LMFDB - Embedded newform 76.5.j.a.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.2
Character	$\chi$	$=$	76.21
Dual form			76.5.j.a.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.77177 + 9.26203i) q^{3} +(42.9478 - 15.6317i) q^{5} +(2.15264 + 3.72849i) q^{7} +(-11.3194 - 64.1954i) q^{9} +O(q^{10})$	\(q+(-7.77177 + 9.26203i) q^{3} +(42.9478 - 15.6317i) q^{5} +(2.15264 + 3.72849i) q^{7} +(-11.3194 - 64.1954i) q^{9} +(-53.2761 + 92.2769i) q^{11} +(157.331 + 187.500i) q^{13} +(-188.999 + 519.270i) q^{15} +(-15.1100 + 85.6928i) q^{17} +(-115.998 + 341.856i) q^{19} +(-51.2632 - 9.03909i) q^{21} +(55.9483 + 20.3635i) q^{23} +(1121.39 - 940.954i) q^{25} +(-165.590 - 95.6032i) q^{27} +(-226.682 + 39.9702i) q^{29} +(581.855 - 335.934i) q^{31} +(-440.622 - 1210.60i) q^{33} +(150.734 + 126.481i) q^{35} +2475.69i q^{37} -2959.37 q^{39} +(-650.315 + 775.016i) q^{41} +(2564.45 - 933.382i) q^{43} +(-1489.63 - 2580.11i) q^{45} +(-270.376 - 1533.38i) q^{47} +(1191.23 - 2063.27i) q^{49} +(-676.259 - 805.934i) q^{51} +(1048.86 - 2881.73i) q^{53} +(-845.645 + 4795.89i) q^{55} +(-2264.77 - 3731.21i) q^{57} +(4897.42 + 863.548i) q^{59} +(-5548.86 - 2019.62i) q^{61} +(214.985 - 180.394i) q^{63} +(9687.97 + 5593.35i) q^{65} +(698.565 - 123.176i) q^{67} +(-623.424 + 359.934i) q^{69} +(-149.426 - 410.545i) q^{71} +(-4824.78 - 4048.47i) q^{73} +17699.2i q^{75} -458.738 q^{77} +(-5317.06 + 6336.63i) q^{79} +(7134.02 - 2596.57i) q^{81} +(-6604.82 - 11439.9i) q^{83} +(690.587 + 3916.51i) q^{85} +(1391.52 - 2410.18i) q^{87} +(5164.02 + 6154.24i) q^{89} +(-360.414 + 990.228i) q^{91} +(-1410.61 + 7999.97i) q^{93} +(361.918 + 16495.2i) q^{95} +(-14459.8 - 2549.65i) q^{97} +(6526.80 + 2375.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

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			0
$2$		0			0
$3$	−7.77177	+	9.26203i	−0.863530	+	1.02911i	0.135734	+	0.990745i	$0.456661\pi$
$3$	−7.77177	+	9.26203i	−0.863530	+	1.02911i	−0.999264	+	0.0383696i	$0.987784\pi$
$4$		0			0
$5$	42.9478	−	15.6317i	1.71791	−	0.625269i	0.720257	−	0.693708i	$-0.244024\pi$
$5$	42.9478	−	15.6317i	1.71791	−	0.625269i	0.997655	+	0.0684387i	$0.0218018\pi$
$6$		0			0
$7$	2.15264	+	3.72849i	0.0439315	+	0.0760916i	0.887155	−	0.461471i	$-0.152678\pi$
$7$	2.15264	+	3.72849i	0.0439315	+	0.0760916i	−0.843224	+	0.537563i	$0.819345\pi$
$8$		0			0
$9$	−11.3194	−	64.1954i	−0.139745	−	0.792536i
$10$		0			0
$11$	−53.2761	+	92.2769i	−0.440298	+	0.762619i	−0.997711	−	0.0676161i	$-0.978461\pi$
$11$	−53.2761	+	92.2769i	−0.440298	+	0.762619i	0.557413	+	0.830235i	$0.311794\pi$
$12$		0			0
$13$	157.331	+	187.500i	0.930954	+	1.10947i	0.993771	+	0.111442i	$0.0355470\pi$
$13$	157.331	+	187.500i	0.930954	+	1.10947i	−0.0628174	+	0.998025i	$0.520009\pi$
$14$		0			0
$15$	−188.999	+	519.270i	−0.839995	+	2.30787i
$16$		0			0
$17$	−15.1100	+	85.6928i	−0.0522836	+	0.296515i	−0.999726	−	0.0234117i	$-0.992547\pi$
$17$	−15.1100	+	85.6928i	−0.0522836	+	0.296515i	0.947442	+	0.319927i	$0.103658\pi$
$18$		0			0
$19$	−115.998	+	341.856i	−0.321325	+	0.946969i
$19$	−115.998	+	341.856i	−0.321325	+	0.946969i
$20$		0			0
$21$	−51.2632	−	9.03909i	−0.116243	−	0.0204968i
$22$		0			0
$23$	55.9483	+	20.3635i	0.105762	+	0.0384943i	0.394359	−	0.918956i	$-0.370967\pi$
$23$	55.9483	+	20.3635i	0.105762	+	0.0384943i	−0.288597	+	0.957451i	$0.593189\pi$
$24$		0			0
$25$	1121.39	−	940.954i	1.79422	−	1.50553i
$26$		0			0
$27$	−165.590	−	95.6032i	−0.227146	−	0.131143i
$28$		0			0
$29$	−226.682	+	39.9702i	−0.269539	+	0.0475270i	−0.306784	−	0.951779i	$-0.599253\pi$
$29$	−226.682	+	39.9702i	−0.269539	+	0.0475270i	0.0372449	+	0.999306i	$0.488142\pi$
$30$		0			0
$31$	581.855	−	335.934i	0.605469	−	0.349567i	−0.165721	−	0.986173i	$-0.552995\pi$
$31$	581.855	−	335.934i	0.605469	−	0.349567i	0.771190	+	0.636605i	$0.219662\pi$
$32$		0			0
$33$	−440.622	−	1210.60i	−0.404612	−	1.11166i
$34$		0			0
$35$	150.734	+	126.481i	0.123048	+	0.103250i
$36$		0			0
$37$			2475.69i			1.80839i	0.427117	+	0.904196i	$0.359529\pi$
$37$			2475.69i			1.80839i	−0.427117	+	0.904196i	$0.640471\pi$
$38$		0			0
$39$	−2959.37			−1.94568
$40$		0			0
$41$	−650.315	+	775.016i	−0.386862	+	0.461045i	−0.923968	−	0.382471i	$-0.875073\pi$
$41$	−650.315	+	775.016i	−0.386862	+	0.461045i	0.537105	+	0.843515i	$0.319518\pi$
$42$		0			0
$43$	2564.45	−	933.382i	1.38694	−	0.504804i	0.462663	−	0.886534i	$-0.346894\pi$
$43$	2564.45	−	933.382i	1.38694	−	0.504804i	0.924274	+	0.381731i	$0.124672\pi$
$44$		0			0
$45$	−1489.63	−	2580.11i	−0.735618	−	1.27413i
$46$		0			0
$47$	−270.376	−	1533.38i	−0.122398	−	0.694151i	−0.982820	−	0.184569i	$-0.940911\pi$
$47$	−270.376	−	1533.38i	−0.122398	−	0.694151i	0.860422	−	0.509582i	$-0.170200\pi$
$48$		0			0
$49$	1191.23	−	2063.27i	0.496140	−	0.859340i
$50$		0			0
$51$	−676.259	−	805.934i	−0.259999	−	0.309855i
$52$		0			0
$53$	1048.86	−	2881.73i	0.373394	−	1.02589i	−0.600646	−	0.799515i	$-0.705090\pi$
$53$	1048.86	−	2881.73i	0.373394	−	1.02589i	0.974040	−	0.226377i	$-0.0726880\pi$
$54$		0			0
$55$	−845.645	+	4795.89i	−0.279552	+	1.58542i
$56$		0			0
$57$	−2264.77	−	3731.21i	−0.697066	−	1.14842i
$58$		0			0
$59$	4897.42	+	863.548i	1.40690	+	0.248075i	0.824976	−	0.565168i	$-0.191189\pi$
$59$	4897.42	+	863.548i	1.40690	+	0.248075i	0.581925	+	0.813242i	$0.302300\pi$
$60$		0			0
$61$	−5548.86	−	2019.62i	−1.49123	−	0.542763i	−0.537457	−	0.843291i	$-0.680615\pi$
$61$	−5548.86	−	2019.62i	−1.49123	−	0.542763i	−0.953773	+	0.300528i	$0.902837\pi$
$62$		0			0
$63$	214.985	−	180.394i	0.0541661	−	0.0454507i
$64$		0			0
$65$	9687.97	+	5593.35i	2.29301	+	1.32387i
$66$		0			0
$67$	698.565	−	123.176i	0.155617	−	0.0274395i	−0.0952968	−	0.995449i	$-0.530380\pi$
$67$	698.565	−	123.176i	0.155617	−	0.0274395i	0.250914	+	0.968009i	$0.419269\pi$
$68$		0			0
$69$	−623.424	+	359.934i	−0.130944	+	0.0756006i
$70$		0			0
$71$	−149.426	−	410.545i	−0.0296422	−	0.0814412i	0.923989	−	0.382419i	$-0.124909\pi$
$71$	−149.426	−	410.545i	−0.0296422	−	0.0814412i	−0.953631	+	0.300978i	$0.902687\pi$
$72$		0			0
$73$	−4824.78	−	4048.47i	−0.905383	−	0.759706i	0.0658524	−	0.997829i	$-0.479023\pi$
$73$	−4824.78	−	4048.47i	−0.905383	−	0.759706i	−0.971235	+	0.238123i	$0.923468\pi$
$74$		0			0
$75$			17699.2i			3.14652i
