0.638479	−	0.638479i	0.0222021	−	0.0222021i	0.718121	+	0.695919i	$0.245003\pi$
$828$	−5.82866	+	6.73948i	−0.202560	+	0.234213i
$829$	2.02012	+	2.02012i	0.0701618	+	0.0701618i	0.741317	−	0.671155i	$-0.234202\pi$
$829$	2.02012	+	2.02012i	0.0701618	+	0.0701618i	−0.671155	+	0.741317i	$0.734202\pi$
$830$	26.4124	−	12.0772i	0.916787	−	0.419205i
$831$	16.9594			0.588316
$832$	7.42561	+	33.6756i	0.257437	+	1.16749i
$833$	1.07692			0.0373129
$834$	37.6311	−	17.2070i	1.30306	−	0.595831i
$835$	16.8890	+	16.8890i	0.584468	+	0.584468i
$836$	6.90419	−	7.98308i	0.238787	−	0.276100i
$837$	−8.74924	+	8.74924i	−0.302418	+	0.302418i
$838$	10.3527	+	3.85580i	0.357629	+	0.133196i
$839$			18.5809i			0.641485i	0.947166	+	0.320743i	$0.103932\pi$
$839$			18.5809i			0.641485i	−0.947166	+	0.320743i	$0.896068\pi$
$840$	27.7950	+	8.11862i	0.959018	+	0.280119i
$841$		−	7.13351i		−	0.245983i
$842$	−3.28902	+	8.83094i	−0.113347	+	0.304334i
$843$	−15.3085	+	15.3085i	−0.527251	+	0.527251i
$844$	−50.6501	+	3.67061i	−1.74345	+	0.126348i
$845$	7.05896	+	7.05896i	0.242836	+	0.242836i
$846$	−1.76483	−	3.85961i	−0.0606761	−	0.132696i
$847$	67.5546			2.32120
$848$	−8.97012	−	6.68856i	−0.308035	−	0.229686i
$849$	20.2431			0.694740
$850$	−0.125660	−	0.274813i	−0.00431009	−	0.00942601i
$851$	−11.7998	−	11.7998i	−0.404493	−	0.404493i
$852$	−1.36209	−	18.7952i	−0.0466645	−	0.643914i
$853$	−15.6295	+	15.6295i	−0.535145	+	0.535145i	−0.922099	−	0.386954i	$-0.873527\pi$
$853$	−15.6295	+	15.6295i	−0.535145	+	0.535145i	0.386954	+	0.922099i	$0.373527\pi$
$854$	18.5889	−	49.9107i	0.636099	−	1.70791i
$855$			1.72095i			0.0588553i
$856$	19.3041	+	35.2341i	0.659799	+	1.20428i
$857$		−	10.1839i		−	0.347876i	−0.984757	−	0.173938i	$-0.944351\pi$
$857$		−	10.1839i		−	0.347876i	0.984757	−	0.173938i	$-0.0556492\pi$
$858$	43.0368	+	16.0288i	1.46925	+	0.547213i
$859$	−15.4702	+	15.4702i	−0.527837	+	0.527837i	−0.919927	−	0.392090i	$-0.871752\pi$
$859$	−15.4702	+	15.4702i	−0.527837	+	0.527837i	0.392090	+	0.919927i	$0.371752\pi$
$860$	31.8223	+	27.5217i	1.08513	+	0.938480i
$861$	−19.2654	−	19.2654i	−0.656563	−	0.656563i
$862$	−14.6231	+	6.68649i	−0.498065	+	0.227743i
$863$	−11.1211			−0.378568			−0.189284	−	0.981922i	$-0.560617\pi$
$863$	−11.1211			−0.378568			−0.189284	+	0.981922i	$0.560617\pi$
$864$	−31.2805	−	6.72739i	−1.06418	−	0.228871i
$865$	−5.40428			−0.183751
$866$	5.17461	−	2.36612i	0.175840	−	0.0804039i
$867$	−17.1460	−	17.1460i	−0.582309	−	0.582309i
$868$	−13.2679	−	11.4748i	−0.450343	−	0.389481i
$869$	−46.1785	+	46.1785i	−1.56650	+	1.56650i
$870$	15.8243	+	5.89366i	0.536494	+	0.199814i
$871$			51.9995i			1.76194i
$872$	−4.94078	+	2.70696i	−0.167316	+	0.0916692i