$76$		0			0
$77$	−458.738			−0.0773719
$78$		0			0
$79$	−5317.06	+	6336.63i	−0.851957	+	1.01532i	0.147698	+	0.989033i	$0.452814\pi$
$79$	−5317.06	+	6336.63i	−0.851957	+	1.01532i	−0.999654	+	0.0262899i	$0.991631\pi$
$80$		0			0
$81$	7134.02	−	2596.57i	1.08734	−	0.395758i
$82$		0			0
$83$	−6604.82	−	11439.9i	−0.958749	−	1.66060i	−0.725546	−	0.688173i	$-0.758413\pi$
$83$	−6604.82	−	11439.9i	−0.958749	−	1.66060i	−0.233202	−	0.972428i	$-0.574920\pi$
$84$		0			0
$85$	690.587	+	3916.51i	0.0955829	+	0.542078i
$86$		0			0
$87$	1391.52	−	2410.18i	0.183844	−	0.318428i
$88$		0			0
$89$	5164.02	+	6154.24i	0.651940	+	0.776952i	0.986205	−	0.165527i	$-0.0529325\pi$
$89$	5164.02	+	6154.24i	0.651940	+	0.776952i	−0.334265	+	0.942479i	$0.608488\pi$
$90$		0			0
$91$	−360.414	+	990.228i	−0.0435230	+	0.119578i
$92$		0			0
$93$	−1410.61	+	7999.97i	−0.163095	+	0.924959i
$94$		0			0
$95$	361.918	+	16495.2i	0.0401018	+	1.82772i
$96$		0			0
$97$	−14459.8	−	2549.65i	−1.53680	−	0.270980i	−0.659791	−	0.751449i	$-0.729355\pi$
$97$	−14459.8	−	2549.65i	−1.53680	−	0.270980i	−0.877012	+	0.480469i	$0.840467\pi$
$98$		0			0
$99$	6526.80	+	2375.56i	0.665933	+	0.242380i
$100$		0			0
$101$	9128.80	−	7659.97i	0.894893	−	0.750904i	−0.0742928	−	0.997236i	$-0.523670\pi$
$101$	9128.80	−	7659.97i	0.894893	−	0.750904i	0.969185	+	0.246332i	$0.0792255\pi$
$102$		0			0
$103$	5202.88	+	3003.89i	0.490421	+	0.283145i	0.724749	−	0.689013i	$-0.241956\pi$
$103$	5202.88	+	3003.89i	0.490421	+	0.283145i	−0.234328	+	0.972158i	$0.575289\pi$
$104$		0			0
$105$	−2342.94	+	413.124i	−0.212512	+	0.0374715i
$106$		0			0
$107$	13797.3	−	7965.87i	1.20511	−	0.695770i	0.243422	−	0.969920i	$-0.421730\pi$
$107$	13797.3	−	7965.87i	1.20511	−	0.695770i	0.961687	+	0.274151i	$0.0883967\pi$
$108$		0			0
$109$	−1127.50	−	3097.78i	−0.0948994	−	0.260734i	0.883156	−	0.469080i	$-0.155414\pi$
$109$	−1127.50	−	3097.78i	−0.0948994	−	0.260734i	−0.978055	+	0.208346i	$0.933192\pi$
$110$		0			0
$111$	−22929.9	−	19240.5i	−1.86104	−	1.56160i
$112$		0			0
$113$		−	5176.20i		−	0.405372i	−0.979244	−	0.202686i	$-0.935033\pi$
$113$		−	5176.20i		−	0.405372i	0.979244	−	0.202686i	$-0.0649671\pi$
$114$		0			0
$115$	2721.17			0.205760
$116$		0			0
$117$	10255.7	−	12222.3i	0.749196	−	0.892857i
$118$		0			0
$119$	−352.031	+	128.129i	−0.0248592	+	0.00904800i
$120$		0			0
$121$	1643.81	+	2847.17i	0.112275	+	0.194465i
$122$		0			0
$123$	−2124.12	−	12046.5i	−0.140401	−	0.796252i
$124$		0			0
$125$	19169.8	−	33203.0i	1.22687	−	2.12499i
$126$		0			0
$127$	−8203.83	−	9776.94i	−0.508638	−	0.606172i	0.449217	−	0.893423i	$-0.351703\pi$
$127$	−8203.83	−	9776.94i	−0.508638	−	0.606172i	−0.957855	+	0.287251i	$0.907259\pi$
$128$		0			0
$129$	−11285.3	+	31006.0i	−0.678160	+	1.86323i
$130$		0			0
$131$	−907.345	+	5145.81i	−0.0528725	+	0.299855i	−0.999765	−	0.0216966i	$-0.993093\pi$
$131$	−907.345	+	5145.81i	−0.0528725	+	0.299855i	0.946892	+	0.321552i	$0.104204\pi$
$132$		0			0
$133$	−1524.31	+	303.395i	−0.0861727	+	0.0171516i
$134$		0			0
$135$	−8606.15	−	1517.50i	−0.472217	−	0.0832646i
$136$		0			0
$137$	−26335.1	−	9585.18i	−1.40311	−	0.510692i	−0.474013	−	0.880518i	$-0.657195\pi$
$137$	−26335.1	−	9585.18i	−1.40311	−	0.510692i	−0.929101	+	0.369826i	$0.879417\pi$
$138$		0			0
$139$	−6235.78	+	5232.44i	−0.322746	+	0.270816i	−0.789737	−	0.613446i	$-0.789783\pi$
$139$	−6235.78	+	5232.44i	−0.322746	+	0.270816i	0.466990	+	0.884263i	$0.345338\pi$
$140$		0			0
$141$	16303.5	+	9412.84i	0.820056	+	0.473459i
$142$		0			0
$143$	−25683.9	+	4528.77i	−1.25600	+	0.221466i
$144$		0			0
$145$	−9110.71	+	5260.07i	−0.433327	+	0.250182i
$146$		0			0
$147$	9852.14	+	27068.5i	0.455928	+	1.25265i
$148$		0			0
$149$	11571.2	+	9709.39i	0.521202	+	0.437340i	0.865050	−	0.501685i	$-0.167286\pi$
$149$	11571.2	+	9709.39i	0.521202	+	0.437340i	−0.343849	+	0.939025i	$0.611731\pi$
$150$		0			0
$151$		−	16283.8i		−	0.714172i	−0.934072	−	0.357086i	$-0.883770\pi$
$151$		−	16283.8i		−	0.714172i	0.934072	−	0.357086i	$-0.116230\pi$
$152$		0			0
$153$	5672.12			0.242305
$154$		0			0
$155$	19738.2	−	23523.0i	0.821568	−	0.979107i
$156$		0			0
$157$	149.451	−	54.3957i	0.00606316	−	0.00220681i	−0.338987	−	0.940791i	$-0.610084\pi$
$157$	149.451	−	54.3957i	0.00606316	−	0.00220681i	0.345050	+	0.938584i	$0.387862\pi$
$158$		0			0
$159$	18539.2	+	32110.8i	0.733324	+	1.27015i
$160$		0			0
$161$	44.5116	+	252.438i	0.00171720	+	0.00973874i
$162$		0			0
$163$	21107.9	−	36559.9i	0.794454	−	1.37603i	−0.128731	−	0.991680i	$-0.541090\pi$
$163$	21107.9	−	36559.9i	0.794454	−	1.37603i	0.923185	−	0.384355i	$-0.125576\pi$
$164$		0			0
$165$	−37847.5	−	45104.9i	−1.39018	−	1.65675i
$166$		0			0
$167$	9351.36	−	25692.7i	0.335307	−	0.921247i	−0.651400	−	0.758735i	$-0.725818\pi$
$167$	9351.36	−	25692.7i	0.335307	−	0.921247i	0.986706	−	0.162513i	$-0.0519598\pi$
$168$		0			0
$169$	−5443.58	+	30872.1i	−0.190595	+	1.08092i
$170$		0			0
$171$	23258.6	+	3576.97i	0.795410	+	0.122327i
$172$		0			0
$173$	20255.6	+	3571.61i	0.676788	+	0.119336i	0.501469	−	0.865176i	$-0.332793\pi$
$173$	20255.6	+	3571.61i	0.676788	+	0.119336i	0.175319	+	0.984512i	$0.443904\pi$
$174$		0			0
$175$	5922.28	+	2155.53i	0.193381	+	0.0703848i
$176$		0			0
$177$	−46059.9	+	38648.8i	−1.47020	+	1.23364i
$178$		0			0
$179$	−23621.9	−	13638.1i	−0.737239	−	0.425645i	0.0838258	−	0.996480i	$-0.473286\pi$
$179$	−23621.9	−	13638.1i	−0.737239	−	0.425645i	−0.821064	+	0.570836i	$0.806619\pi$
$180$		0			0
$181$	938.228	−	165.435i	0.0286386	−	0.00504975i	−0.159311	−	0.987229i	$-0.550927\pi$
$181$	938.228	−	165.435i	0.0286386	−	0.00504975i	0.187949	+	0.982179i	$0.439816\pi$
$182$		0			0
$183$	61830.3	−	35697.7i	1.84629	−	1.06595i
$184$		0			0
$185$	38699.3	+	106325.i	1.13073	+	3.10666i
$186$		0			0
$187$	−7102.47	−	5959.68i	−0.203108	−	0.170427i
$188$		0			0
$189$		−	823.199i		−	0.0230452i
$190$		0			0
$191$	30843.6			0.845471			0.422736	−	0.906253i	$-0.361070\pi$
$191$	30843.6			0.845471			0.422736	+	0.906253i	$0.361070\pi$
$192$		0			0
$193$	−16809.0	+	20032.1i	−0.451259	+	0.537790i	−0.942930	−	0.332991i	$-0.891942\pi$
$193$	−16809.0	+	20032.1i	−0.451259	+	0.537790i	0.491671	+	0.870781i	$0.336386\pi$
$194$		0			0
$195$	−127099.	+	46260.1i	−3.34250	+	1.21657i
$196$		0			0
$197$	20383.7	+	35305.7i	0.525232	+	0.909728i	0.999568	+	0.0293847i	$0.00935479\pi$
$197$	20383.7	+	35305.7i	0.525232	+	0.909728i	−0.474336	+	0.880344i	$0.657312\pi$
$198$		0			0
$199$	9655.08	+	54756.7i	0.243809	+	1.38271i	0.823242	+	0.567690i	$0.192163\pi$
$199$	9655.08	+	54756.7i	0.243809	+	1.38271i	−0.579433	+	0.815020i	$0.696726\pi$
$200$		0			0
$201$	−4288.23	+	7427.43i	−0.106142	+	0.183843i
$202$		0			0
$203$	−636.995	−	759.141i	−0.0154577	−	0.0184217i
$204$		0			0
$205$	−15814.8	+	43450.8i	−0.376319	+	1.03393i
$206$		0			0
$207$	673.943	−	3822.12i	0.0157283	−	0.0891998i
$208$		0			0
$209$	−25365.5	−	28916.7i	−0.580698	−	0.661998i
$210$		0			0
$211$	−55860.4	−	9849.70i	−1.25470	−	0.221237i	−0.493494	−	0.869749i	$-0.664281\pi$
$211$	−55860.4	−	9849.70i	−1.25470	−	0.221237i	−0.761204	+	0.648512i	$0.775392\pi$
$212$		0			0
$213$	4963.79	+	1806.67i	0.109409	+	0.0398217i
$214$		0			0
$215$	95546.9	−	80173.4i	2.06700	−	1.73442i
$216$		0			0
$217$	2505.05	+	1446.29i	0.0531983	+	0.0307140i
$218$		0			0
$219$	74994.2	−	13223.5i	1.56365	−	0.275714i
$220$		0			0
$221$	−18444.7	+	10649.0i	−0.377647	+	0.218035i
$222$		0			0
$223$	−3325.90	−	9137.83i	−0.0668804	−	0.183752i	0.901750	−	0.432258i	$-0.142283\pi$
$223$	−3325.90	−	9137.83i	−0.0668804	−	0.183752i	−0.968631	+	0.248505i	$0.920061\pi$
$224$		0			0
$225$	−73098.3	−	61336.7i	−1.44392	−	1.21159i
$226$		0			0
$227$		−	46967.0i		−	0.911468i	−0.890116	−	0.455734i	$-0.849377\pi$
$227$		−	46967.0i		−	0.911468i	0.890116	−	0.455734i	$-0.150623\pi$
$228$		0			0
$229$	64077.4			1.22190			0.610948	−	0.791671i	$-0.290788\pi$
$229$	64077.4			1.22190			0.610948	+	0.791671i	$0.290788\pi$
$230$		0			0
$231$	3565.21	−	4248.85i	0.0668130	−	0.0796246i
$232$		0			0
$233$	16649.0	−	6059.75i	0.306674	−	0.111620i	−0.184099	−	0.982908i	$-0.558937\pi$
$233$	16649.0	−	6059.75i	0.306674	−	0.111620i	0.490773	+	0.871287i	$0.336714\pi$
$234$		0			0
$235$	−35581.4	−	61628.9i	−0.644300	−	1.11596i
$236$		0			0
$237$	−17367.1	−	98493.6i	−0.309193	−	1.75352i
$238$		0			0
$239$	−16641.4	+	28823.7i	−0.291335	+	0.504607i	−0.974126	−	0.226007i	$-0.927433\pi$
$239$	−16641.4	+	28823.7i	−0.291335	+	0.504607i	0.682791	+	0.730614i	$0.260766\pi$
$240$		0			0
$241$	2883.17	+	3436.03i	0.0496405	+	0.0591593i	0.790293	−	0.612729i	$-0.209928\pi$
$241$	2883.17	+	3436.03i	0.0496405	+	0.0591593i	−0.740653	+	0.671888i	$0.765484\pi$
$242$		0			0
$243$	−26097.3	+	71701.8i	−0.441960	+	1.21428i
$244$		0			0
$245$	18908.3	−	107234.i	0.315007	−	1.78649i
$246$		0			0
$247$	−82348.1	+	32034.9i	−1.34977	+	0.525084i
$248$		0			0
$249$	157288.	+	27734.1i	2.53686	+	0.447317i
$250$		0			0
$251$	49755.7	+	18109.6i	0.789760	+	0.287449i	0.705236	−	0.708972i	$-0.250841\pi$
$251$	49755.7	+	18109.6i	0.789760	+	0.287449i	0.0845238	+	0.996421i	$0.473063\pi$
$252$		0			0
$253$	−4859.79	+	4077.85i	−0.0759235	+	0.0637074i
$254$		0			0
$255$	−41641.9	−	24042.0i	−0.640399	−	0.369735i
$256$		0			0
$257$	59276.0	−	10452.0i	0.897455	−	0.158245i	0.294153	−	0.955758i	$-0.404963\pi$
$257$	59276.0	−	10452.0i	0.897455	−	0.158245i	0.603302	+	0.797513i	$0.293851\pi$
$258$		0			0
$259$	−9230.58	+	5329.28i	−0.137603	+	0.0794454i
$260$		0			0
$261$	5131.81	+	14099.5i	0.0753337	+	0.206978i
$262$		0			0
$263$	−22538.1	−	18911.8i	−0.325842	−	0.273414i	0.465161	−	0.885226i	$-0.345996\pi$
$263$	−22538.1	−	18911.8i	−0.325842	−	0.273414i	−0.791003	+	0.611812i	$0.790441\pi$
$264$		0			0
$265$		−	140160.i		−	1.99586i
$266$		0			0
$267$	−97134.3			−1.36254
$268$		0			0
$269$	−40065.0	+	47747.6i	−0.553682	+	0.659853i	−0.968197	−	0.250190i	$-0.919507\pi$
$269$	−40065.0	+	47747.6i	−0.553682	+	0.659853i	0.414514	+	0.910043i	$0.363951\pi$
$270$		0			0
$271$	−98266.8	+	35766.2i	−1.33804	+	0.487006i	−0.909194	−	0.416373i	$-0.863301\pi$
$271$	−98266.8	+	35766.2i	−1.33804	+	0.487006i	−0.428844	+	0.903379i	$0.641079\pi$
$272$		0			0
$273$	−6370.48	−	11034.0i	−0.0854765	−	0.148050i
$274$		0			0
$275$	27085.3	+	153608.i	0.358153	+	2.03118i
$276$		0			0
$277$	22345.6	−	38703.8i	0.291228	−	0.504422i	−0.682872	−	0.730538i	$-0.739269\pi$
$277$	22345.6	−	38703.8i	0.291228	−	0.504422i	0.974100	+	0.226116i	$0.0726028\pi$
$278$		0			0
$279$	−28151.7	−	33549.9i	−0.361656	−	0.431005i
$280$		0			0
$281$	−20650.9	+	56738.0i	−0.261533	+	0.718557i	0.737531	+	0.675313i	$0.235991\pi$
$281$	−20650.9	+	56738.0i	−0.261533	+	0.718557i	−0.999065	+	0.0432439i	$0.986231\pi$
$282$		0			0
$283$	−5636.27	+	31964.9i	−0.0703751	+	0.399117i	0.929189	+	0.369604i	$0.120507\pi$
$283$	−5636.27	+	31964.9i	−0.0703751	+	0.399117i	−0.999564	+	0.0295128i	$0.990604\pi$
$284$		0			0
$285$	−155592.	−	124845.i	−1.91557	−	1.53703i
$286$		0			0
$287$	−4289.54	−	756.361i	−0.0520771	−	0.00918259i
$288$		0			0
$289$	71369.1	+	25976.2i	0.854505	+	0.311014i
$290$		0			0
$291$	135993.	−	114112.i	1.60595	−	1.34755i
$292$		0			0
$293$	80889.4	+	46701.5i	0.942229	+	0.543996i	0.890658	−	0.454673i	$-0.150244\pi$
$293$	80889.4	+	46701.5i	0.942229	+	0.543996i	0.0515704	+	0.998669i	$0.483577\pi$
$294$		0			0
$295$	223832.	−	39467.7i	2.57205	−	0.453521i
$296$		0			0
$297$	17643.9	−	10186.7i	0.200024	−	0.115484i
$298$		0			0
$299$	4984.25	+	13694.1i	0.0557516	+	0.153176i
$300$		0			0
$301$	9000.44	+	7552.27i	0.0993415	+	0.0833574i
$302$		0			0
$303$			144083.i			1.56938i
$304$		0			0
$305$	−269882.			−2.90117
$306$		0			0
$307$	−57343.3	+	68339.1i	−0.608424	+	0.725091i	−0.979034	−	0.203697i	$-0.934704\pi$
$307$	−57343.3	+	68339.1i	−0.608424	+	0.725091i	0.370610	+	0.928788i	$0.379149\pi$
$308$		0			0
$309$	−68257.7	+	24843.8i	−0.714882	+	0.260196i
$310$		0			0
$311$	28338.0	+	49082.9i	0.292987	+	0.507469i	0.974515	−	0.224324i	$-0.0720174\pi$
$311$	28338.0	+	49082.9i	0.292987	+	0.507469i	−0.681528	+	0.731792i	$0.738684\pi$
$312$		0			0
$313$	25753.8	+	146057.i	0.262877	+	1.49085i	0.775013	+	0.631945i	$0.217743\pi$
$313$	25753.8	+	146057.i	0.262877	+	1.49085i	−0.512136	+	0.858904i	$0.671146\pi$
$314$		0			0
$315$	6413.27	−	11108.1i	0.0646336	−	0.111949i
$316$		0			0
$317$	−118529.	−	141258.i	−1.17952	−	1.40570i	−0.894433	−	0.447203i	$-0.852420\pi$
$317$	−118529.	−	141258.i	−1.17952	−	1.40570i	−0.285092	−	0.958500i	$-0.592024\pi$
$318$		0			0