$873$		−	6.90674i		−	0.233758i
$874$	−2.28561	+	6.13679i	−0.0773117	+	0.207580i
$875$	−34.4857	+	34.4857i	−1.16583	+	1.16583i
$876$	1.52144	+	20.9940i	0.0514046	+	0.709322i
$877$	5.39441	+	5.39441i	0.182156	+	0.182156i	0.792295	−	0.610139i	$-0.208886\pi$
$877$	5.39441	+	5.39441i	0.182156	+	0.182156i	−0.610139	+	0.792295i	$0.708886\pi$
$878$	−10.1646	−	22.2296i	−0.343038	−	0.750212i
$879$	−8.92655			−0.301085
$880$	37.3632	−	5.44402i	1.25951	−	0.183518i
$881$	−44.6534			−1.50441			−0.752206	−	0.658928i	$-0.771010\pi$
$881$	−44.6534			−1.50441			−0.752206	+	0.658928i	$0.771010\pi$
$882$	5.13464	+	11.2293i	0.172892	+	0.378109i
$883$	3.36987	+	3.36987i	0.113405	+	0.113405i	0.761532	−	0.648127i	$-0.224447\pi$
$883$	3.36987	+	3.36987i	0.113405	+	0.113405i	−0.648127	+	0.761532i	$0.724447\pi$
$884$	1.02041	−	0.0739494i	0.0343202	−	0.00248719i
$885$	4.97464	−	4.97464i	0.167221	−	0.167221i
$886$	−15.6606	+	42.0483i	−0.526129	+	1.41264i
$887$			22.3314i			0.749815i	0.927062	+	0.374908i	$0.122326\pi$
$887$			22.3314i			0.749815i	−0.927062	+	0.374908i	$0.877674\pi$
$888$	4.07971	−	13.9673i	0.136906	−	0.468713i
$889$			38.6975i			1.29787i
$890$	42.1892	+	15.7131i	1.41418	+	0.526704i
$891$	−19.3593	+	19.3593i	−0.648560	+	0.648560i
$892$	6.23938	−	7.21437i	0.208910	−	0.241555i
$893$	−2.20552	−	2.20552i	−0.0738050	−	0.0738050i
$894$	43.0918	−	19.7040i	1.44121	−	0.658999i
$895$	8.47190			0.283185
$896$	6.30711	−	44.9198i	0.210706	−	1.50066i
$897$	−28.4943			−0.951397
$898$	6.34901	−	2.90312i	0.211869	−	0.0968783i
$899$	−7.23341	−	7.23341i	−0.241248	−	0.241248i
$900$	2.26641	−	2.62057i	0.0755469	−	0.0873522i
$901$	−0.234733	+	0.234733i	−0.00782010	+	0.00782010i
$902$	−33.2925	−	12.3996i	−1.10852	−	0.412861i
$903$		−	67.3119i		−	2.24000i
$904$	6.92722	−	23.7161i	0.230396	−	0.788785i
$905$		−	7.42661i		−	0.246869i
$906$	−2.35119	+	6.31289i	−0.0781132	+	0.209732i
$907$	−34.4426	+	34.4426i	−1.14365	+	1.14365i	−0.155872	+	0.987777i	$0.549819\pi$
$907$	−34.4426	+	34.4426i	−1.14365	+	1.14365i	−0.987777	+	0.155872i	$0.950181\pi$
$908$	29.5172	−	2.13912i	0.979563	−	0.0709890i
$909$	−6.41969	−	6.41969i	−0.212928	−	0.212928i
$910$	−18.1799	−	39.7588i	−0.602658	−	1.31799i
$911$	5.18704			0.171854			0.0859272	−	0.996301i	$-0.472615\pi$
$911$	5.18704			0.171854			0.0859272	+	0.996301i	$0.472615\pi$
$912$	−5.65051	+	0.823309i	−0.187107	+	0.0272625i
$913$	−60.5884			−2.00518
$914$	−15.1421	−	33.1153i	−0.500857	−	1.09536i
$915$	−16.9600	−	16.9600i	−0.560681	−	0.560681i
$916$	2.57790	+	35.5719i	0.0851761	+	1.17533i
$917$	15.0264	−	15.0264i	0.496216	−	0.496216i
$918$	−0.331308	+	0.889554i	−0.0109348	+	0.0293597i
$919$			16.9704i			0.559802i	0.960029	+	0.279901i	$0.0903017\pi$