$319$	8388.43	−	23047.0i	0.0824326	−	0.226482i
$320$		0			0
$321$	−33449.2	+	189700.i	−0.324620	+	1.84101i
$322$		0			0
$323$	−27541.8	−	15105.7i	−0.263990	−	0.144789i
$324$		0			0
$325$	352858.	+	62218.3i	3.34066	+	0.589049i
$326$		0			0
$327$	37454.4	+	13632.3i	0.350274	+	0.127489i
$328$		0			0
$329$	5135.17	−	4308.92i	0.0474420	−	0.0398085i
$330$		0			0
$331$	−24255.8	−	14004.1i	−0.221391	−	0.127820i	0.385203	−	0.922832i	$-0.374131\pi$
$331$	−24255.8	−	14004.1i	−0.221391	−	0.127820i	−0.606594	+	0.795012i	$0.707465\pi$
$332$		0			0
$333$	158928.	−	28023.3i	1.43322	−	0.252715i
$334$		0			0
$335$	28076.4	−	16209.9i	0.250179	−	0.144441i
$336$		0			0
$337$	−25143.3	−	69080.7i	−0.221392	−	0.608271i	0.778418	−	0.627746i	$-0.216023\pi$
$337$	−25143.3	−	69080.7i	−0.221392	−	0.608271i	−0.999810	+	0.0194757i	$0.993800\pi$
$338$		0			0
$339$	47942.2	+	40228.2i	0.417175	+	0.350051i
$340$		0			0
$341$			71589.1i			0.615656i
$342$		0			0
$343$	20594.2			0.175048
$344$		0			0
$345$	−21148.3	+	25203.6i	−0.177680	+	0.211750i
$346$		0			0
$347$	−71229.0	+	25925.2i	−0.591559	+	0.215310i	−0.620415	−	0.784274i	$-0.713036\pi$
$347$	−71229.0	+	25925.2i	−0.591559	+	0.215310i	0.0288561	+	0.999584i	$0.490814\pi$
$348$		0			0
$349$	−21076.6	−	36505.7i	−0.173041	−	0.299716i	0.766440	−	0.642315i	$-0.222026\pi$
$349$	−21076.6	−	36505.7i	−0.173041	−	0.299716i	−0.939482	+	0.342599i	$0.888693\pi$
$350$		0			0
$351$	−8126.81	−	46089.4i	−0.0659638	−	0.374099i
$352$		0			0
$353$	−24819.5	+	42988.7i	−0.199179	+	0.344988i	−0.948263	−	0.317487i	$-0.897161\pi$
$353$	−24819.5	+	42988.7i	−0.199179	+	0.344988i	0.749083	+	0.662476i	$0.230494\pi$
$354$		0			0
$355$	−12835.0	−	15296.2i	−0.101845	−	0.121374i
$356$		0			0
$357$	1549.17	−	4256.31i	0.0121552	−	0.0333962i
$358$		0			0
$359$	14713.1	−	83442.1i	0.114160	−	0.647435i	−0.873002	−	0.487716i	$-0.837830\pi$
$359$	14713.1	−	83442.1i	0.114160	−	0.647435i	0.987163	−	0.159719i	$-0.0510588\pi$
$360$		0			0
$361$	−103410.	−	79309.4i	−0.793500	−	0.608570i
$362$		0			0
$363$	−39145.9	−	6902.48i	−0.297080	−	0.0523831i
$364$		0			0
$365$	−270498.	−	98453.4i	−2.03039	−	0.739001i
$366$		0			0
$367$	38648.6	−	32430.0i	0.286947	−	0.240777i	−0.487940	−	0.872877i	$-0.662251\pi$
$367$	38648.6	−	32430.0i	0.286947	−	0.240777i	0.774887	+	0.632100i	$0.217807\pi$
$368$		0			0
$369$	57113.6	+	32974.6i	0.419456	+	0.242173i
$370$		0			0
$371$	13002.3	−	2292.66i	0.0944655	−	0.0166568i
$372$		0			0
$373$	−42536.7	+	24558.6i	−0.305735	+	0.176516i	−0.645017	−	0.764169i	$-0.723150\pi$
$373$	−42536.7	+	24558.6i	−0.305735	+	0.176516i	0.339281	+	0.940685i	$0.389816\pi$
$374$		0			0
$375$	158544.	+	435597.i	1.12743	+	3.09758i
$376$		0			0
$377$	−43158.6	−	36214.4i	−0.303658	−	0.254799i
$378$		0			0
$379$		−	46677.4i		−	0.324959i	−0.986712	−	0.162479i	$-0.948051\pi$
$379$		−	46677.4i		−	0.324959i	0.986712	−	0.162479i	$-0.0519491\pi$
$380$		0			0
$381$	154313.			1.06304
$382$		0			0
$383$	−74647.5	+	88961.5i	−0.508883	+	0.606463i	−0.957915	−	0.287053i	$-0.907325\pi$
$383$	−74647.5	+	88961.5i	−0.508883	+	0.606463i	0.449032	+	0.893516i	$0.351769\pi$
$384$		0			0
$385$	−19701.8	+	7170.86i	−0.132918	+	0.0483782i
$386$		0			0
$387$	−88946.7	−	154060.i	−0.593893	−	1.02865i
$388$		0			0
$389$	−37952.9	−	215242.i	−0.250811	−	1.42242i	−0.806601	−	0.591096i	$-0.798695\pi$
$389$	−37952.9	−	215242.i	−0.250811	−	1.42242i	0.555791	−	0.831322i	$-0.312416\pi$
$390$		0			0
$391$	−2590.38	+	4486.67i	−0.0169438	+	0.0293475i
$392$		0			0
$393$	−40609.0	−	48395.9i	−0.262928	−	0.313346i
$394$		0			0
$395$	−129304.	+	355259.i	−0.828737	+	2.27694i
$396$		0			0
$397$	−6390.11	+	36240.1i	−0.0405441	+	0.229937i	−0.998346	−	0.0574924i	$-0.981689\pi$
$397$	−6390.11	+	36240.1i	−0.0405441	+	0.229937i	0.957802	+	0.287429i	$0.0928006\pi$
$398$		0			0
$399$	9036.52	−	16476.1i	0.0567617	−	0.103493i
$400$		0			0
$401$	−67077.2	−	11827.5i	−0.417144	−	0.0735537i	−0.0388629	−	0.999245i	$-0.512374\pi$
$401$	−67077.2	−	11827.5i	−0.417144	−	0.0735537i	−0.378281	+	0.925691i	$0.623485\pi$
$402$		0			0
$403$	154532.	+	56244.9i	0.951497	+	0.346316i
$404$		0			0
$405$	265802.	−	223034.i	1.62049	−	1.35976i
$406$		0			0
$407$	−228449.	−	131895.i	−1.37911	−	0.796232i
$408$		0			0
$409$	44057.4	−	7768.52i	0.263374	−	0.0464399i	−0.0404018	−	0.999184i	$-0.512864\pi$
$409$	44057.4	−	7768.52i	0.263374	−	0.0464399i	0.303776	+	0.952744i	$0.401753\pi$
$410$		0			0
$411$	293448.	−	169422.i	1.73719	−	1.00297i
$412$		0			0
$413$	7322.68	+	20118.9i	0.0429309	+	0.117952i
$414$		0			0
$415$	−462488.	−	388073.i	−2.68537	−	2.25329i
$416$		0			0
$417$		−	98421.4i		−	0.566001i
$418$		0			0
$419$	203865.			1.16122			0.580612	−	0.814181i	$-0.302814\pi$
$419$	203865.			1.16122			0.580612	+	0.814181i	$0.302814\pi$
$420$		0			0
$421$	146420.	−	174497.i	0.826108	−	0.984517i	−0.173892	−	0.984765i	$-0.555634\pi$
$421$	146420.	−	174497.i	0.826108	−	0.984517i	1.00000		0.000248007i	$7.89430e-5\pi$
$422$		0			0
$423$	−95375.4	+	34713.8i	−0.533035	+	0.194009i
$424$		0			0
$425$	63688.9	+	110312.i	0.352603	+	0.610726i
$426$		0			0
$427$	−4414.59	−	25036.4i	−0.0242122	−	0.137314i
$428$		0			0
$429$	157664.	−	273082.i	0.856678	−	1.48381i
$430$		0			0
$431$	34977.2	+	41684.2i	0.188292	+	0.224397i	0.851929	−	0.523657i	$-0.175433\pi$
$431$	34977.2	+	41684.2i	0.188292	+	0.224397i	−0.663638	+	0.748054i	$0.730988\pi$
$432$		0			0
$433$	27973.5	−	76856.7i	0.149201	−	0.409926i	−0.842467	−	0.538748i	$-0.818897\pi$
$433$	27973.5	−	76856.7i	0.149201	−	0.409926i	0.991668	+	0.128822i	$0.0411196\pi$
$434$		0			0
$435$	22087.4	−	125264.i	0.116725	−	0.661983i
$436$		0			0
$437$	−13451.3	+	16764.1i	−0.0704370	+	0.0877844i
$438$		0			0
$439$	−320915.	−	56585.9i	−1.66518	−	0.293616i	−0.739846	−	0.672776i	$-0.765102\pi$
$439$	−320915.	−	56585.9i	−1.66518	−	0.293616i	−0.925331	+	0.379160i	$0.876213\pi$
$440$		0			0
$441$	−145937.	−	53116.6i	−0.750391	−	0.273120i
$442$		0			0
$443$	1195.82	−	1003.41i	0.00609337	−	0.00511295i	−0.639736	−	0.768595i	$-0.720956\pi$
$443$	1195.82	−	1003.41i	0.00609337	−	0.00511295i	0.645829	+	0.763482i	$0.276512\pi$
$444$		0			0
$445$	317984.	+	183588.i	1.60578	+	0.927097i
$446$		0			0
$447$	−179857.	+	31713.7i	−0.900147	+	0.158720i
$448$		0			0
$449$	179448.	−	103604.i	0.890113	−	0.513907i	0.0161336	−	0.999870i	$-0.494864\pi$
$449$	179448.	−	103604.i	0.890113	−	0.513907i	0.873979	+	0.485963i	$0.161531\pi$
$450$		0			0
$451$	−36869.8	−	101299.i	−0.181267	−	0.498026i
$452$		0			0
$453$	150821.	+	126554.i	0.734965	+	0.616709i
$454$		0			0
$455$			48162.0i			0.232639i
$456$		0			0
$457$	−115293.			−0.552040			−0.276020	−	0.961152i	$-0.589016\pi$
$457$	−115293.			−0.552040			−0.276020	+	0.961152i	$0.589016\pi$
$458$		0			0
$459$	10694.6	−	12745.3i	0.0507619	−	0.0604956i
$460$		0			0
$461$	−299131.	+	108875.i	−1.40754	+	0.512302i	−0.930406	−	0.366530i	$-0.880546\pi$
$461$	−299131.	+	108875.i	−1.40754	+	0.512302i	−0.477131	+	0.878832i	$0.658323\pi$
$462$		0			0
$463$	54789.1	+	94897.4i	0.255583	+	0.442683i	0.965054	−	0.262052i	$-0.0843993\pi$
$463$	54789.1	+	94897.4i	0.255583	+	0.442683i	−0.709471	+	0.704735i	$0.751066\pi$
$464$		0			0
$465$	64470.7	+	365631.i	0.298165	+	1.69098i
$466$		0			0
$467$	159310.	−	275933.i	0.730482	−	1.26523i	−0.226195	−	0.974082i	$-0.572629\pi$
$467$	159310.	−	275933.i	0.730482	−	1.26523i	0.956677	−	0.291151i	$-0.0940380\pi$
$468$		0			0
$469$	1963.02	+	2339.44i	0.00892440	+	0.0106357i
$470$		0			0
$471$	−657.683	+	1806.97i	−0.00296466	+	0.00814534i
$472$		0			0
$473$	−50494.1	+	286366.i	−0.225693	+	1.27997i
$474$		0			0
$475$	191592.	+	492501.i	0.849160	+	2.18283i
$476$		0			0
$477$	−196866.	−	34712.8i	−0.865236	−	0.152564i
$478$		0			0
$479$	335823.	+	122229.i	1.46366	+	0.532727i	0.946370	−	0.323085i	$-0.104720\pi$
$479$	335823.	+	122229.i	1.46366	+	0.532727i	0.517286	+	0.855812i	$0.326942\pi$
$480$		0			0
$481$	−464192.	+	389503.i	−2.00635	+	1.68353i
$482$		0			0
$483$	−2684.02	−	1549.62i	−0.0115051	−	0.00664249i
$484$		0			0
$485$	−660871.	+	116529.i	−2.80953	+	0.495396i
$486$		0			0
$487$	−213167.	+	123072.i	−0.898800	+	0.518922i	−0.876811	−	0.480836i	$-0.840333\pi$
$487$	−213167.	+	123072.i	−0.898800	+	0.518922i	−0.0219892	+	0.999758i	$0.507000\pi$
$488$		0			0
$489$	174573.	+	479637.i	0.730063	+	2.00583i
$490$		0			0
$491$	−37914.8	−	31814.3i	−0.157270	−	0.131965i	0.560757	−	0.827980i	$-0.310510\pi$
$491$	−37914.8	−	31814.3i	−0.157270	−	0.131965i	−0.718027	+	0.696015i	$0.754955\pi$
$492$		0			0
$493$		−	20029.0i		−	0.0824072i
$494$		0			0
$495$	317446.			1.29557
$496$		0			0
$497$	1209.05	−	1440.89i	0.00489476	−	0.00583335i
$498$		0			0
$499$	170320.	−	61991.4i	0.684013	−	0.248960i	0.0234434	−	0.999725i	$-0.492537\pi$
$499$	170320.	−	61991.4i	0.684013	−	0.248960i	0.660570	+	0.750765i	$0.270315\pi$
$500$		0			0
$501$	165290.	+	286290.i	0.658522	+	1.14059i
$502$		0			0
$503$	−72462.0	−	410952.i	−0.286401	−	1.62426i	−0.700239	−	0.713909i	$-0.746923\pi$
$503$	−72462.0	−	410952.i	−0.286401	−	1.62426i	0.413838	−	0.910350i	$-0.364188\pi$
$504$		0			0
$505$	272323.	−	471678.i	1.06783	−	1.84954i
$506$		0			0
$507$	−243632.	−	290349.i	−0.947804	−	1.12955i
$508$		0			0
$509$	14428.3	−	39641.3i	0.0556902	−	0.153007i	−0.908728	−	0.417389i	$-0.862945\pi$
$509$	14428.3	−	39641.3i	0.0556902	−	0.153007i	0.964418	+	0.264381i	$0.0851677\pi$
$510$		0			0
$511$	4708.65	−	26704.1i	0.0180324	−	0.102267i
$512$		0			0
$513$	51890.6	−	45518.0i	0.197176	−	0.172961i
$514$		0			0
$515$	270408.	+	47680.3i	1.01954	+	0.179773i
$516$		0			0
$517$	155900.	+	56743.0i	0.583265	+	0.212291i
$518$		0			0
$519$	−190502.	+	159850.i	−0.707237	+	0.593443i
$520$		0			0
$521$	237664.	+	137216.i	0.875566	+	0.505508i	0.869194	−	0.494472i	$-0.164638\pi$
$521$	237664.	+	137216.i	0.875566	+	0.505508i	0.00637184	+	0.999980i	$0.497972\pi$
$522$		0			0
$523$	188131.	−	33172.6i	0.687793	−	0.121276i	0.181180	−	0.983450i	$-0.442008\pi$
$523$	188131.	−	33172.6i	0.687793	−	0.121276i	0.506613	+	0.862174i	$0.330897\pi$
$524$		0			0
$525$	−65991.2	+	38100.0i	−0.239424	+	0.138231i
$526$		0			0
$527$	19995.3	+	54936.8i	0.0719959	+	0.197807i
$528$		0			0
$529$	−211655.	−	177600.i	−0.756341	−	0.634645i
$530$		0			0
$531$		−	324167.i		−	1.14969i
$532$		0			0
$533$	−247630.			−0.871665
$534$		0			0
$535$	468043.	−	557792.i	1.63523	−	1.94879i
$536$		0			0
$537$	309900.	−	112794.i	1.07467	−	0.391146i
$538$		0			0
$539$	126928.	+	219847.i	0.436899	+	0.756732i
$540$		0			0
$541$	92745.0	+	525983.i	0.316881	+	1.79712i	0.561474	+	0.827495i	$0.310235\pi$
$541$	92745.0	+	525983.i	0.316881	+	1.79712i	−0.244593	+	0.969626i	$0.578654\pi$
$542$		0			0
$543$	−5759.43	+	9975.62i	−0.0195335	+	0.0338330i
$544$		0			0
$545$	−96847.3	−	115418.i	−0.326058	−	0.388581i
$546$		0			0
$547$	−143720.	+	394868.i	−0.480334	+	1.31971i	0.428873	+	0.903365i	$0.358911\pi$
$547$	−143720.	+	394868.i	−0.480334	+	1.31971i	−0.909208	+	0.416343i	$0.863312\pi$
$548$		0			0
$549$	−66840.7	+	379072.i	−0.221767	+	1.25770i
$550$		0			0
$551$	12630.7	−	82129.2i	0.0416031	−	0.270517i
$552$		0			0
$553$	−35071.8	−	6184.10i	−0.114685	−	0.0202221i
$554$		0			0
$555$	−1.28555e6	−	467903.i	−4.17353	−	1.51904i
$556$		0			0
$557$	−99053.6	+	83115.8i	−0.319271	+	0.267900i	−0.788311	−	0.615276i	$-0.789044\pi$
$557$	−99053.6	+	83115.8i	−0.319271	+	0.267900i	0.469040	+	0.883177i	$0.344600\pi$
$558$		0			0
$559$	578476.	+	333983.i	1.85124	+	1.06881i
$560$		0			0
$561$	110398.	−	19466.1i	0.350779	−	0.0618518i
$562$		0			0
$563$	261889.	−	151202.i	0.826229	−	0.477024i	−0.0263308	−	0.999653i	$-0.508382\pi$
$563$	261889.	−	151202.i	0.826229	−	0.477024i	0.852560	+	0.522630i	$0.175049\pi$
$564$		0			0
$565$	−80912.9	−	222306.i	−0.253467	−	0.696394i
$566$		0			0
$567$	25038.3	+	21009.6i	0.0778823	+	0.0653510i
$568$		0			0
$569$			360748.i			1.11424i	0.830431	+	0.557121i	$0.188094\pi$
$569$			360748.i			1.11424i	−0.830431	+	0.557121i	$0.811906\pi$
$570$		0			0
$571$	232100.			0.711872			0.355936	−	0.934510i	$-0.384162\pi$
$571$	232100.			0.711872			0.355936	+	0.934510i	$0.384162\pi$
$572$		0			0
$573$	−239710.	+	285675.i	−0.730090	+	0.870087i
$574$		0			0
$575$	81900.7	−	29809.4i	0.247715	−	0.0901608i
$576$		0			0
$577$	−310604.	−	537982.i	−0.932944	−	1.61591i	−0.778259	−	0.627943i	$-0.783897\pi$
$577$	−310604.	−	537982.i	−0.932944	−	1.61591i	−0.154685	−	0.987964i	$-0.549436\pi$
$578$		0			0
$579$	−54903.0	−	311370.i	−0.163772	−	0.928796i
$580$		0			0
$581$	28435.7	−	49252.0i	0.0842386	−	0.145905i