$919$			16.9704i			0.559802i	−0.960029	+	0.279901i	$0.909698\pi$
$920$	−20.5455	+	11.2565i	−0.677364	+	0.371115i
$921$			20.1708i			0.664649i
$922$	−29.1844	−	10.8695i	−0.961137	−	0.357969i
$923$	−20.1181	+	20.1181i	−0.662194	+	0.662194i
$924$	−45.6911	−	39.5161i	−1.50313	−	1.29998i
$925$	4.58823	+	4.58823i	0.150860	+	0.150860i
$926$	−3.93308	+	1.79842i	−0.129249	+	0.0590998i
$927$	10.4820			0.344274
$928$	5.56185	−	25.8610i	0.182577	−	0.848930i
$929$	14.2902			0.468846			0.234423	−	0.972135i	$-0.424680\pi$
$929$	14.2902			0.468846			0.234423	+	0.972135i	$0.424680\pi$
$930$	−7.18428	+	3.28505i	−0.235582	+	0.107721i
$931$	6.41681	+	6.41681i	0.210302	+	0.210302i
$932$	0.676230	+	0.584840i	0.0221507	+	0.0191571i
$933$	−5.38316	+	5.38316i	−0.176237	+	0.176237i
$934$	−12.1629	−	4.52999i	−0.397982	−	0.148226i
$935$		−	1.12020i		−	0.0366343i
$936$	5.63632	+	10.2875i	0.184229	+	0.336257i
$937$			33.1892i			1.08424i	0.840300	+	0.542122i	$0.182379\pi$
$937$			33.1892i			1.08424i	−0.840300	+	0.542122i	$0.817621\pi$
$938$	23.8728	−	64.0979i	0.779475	−	2.09287i
$939$	−5.47950	+	5.47950i	−0.178817	+	0.178817i
$940$	−0.806523	−	11.1290i	−0.0263059	−	0.362989i
$941$	26.3268	+	26.3268i	0.858228	+	0.858228i	0.991129	−	0.132901i	$-0.0424293\pi$
$941$	26.3268	+	26.3268i	0.858228	+	0.858228i	−0.132901	+	0.991129i	$0.542429\pi$
$942$	−10.2140	−	22.3376i	−0.332789	−	0.727798i
$943$	22.0427			0.717810
$944$	−8.83497	−	6.58779i	−0.287554	−	0.214414i
$945$	40.5627			1.31951
$946$	−36.4992	−	79.8225i	−1.18669	−	2.59525i
$947$	−1.03795	−	1.03795i	−0.0337290	−	0.0337290i	0.690041	−	0.723770i	$-0.257592\pi$
$947$	−1.03795	−	1.03795i	−0.0337290	−	0.0337290i	−0.723770	+	0.690041i	$0.757592\pi$
$948$	35.2394	−	2.55380i	1.14452	−	0.0829437i
$949$	22.4716	−	22.4716i	0.729459	−	0.729459i
$950$	0.888731	−	2.38622i	0.0288342	−	0.0774191i
$951$		−	49.9038i		−	1.61824i
$952$	−1.29177	−	0.377313i	−0.0418666	−	0.0122288i
$953$		−	55.3913i		−	1.79430i	−0.441724	−	0.897151i	$-0.645633\pi$
$953$		−	55.3913i		−	1.79430i	0.441724	−	0.897151i	$-0.354367\pi$
$954$	−3.56681	−	1.32843i	−0.115480	−	0.0430096i
$955$	9.22738	−	9.22738i	0.298591	−	0.298591i
$956$	−26.9214	+	31.1283i	−0.870701	+	1.00676i
$957$	−24.9099	−	24.9099i	−0.805221	−	0.805221i
$958$	7.09007	−	3.24197i	0.229070	−	0.104743i
$959$	20.3123			0.655918
$960$	−17.2160	−	10.9953i	−0.555644	−	0.354872i
$961$	−26.2144			−0.845626
$962$	−19.9793	+	9.13563i	−0.644158	+	0.294545i
$963$	9.66348	+	9.66348i	0.311401	+	0.311401i
$964$	26.3429	−	30.4593i	0.848446	−	0.981028i
$965$	−16.1622	+	16.1622i	−0.520280	+	0.520280i
$966$	35.1238	+	13.0816i	1.13009	+	0.420895i
$967$			44.1068i			1.41838i	0.705018	+	0.709189i	$0.250939\pi$