$582$		0			0
$583$	210038.	+	250313.i	0.617960	+	0.736456i
$584$		0			0
$585$	249406.	−	685236.i	0.728777	−	2.00230i
$586$		0			0
$587$	−103359.	+	586178.i	−0.299966	+	1.70119i	0.346336	+	0.938111i	$0.387426\pi$
$587$	−103359.	+	586178.i	−0.299966	+	1.70119i	−0.646302	+	0.763082i	$0.723685\pi$
$588$		0			0
$589$	47346.8	+	237878.i	0.136477	+	0.685685i
$590$		0			0
$591$	−485420.	−	85592.6i	−1.38977	−	0.245054i
$592$		0			0
$593$	426488.	+	155229.i	1.21282	+	0.441431i	0.867682	−	0.497120i	$-0.165609\pi$
$593$	426488.	+	155229.i	1.21282	+	0.441431i	0.345140	+	0.938551i	$0.387831\pi$
$594$		0			0
$595$	−13116.1	+	11005.7i	−0.0370485	+	0.0310874i
$596$		0			0
$597$	−582196.	−	336131.i	−1.63350	−	0.943104i
$598$		0			0
$599$	−318910.	+	56232.5i	−0.888822	+	0.156723i	−0.599373	−	0.800470i	$-0.704583\pi$
$599$	−318910.	+	56232.5i	−0.888822	+	0.156723i	−0.289449	+	0.957193i	$0.593472\pi$
$600$		0			0
$601$	−146181.	+	84397.6i	−0.404708	+	0.233658i	−0.688513	−	0.725224i	$-0.741736\pi$
$601$	−146181.	+	84397.6i	−0.404708	+	0.233658i	0.283805	+	0.958882i	$0.408403\pi$
$602$		0			0
$603$	−15814.6	−	43450.4i	−0.0434935	−	0.119497i
$604$		0			0
$605$	115104.	+	96583.9i	0.314471	+	0.263872i
$606$		0			0
$607$		−	259583.i		−	0.704529i	−0.935900	−	0.352265i	$-0.885412\pi$
$607$		−	259583.i		−	0.704529i	0.935900	−	0.352265i	$-0.114588\pi$
$608$		0			0
$609$	11981.8			0.0323062
$610$		0			0
$611$	244970.	−	291944.i	0.656192	−	0.782019i
$612$		0			0
$613$	111054.	−	40420.2i	0.295537	−	0.107567i	−0.189997	−	0.981785i	$-0.560848\pi$
$613$	111054.	−	40420.2i	0.295537	−	0.107567i	0.485533	+	0.874218i	$0.338625\pi$
$614$		0			0
$615$	−279534.	−	484167.i	−0.739067	−	1.28010i
$616$		0			0
$617$	−108570.	−	615731.i	−0.285193	−	1.61741i	−0.704594	−	0.709611i	$-0.748871\pi$
$617$	−108570.	−	615731.i	−0.285193	−	1.61741i	0.419400	−	0.907801i	$-0.362240\pi$
$618$		0			0
$619$	−244052.	+	422710.i	−0.636943	+	1.10322i	0.349157	+	0.937064i	$0.386468\pi$
$619$	−244052.	+	422710.i	−0.636943	+	1.10322i	−0.986100	+	0.166154i	$0.946865\pi$
$620$		0			0
$621$	−7317.63	−	8720.82i	−0.0189753	−	0.0226138i
$622$		0			0
$623$	−11829.7	+	32501.9i	−0.0304788	+	0.0837398i
$624$		0			0
$625$	145406.	−	824637.i	0.372239	−	2.11107i
$626$		0			0
$627$	464962.	−	10201.6i	1.18272	−	0.0259499i
$628$		0			0
$629$	−212149.	−	37407.5i	−0.536215	−	0.0945492i
$630$		0			0
$631$	135771.	+	49416.5i	0.340994	+	0.124112i	0.506840	−	0.862040i	$-0.330813\pi$
$631$	135771.	+	49416.5i	0.340994	+	0.124112i	−0.165846	+	0.986152i	$0.553036\pi$
$632$		0			0
$633$	525363.	−	440832.i	1.31115	−	1.10018i
$634$		0			0
$635$	−505167.	−	291658.i	−1.25282	−	0.723314i
$636$		0			0
$637$	574282.	−	101261.i	1.41529	−	0.249554i
$638$		0			0
$639$	−24663.7	+	14239.6i	−0.0604027	+	0.0348735i
$640$		0			0
$641$	−221079.	−	607409.i	−0.538061	−	1.47831i	−0.849265	−	0.527966i	$-0.822955\pi$
$641$	−221079.	−	607409.i	−0.538061	−	1.47831i	0.311205	−	0.950343i	$-0.399268\pi$
$642$		0			0
$643$	−162219.	−	136118.i	−0.392355	−	0.329225i	0.425175	−	0.905111i	$-0.360213\pi$
$643$	−162219.	−	136118.i	−0.392355	−	0.329225i	−0.817530	+	0.575886i	$0.804657\pi$
$644$		0			0
$645$			1.50805e6i			3.62490i
$646$		0			0
$647$	417859.			0.998208			0.499104	−	0.866542i	$-0.333663\pi$
$647$	417859.			0.998208			0.499104	+	0.866542i	$0.333663\pi$
$648$		0			0
$649$	−340601.	+	405913.i	−0.808643	+	0.963703i
$650$		0			0
$651$	−32864.3	+	11961.6i	−0.0775466	+	0.0282247i
$652$		0			0
$653$	−84288.8	−	145993.i	−0.197671	−	0.342377i	0.750102	−	0.661323i	$-0.230005\pi$
$653$	−84288.8	−	145993.i	−0.197671	−	0.342377i	−0.947773	+	0.318946i	$0.896671\pi$
$654$		0			0
$655$	41469.4	+	235185.i	0.0966596	+	0.548184i
$656$		0			0
$657$	−205280.	+	355555.i	−0.475571	+	0.823713i
$658$		0			0
$659$	439281.	+	523515.i	1.01151	+	1.20548i	0.978548	+	0.206019i	$0.0660508\pi$
$659$	439281.	+	523515.i	1.01151	+	1.20548i	0.0329657	+	0.999456i	$0.489505\pi$
$660$		0			0
$661$	46527.5	−	127833.i	0.106490	−	0.292578i	−0.874991	−	0.484139i	$-0.839133\pi$
$661$	46527.5	−	127833.i	0.106490	−	0.292578i	0.981481	+	0.191561i	$0.0613551\pi$
$662$		0			0
$663$	44716.0	−	253597.i	0.101727	−	0.576922i
$664$		0			0
$665$	−60723.1	+	36857.7i	−0.137313	+	0.0833461i
$666$		0			0
$667$	−13496.4	−	2379.78i	−0.0303366	−	0.00534916i
$668$		0			0
$669$	110483.	+	40212.5i	0.246856	+	0.0898481i
$670$		0			0
$671$	481986.	−	404435.i	1.07051	−	0.898263i
$672$		0			0
$673$	102257.	+	59038.0i	0.225768	+	0.130347i	0.608618	−	0.793463i	$-0.291724\pi$
$673$	102257.	+	59038.0i	0.225768	+	0.130347i	−0.382850	+	0.923810i	$0.625057\pi$
$674$		0			0
$675$	−275648.	+	48604.2i	−0.604989	+	0.106676i
$676$		0			0
$677$	464689.	−	268288.i	1.01388	−	0.585361i	0.101551	−	0.994830i	$-0.467619\pi$
$677$	464689.	−	268288.i	1.01388	−	0.585361i	0.912324	+	0.409469i	$0.134286\pi$
$678$		0			0
$679$	−21620.4	−	59401.6i	−0.0468948	−	0.128842i
$680$		0			0
$681$	435010.	+	365017.i	0.938005	+	0.787080i
$682$		0			0
$683$		−	231574.i		−	0.496420i	−0.968706	−	0.248210i	$-0.920158\pi$
$683$		−	231574.i		−	0.496420i	0.968706	−	0.248210i	$-0.0798423\pi$
$684$		0			0
$685$	−1.28087e6			−2.72975
$686$		0			0
$687$	−497995.	+	593487.i	−1.05514	+	1.25747i
$688$		0			0
$689$	705343.	−	256724.i	1.48581	−	0.540789i
$690$		0			0
$691$	111751.	+	193558.i	0.234043	+	0.405374i	0.958994	−	0.283426i	$-0.0914711\pi$
$691$	111751.	+	193558.i	0.234043	+	0.405374i	−0.724951	+	0.688800i	$0.758138\pi$
$692$		0			0
$693$	5192.63	+	29448.9i	0.0108124	+	0.0613200i
$694$		0			0
$695$	−186021.	+	322198.i	−0.385117	+	0.667042i
$696$		0			0
$697$	−56587.0	−	67437.8i	−0.116480	−	0.138815i
$698$		0			0
$699$	−73266.8	+	201299.i	−0.149952	+	0.411990i
$700$		0			0
$701$	20429.4	−	115861.i	0.0415737	−	0.235776i	−0.956939	−	0.290288i	$-0.906249\pi$
$701$	20429.4	−	115861.i	0.0415737	−	0.235776i	0.998513	+	0.0545114i	$0.0173601\pi$
$702$		0			0
$703$	−846329.	−	287176.i	−1.71249	−	0.581082i
$704$		0			0
$705$	847339.	+	149409.i	1.70482	+	0.300606i
$706$		0			0
$707$	48211.2	+	17547.4i	0.0964515	+	0.0351055i
$708$		0			0
$709$	−57886.1	+	48572.2i	−0.115155	+	0.0966264i	−0.698547	−	0.715564i	$-0.746170\pi$
$709$	−57886.1	+	48572.2i	−0.115155	+	0.0966264i	0.583392	+	0.812191i	$0.301725\pi$
$710$		0			0
$711$	466968.	+	269604.i	0.923736	+	0.533319i
$712$		0			0
$713$	39394.6	−	6946.33i	0.0774921	−	0.0136639i
$714$		0			0
$715$	−1.03228e6	+	595984.i	−2.01922	+	1.16580i
$716$		0			0
$717$	−137633.	−	378144.i	−0.267722	−	0.735561i
$718$		0			0
$719$	422817.	+	354785.i	0.817889	+	0.686291i	0.952477	−	0.304611i	$-0.0985265\pi$
$719$	422817.	+	354785.i	0.817889	+	0.686291i	−0.134587	+	0.990902i	$0.542971\pi$
$720$		0			0
$721$			25865.2i			0.0497559i
$722$		0			0
$723$	−54232.0			−0.103748
$724$		0			0
$725$	−216588.	+	258120.i	−0.412058	+	0.491072i
$726$		0			0
$727$	170252.	−	61966.5i	0.322123	−	0.117243i	−0.175897	−	0.984409i	$-0.556283\pi$
$727$	170252.	−	61966.5i	0.322123	−	0.117243i	0.498021	+	0.867165i	$0.334060\pi$
$728$		0			0
$729$	−153812.	−	266410.i	−0.289424	−	0.501297i
$730$		0			0
$731$	41235.4	+	233858.i	0.0771678	+	0.437640i
$732$		0			0
$733$	−340098.	+	589067.i	−0.632989	+	1.09637i	0.353948	+	0.935265i	$0.384839\pi$
$733$	−340098.	+	589067.i	−0.632989	+	1.09637i	−0.986937	+	0.161105i	$0.948494\pi$
$734$		0			0
$735$	846255.	+	1.00853e6i	1.56649	+	1.86687i
$736$		0			0
$737$	−25850.5	+	71023.7i	−0.0475921	+	0.130758i
$738$		0			0
$739$	−18375.1	+	104210.i	−0.0336466	+	0.190819i	−0.996998	−	0.0774216i	$-0.975331\pi$
$739$	−18375.1	+	104210.i	−0.0336466	+	0.190819i	0.963352	+	0.268241i	$0.0864424\pi$
$740$		0			0
$741$	343282.	−	1.01168e6i	0.625195	−	1.84249i
$742$		0			0
$743$	621964.	+	109669.i	1.12665	+	0.198658i	0.705757	−	0.708454i	$-0.250607\pi$
$743$	621964.	+	109669.i	1.12665	+	0.198658i	0.420889	+	0.907112i	$0.361718\pi$
$744$		0			0
$745$	648732.	+	236119.i	1.16883	+	0.425421i
$746$		0			0
$747$	−659625.	+	553491.i	−1.18211	+	0.991904i
$748$		0			0
$749$	59401.3	+	34295.4i	0.105884	+	0.0611324i
$750$		0			0
$751$	−987429.	+	174110.i	−1.75076	+	0.308706i	−0.954933	−	0.296822i	$-0.904073\pi$
$751$	−987429.	+	174110.i	−1.75076	+	0.308706i	−0.795825	+	0.605527i	$0.792962\pi$
$752$		0			0
$753$	−554421.	+	320095.i	−0.977800	+	0.564533i
$754$		0			0
$755$	−254544.	−	699355.i	−0.446549	−	1.22688i
$756$		0			0
$757$	180218.	+	151221.i	0.314489	+	0.263888i	0.786344	−	0.617788i	$-0.211971\pi$
$757$	180218.	+	151221.i	0.314489	+	0.263888i	−0.471855	+	0.881676i	$0.656416\pi$
$758$		0			0
$759$		−	76703.6i		−	0.133147i
$760$		0			0
$761$	−448159.			−0.773861			−0.386931	−	0.922109i	$-0.626465\pi$
$761$	−448159.			−0.773861			−0.386931	+	0.922109i	$0.626465\pi$
$762$		0			0
$763$	9122.94	−	10872.3i	0.0156706	−	0.0186755i
$764$		0			0
$765$	243605.	−	88664.9i	0.416259	−	0.151506i
$766$		0			0
$767$	608602.	+	1.05413e6i	1.03453	+	1.79186i
$768$		0			0
$769$	7459.51	+	42305.0i	0.0126141	+	0.0715383i	0.990465	−	0.137764i	$-0.0439917\pi$
$769$	7459.51	+	42305.0i	0.0126141	+	0.0715383i	−0.977851	+	0.209303i	$0.932881\pi$
$770$		0			0
$771$	−363873.	+	630247.i	−0.612126	+	1.06023i
$772$		0			0
$773$	11898.2	+	14179.7i	0.0199124	+	0.0237306i	0.775909	−	0.630845i	$-0.217292\pi$
$773$	11898.2	+	14179.7i	0.0199124	+	0.0237306i	−0.755996	+	0.654576i	$0.772847\pi$
$774$		0			0
$775$	336385.	−	924211.i	0.560059	−	1.53875i
$776$		0			0
$777$	22378.0	−	126912.i	0.0370663	−	0.210213i
$778$		0			0
$779$	−189508.	−	312215.i	−0.312286	−	0.514492i
$780$		0			0
$781$	45844.7	+	8083.65i	0.0751600	+	0.0132527i
$782$		0			0
$783$	41357.5	+	15052.9i	0.0674576	+	0.0245526i
$784$		0			0
$785$	5568.29	−	4672.35i	0.00903613	−	0.00758221i
$786$		0			0
$787$	−146996.	−	84868.4i	−0.237332	−	0.137024i	0.376618	−	0.926369i	$-0.377087\pi$
$787$	−146996.	−	84868.4i	−0.237332	−	0.137024i	−0.613950	+	0.789345i	$0.710420\pi$
$788$		0			0
$789$	350323.	−	61771.3i	0.562748	−	0.0992277i
$790$		0			0
$791$	19299.4	−	11142.5i	0.0308454	−	0.0178086i
$792$		0			0
$793$	−494330.	−	1.35816e6i	−0.786087	−	2.15976i
$794$		0			0
$795$	1.29816e6	+	1.08929e6i	2.05397	+	1.72349i
$796$		0			0
$797$		−	595156.i		−	0.936946i	−0.883478	−	0.468473i	$-0.844804\pi$
$797$		−	595156.i		−	0.936946i	0.883478	−	0.468473i	$-0.155196\pi$
$798$		0			0
$799$	135485.			0.212226
$800$		0			0
$801$	336620.	−	401168.i	0.524656	−	0.625261i
$802$		0			0
$803$	630626.	−	229529.i	0.978005	−	0.355965i
$804$		0			0
$805$	5857.71	+	10145.9i	0.00903933	+	0.0156566i
$806$		0			0
$807$	−130864.	−	742167.i	−0.200943	−	1.13961i
$808$		0			0
$809$	−43119.3	+	74684.7i	−0.0658831	+	0.114113i	−0.897085	−	0.441857i	$-0.854320\pi$
$809$	−43119.3	+	74684.7i	−0.0658831	+	0.114113i	0.831202	+	0.555970i	$0.187653\pi$
$810$		0			0
$811$	−487993.	−	581567.i	−0.741945	−	0.884215i	0.254619	−	0.967041i	$-0.418050\pi$
$811$	−487993.	−	581567.i	−0.741945	−	0.884215i	−0.996564	+	0.0828260i	$0.973605\pi$
$812$		0			0
$813$	432439.	−	1.18812e6i	0.654251	−	1.79754i
$814$		0			0
$815$	335042.	−	1.90012e6i	0.504411	−	2.86065i
$816$		0			0
$817$	21610.4	+	984941.i	0.0323757	+	1.47559i
$818$		0			0
$819$	67647.7	+	11928.1i	0.100852	+	0.0177830i
$820$		0			0
$821$	−158492.	−	57686.4i	−0.235137	−	0.0855829i	0.221764	−	0.975100i	$-0.428819\pi$
$821$	−158492.	−	57686.4i	−0.235137	−	0.0855829i	−0.456901	+	0.889517i	$0.651041\pi$
$822$		0			0
$823$	−729226.	+	611893.i	−1.07662	+	0.903391i	−0.995636	−	0.0933244i	$-0.970251\pi$
$823$	−729226.	+	611893.i	−1.07662	+	0.903391i	−0.0809838	+	0.996715i	$0.525806\pi$
$824$		0			0
$825$	−1.63323e6	−	942944.i	−2.39960	−	1.38541i
$826$		0			0
$827$	807926.	−	142459.i	1.18130	−	0.208295i	0.451701	−	0.892170i	$-0.350818\pi$
$827$	807926.	−	142459.i	1.18130	−	0.208295i	0.729600	+	0.683874i	$0.239706\pi$
$828$		0			0
$829$	−80911.6	+	46714.3i	−0.117734	+	0.0679737i	−0.557711	−	0.830036i	$-0.688320\pi$
$829$	−80911.6	+	46714.3i	−0.117734	+	0.0679737i	0.439977	+	0.898009i	$0.354987\pi$
$830$		0			0
$831$	184811.	+	507763.i	0.267624	+	0.735291i
$832$		0			0
$833$	158808.	+	133256.i	0.228867	+	0.192042i
$834$		0			0
$835$		−	1.24962e6i		−	1.79228i
$836$		0			0
$837$	−128466.			−0.183373
$838$		0			0
$839$	−563360.	+	671386.i	−0.800317	+	0.953781i	−0.999658	−	0.0261496i	$-0.991675\pi$
$839$	−563360.	+	671386.i	−0.800317	+	0.953781i	0.199341	+	0.979930i	$0.436120\pi$
$840$		0			0
$841$	−614839.	+	223783.i	−0.869300	+	0.316399i
$842$		0			0