$967$			44.1068i			1.41838i	−0.705018	+	0.709189i	$0.749061\pi$
$968$	−45.7457	−	13.3618i	−1.47032	−	0.429465i
$969$			0.169409i			0.00544220i
$970$	6.33795	−	17.0172i	0.203499	−	0.546390i
$971$	−2.44848	+	2.44848i	−0.0785755	+	0.0785755i	−0.745302	−	0.666727i	$-0.767695\pi$
$971$	−2.44848	+	2.44848i	−0.0785755	+	0.0785755i	0.666727	+	0.745302i	$0.267695\pi$
$972$	−19.0745	+	1.38233i	−0.611815	+	0.0443383i
$973$	58.1069	+	58.1069i	1.86282	+	1.86282i
$974$	6.79389	+	14.8580i	0.217690	+	0.476081i
$975$	11.0797			0.354833
$976$	−22.4597	+	30.1211i	−0.718919	+	0.964151i
$977$	33.5416			1.07309			0.536545	−	0.843871i	$-0.319729\pi$
$977$	33.5416			1.07309			0.536545	+	0.843871i	$0.319729\pi$
$978$	−15.0523	−	32.9188i	−0.481319	−	1.05263i
$979$	−66.4122	−	66.4122i	−2.12254	−	2.12254i
$980$	2.34652	+	32.3791i	0.0749567	+	1.03431i
$981$	−1.35508	+	1.35508i	−0.0432645	+	0.0432645i
$982$	0.643818	−	1.72863i	0.0205451	−	0.0551630i
$983$		−	54.7862i		−	1.74741i	−0.486458	−	0.873704i	$-0.661711\pi$
$983$		−	54.7862i		−	1.74741i	0.486458	−	0.873704i	$-0.338289\pi$
$984$	9.23530	+	16.8564i	0.294411	+	0.537363i
$985$			19.3376i			0.616148i
$986$	−0.735436	−	0.273908i	−0.0234211	−	0.00872301i
$987$	−12.6233	+	12.6233i	−0.401804	+	0.401804i
$988$	6.52076	+	5.63950i	0.207453	+	0.179416i
$989$	38.5078	+	38.5078i	1.22448	+	1.22448i
$990$	11.6805	−	5.34099i	0.371232	−	0.169748i
$991$	−53.2188			−1.69055			−0.845276	−	0.534330i	$-0.820564\pi$
$991$	−53.2188			−1.69055			−0.845276	+	0.534330i	$0.820564\pi$
$992$	6.71495	+	10.3947i	0.213200	+	0.330031i
$993$	13.5684			0.430581
$994$	34.0349	−	15.5626i	1.07952	−	0.493617i
$995$	−23.0861	−	23.0861i	−0.731880	−	0.731880i
$996$	24.7933	+	21.4426i	0.785605	+	0.679433i
$997$	−12.3452	+	12.3452i	−0.390978	+	0.390978i	−0.875036	−	0.484058i	$-0.839162\pi$
$997$	−12.3452	+	12.3452i	−0.390978	+	0.390978i	0.484058	+	0.875036i	$0.339162\pi$
$998$	12.8077	+	4.77013i	0.405419	+	0.150996i
$999$		−	20.3833i		−	0.644899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.30	✓	68
4.3	odd	2		1216.2.k.b.913.11		68
16.5	even	4	inner	304.2.k.b.229.30	yes	68
16.11	odd	4		1216.2.k.b.305.11		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.30	✓	68	1.1	even	1	trivial
304.2.k.b.229.30	yes	68	16.5	even	4	inner
1216.2.k.b.305.11		68	16.11	odd	4
1216.2.k.b.913.11		68	4.3	odd	2

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28614 - 0.588093i) q^{2} +(1.00943 + 1.00943i) q^{3} +(1.30829 - 1.51273i) q^{4} +(1.26480 - 1.26480i) q^{5} +(1.89189 + 0.704623i) q^{6} +4.00933i q^{7} +(0.793017 - 2.71498i) q^{8} -0.962122i q^{9} +O(q^{10})\)	\(q+(1.28614 - 0.588093i) q^{2} +(1.00943 + 1.00943i) q^{3} +(1.30829 - 1.51273i) q^{4} +(1.26480 - 1.26480i) q^{5} +(1.89189 + 0.704623i) q^{6} +4.00933i q^{7} +(0.793017 - 2.71498i) q^{8} -0.962122i q^{9} +(0.882889 - 2.37053i) q^{10} +(-3.73158 + 3.73158i) q^{11} +(2.84762 - 0.206367i) q^{12} +(-3.04804 - 3.04804i) q^{13} +(2.35786 + 5.15655i) q^{14} +2.55345 q^{15} +(-0.576732 - 3.95820i) q^{16} -0.118672 q^{17} +(-0.565817 - 1.23742i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-0.258577 - 3.56805i) q^{20} +(-4.04712 + 4.04712i) q^{21} +(-2.60481 + 6.99383i) q^{22} -4.63056i q^{23} +(3.54106 - 1.94008i) q^{24} +1.80054i q^{25} +(-5.71272 - 2.12766i) q^{26} +(3.99947 - 3.99947i) q^{27} +(6.06505 + 5.24538i) q^{28} +(3.30655 + 3.30655i) q^{29} +(3.28409 - 1.50167i) q^{30} -2.18760 q^{31} +(-3.06955 - 4.75162i) q^{32} -7.53350 q^{33} +(-0.152628 + 0.0697900i) q^{34} +(5.07102 + 5.07102i) q^{35} +(-1.45544 - 1.25874i) q^{36} +(2.54825 - 2.54825i) q^{37} +(-1.32528 - 0.493592i) q^{38} -6.15353i q^{39} +(-2.43091 - 4.43693i) q^{40} +4.76027i q^{41} +(-2.82507 + 7.58523i) q^{42} +(-8.31602 + 8.31602i) q^{43} +(0.762885 + 10.5269i) q^{44} +(-1.21690 - 1.21690i) q^{45} +(-2.72320 - 5.95553i) q^{46} +3.11908 q^{47} +(3.41334 - 4.57768i) q^{48} -9.07473 q^{49} +(1.05888 + 2.31574i) q^{50} +(-0.119790 - 0.119790i) q^{51} +(-8.59860 + 0.623142i) q^{52} +(1.97800 - 1.97800i) q^{53} +(2.79180 - 7.49591i) q^{54} +9.43944i q^{55} +(10.8853 + 3.17947i) q^{56} -1.42754i q^{57} +(6.19722 + 2.30811i) q^{58} +(1.94820 - 1.94820i) q^{59} +(3.34067 - 3.86269i) q^{60} +(-6.64200 - 6.64200i) q^{61} +(-2.81356 + 1.28651i) q^{62} +3.85746 q^{63} +(-6.74225 - 4.30605i) q^{64} -7.71034 q^{65} +(-9.68911 + 4.43039i) q^{66} +(-8.53000 - 8.53000i) q^{67} +(-0.155258 + 0.179519i) q^{68} +(4.67420 - 4.67420i) q^{69} +(9.50425 + 3.53980i) q^{70} -6.60033i q^{71} +(-2.61214 - 0.762979i) q^{72} +7.37248i q^{73} +(1.77879 - 4.77601i) q^{74} +(-1.81751 + 1.81751i) q^{75} +(-1.99477 + 0.144561i) q^{76} +(-14.9611 - 14.9611i) q^{77} +(-3.61885 - 7.91428i) q^{78} +12.3751 q^{79} +(-5.73581 - 4.27690i) q^{80} +5.18796 q^{81} +(2.79948 + 6.12236i) q^{82} +(8.11833 + 8.11833i) q^{83} +(0.827394 + 11.4170i) q^{84} +(-0.150097 + 0.150097i) q^{85} +(-5.80495 + 15.5861i) q^{86} +6.67542i q^{87} +(7.17196 + 13.0904i) q^{88} +17.7973i q^{89} +(-2.28074 - 0.849447i) q^{90} +(12.2206 - 12.2206i) q^{91} +(-7.00481 - 6.05813i) q^{92} +(-2.20822 - 2.20822i) q^{93} +(4.01157 - 1.83431i) q^{94} -1.78870 q^{95} +(1.69793 - 7.89488i) q^{96} +7.17865 q^{97} +(-11.6713 + 5.33678i) q^{98} +(3.59023 + 3.59023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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