$843$	−365015.	−	632224.i	−0.513636	−	0.889643i
$844$		0			0
$845$	248794.	+	1.41098e6i	0.348439	+	1.97609i
$846$		0			0
$847$	−7077.08	+	12257.9i	−0.00986478	+	0.0170863i
$848$		0			0
$849$	−252256.	−	300627.i	−0.349966	−	0.417074i
$850$		0			0
$851$	−50413.7	+	138510.i	−0.0696129	+	0.191260i
$852$		0			0
$853$	−39511.4	+	224080.i	−0.0543030	+	0.307968i	−0.999846	−	0.0175284i	$-0.994420\pi$
$853$	−39511.4	+	224080.i	−0.0543030	+	0.307968i	0.945543	+	0.325496i	$0.105531\pi$
$854$		0			0
$855$	1.05482e6	−	209949.i	1.44293	−	0.287198i
$856$		0			0
$857$	−344537.	−	60751.2i	−0.469110	−	0.0827167i	−0.0659037	−	0.997826i	$-0.520993\pi$
$857$	−344537.	−	60751.2i	−0.469110	−	0.0827167i	−0.403206	+	0.915109i	$0.632104\pi$
$858$		0			0
$859$	461316.	+	167905.i	0.625191	+	0.227551i	0.635137	−	0.772400i	$-0.280944\pi$
$859$	461316.	+	167905.i	0.625191	+	0.227551i	−0.00994611	+	0.999951i	$0.503166\pi$
$860$		0			0
$861$	40342.7	−	33851.6i	0.0544200	−	0.0456638i
$862$		0			0
$863$	−513261.	−	296332.i	−0.689155	−	0.397884i	0.114140	−	0.993465i	$-0.463589\pi$
$863$	−513261.	−	296332.i	−0.689155	−	0.397884i	−0.803295	+	0.595581i	$0.796922\pi$
$864$		0			0
$865$	925764.	−	163237.i	1.23728	−	0.218166i
$866$		0			0
$867$	−795257.	+	459142.i	−1.05796	+	0.610814i
$868$		0			0
$869$	−301452.	−	828233.i	−0.399189	−	1.09676i
$870$		0			0
$871$	133001.	+	111601.i	0.175315	+	0.147107i
$872$		0			0
$873$			957112.i			1.25584i
$874$		0			0
$875$	165063.			0.215592
$876$		0			0
$877$	543713.	−	647971.i	0.706920	−	0.842474i	−0.286371	−	0.958119i	$-0.592449\pi$
$877$	543713.	−	647971.i	0.706920	−	0.842474i	0.993291	+	0.115645i	$0.0368933\pi$
$878$		0			0
$879$	−1.06120e6	+	386247.i	−1.37348	+	0.499905i
$880$		0			0
$881$	−59626.2	−	103276.i	−0.0768220	−	0.133060i	0.825055	−	0.565052i	$-0.191144\pi$
$881$	−59626.2	−	103276.i	−0.0768220	−	0.133060i	−0.901877	+	0.431993i	$0.857811\pi$
$882$		0			0
$883$	−33156.0	−	188037.i	−0.0425246	−	0.241169i	0.956135	−	0.292926i	$-0.0946290\pi$
$883$	−33156.0	−	188037.i	−0.0425246	−	0.241169i	−0.998660	+	0.0517570i	$0.983518\pi$
$884$		0			0
$885$	−1.37402e6	+	2.37988e6i	−1.75431	+	3.03856i
$886$		0			0
$887$	−62444.6	−	74418.6i	−0.0793684	−	0.0945876i	0.724899	−	0.688855i	$-0.241886\pi$
$887$	−62444.6	−	74418.6i	−0.0793684	−	0.0945876i	−0.804267	+	0.594268i	$0.797442\pi$
$888$		0			0
$889$	18793.3	−	51634.2i	0.0237793	−	0.0653332i
$890$		0			0
$891$	−140469.	+	796641.i	−0.176940	+	1.00348i
$892$		0			0
$893$	555558.	+	85439.9i	0.696669	+	0.107142i
$894$		0			0
$895$	−1.22769e6	−	216476.i	−1.53265	−	0.270248i
$896$		0			0
$897$	−165572.	−	60263.2i	−0.205779	−	0.0748975i
$898$		0			0
$899$	−118469.	+	99407.3i	−0.146584	+	0.122998i
$900$		0			0
$901$	231095.	+	133423.i	0.284670	+	0.164354i
$902$		0			0
$903$	−139899.	+	24667.9i	−0.171569	+	0.0302522i
$904$		0			0
$905$	37708.8	−	21771.2i	0.0460411	−	0.0265818i
$906$		0			0
$907$	285820.	+	785284.i	0.347439	+	0.954580i	0.983174	+	0.182672i	$0.0584748\pi$
$907$	285820.	+	785284.i	0.347439	+	0.954580i	−0.635735	+	0.771907i	$0.719303\pi$
$908$		0			0
$909$	−595067.	−	499321.i	−0.720175	−	0.604299i
$910$		0			0
$911$		−	1.47071e6i		−	1.77210i	−0.463585	−	0.886052i	$-0.653437\pi$
$911$		−	1.47071e6i		−	1.77210i	0.463585	−	0.886052i	$-0.346563\pi$
$912$		0			0
$913$	1.40752e6			1.68854
$914$		0			0
$915$	2.09746e6	−	2.49965e6i	2.50525	−	2.98564i
$916$		0			0
$917$	−21139.3	+	7694.07i	−0.0251392	+	0.00914993i
$918$		0			0
$919$	64742.8	+	112138.i	0.0766585	+	0.132776i	0.901806	−	0.432140i	$-0.142242\pi$
$919$	64742.8	+	112138.i	0.0766585	+	0.132776i	−0.825148	+	0.564917i	$0.808908\pi$
$920$		0			0
$921$	−187300.	−	1.06223e6i	−0.220810	−	1.25228i
$922$		0			0
$923$	53467.8	−	92608.9i	0.0627608	−	0.108705i
$924$		0			0
$925$	2.32951e6	+	2.77620e6i	2.72258	+	3.24465i
$926$		0			0
$927$	133942.	−	368003.i	0.155868	−	0.428245i
$928$		0			0
$929$	185492.	−	1.05197e6i	0.214928	−	1.21892i	−0.666104	−	0.745859i	$-0.732039\pi$
$929$	185492.	−	1.05197e6i	0.214928	−	1.21892i	0.881032	−	0.473057i	$-0.156850\pi$
$930$		0			0
$931$	567161.	+	646566.i	0.654346	+	0.745957i
$932$		0			0
$933$	−674844.	−	118993.i	−0.775247	−	0.136697i
$934$		0			0
$935$	−398195.	−	144931.i	−0.455484	−	0.165783i
$936$		0			0
$937$	424183.	−	355932.i	0.483141	−	0.405404i	−0.368419	−	0.929660i	$-0.620101\pi$
$937$	424183.	−	355932.i	0.483141	−	0.405404i	0.851561	+	0.524256i	$0.175656\pi$
$938$		0			0
$939$	−1.55294e6	−	896589.i	−1.76126	−	1.01686i
$940$		0			0
$941$	−1.47323e6	+	259770.i	−1.66376	+	0.293366i	−0.924820	−	0.380404i	$-0.875785\pi$
$941$	−1.47323e6	+	259770.i	−1.66376	+	0.293366i	−0.738941	+	0.673770i	$0.764674\pi$
$942$		0			0
$943$	−52166.1	+	30118.1i	−0.0586630	+	0.0338691i
$944$		0			0
$945$	−12868.0	−	35354.6i	−0.0144095	−	0.0395897i
$946$		0			0
$947$	1.06564e6	+	894179.i	1.18826	+	0.997068i	0.999888	+	0.0149697i	$0.00476519\pi$
$947$	1.06564e6	+	894179.i	1.18826	+	0.997068i	0.188371	+	0.982098i	$0.439679\pi$
$948$		0			0
$949$		−	1.54160e6i		−	1.71174i
$950$		0			0
$951$	2.22952e6			2.46518
$952$		0			0
$953$	−1.05208e6	+	1.25382e6i	−1.15841	+	1.38054i	−0.247020	+	0.969011i	$0.579451\pi$
$953$	−1.05208e6	+	1.25382e6i	−1.15841	+	1.38054i	−0.911395	+	0.411534i	$0.864993\pi$
$954$		0			0
$955$	1.32467e6	−	482139.i	1.45245	−	0.528647i
$956$		0			0
$957$	148269.	+	256810.i	0.161893	+	0.280406i
$958$		0			0
$959$	−20951.8	−	118823.i	−0.0227816	−	0.129201i
$960$		0			0
$961$	−236057.	+	408862.i	−0.255605	+	0.442721i
$962$		0			0
$963$	−667549.	−	795554.i	−0.719831	−	0.857861i
$964$		0			0
$965$	−408771.	+	1.12309e6i	−0.438961	+	1.20603i
$966$		0			0
$967$	114862.	−	651414.i	0.122835	−	0.696633i	−0.859735	−	0.510741i	$-0.829371\pi$
$967$	114862.	−	651414.i	0.122835	−	0.696633i	0.982570	−	0.185893i	$-0.0595177\pi$
$968$		0			0
$969$	353958.	−	137696.i	0.376968	−	0.146647i
$970$		0			0
$971$	−511948.	−	90270.2i	−0.542984	−	0.0957428i	−0.104573	−	0.994517i	$-0.533348\pi$
$971$	−511948.	−	90270.2i	−0.542984	−	0.0957428i	−0.438411	+	0.898774i	$0.644459\pi$
$972$		0			0
$973$	−32932.5	−	11986.5i	−0.0347856	−	0.0126609i
$974$		0			0
$975$	−3.31860e6	+	2.78463e6i	−3.49096	+	2.92927i
$976$		0			0
$977$	717155.	+	414050.i	0.751318	+	0.433774i	0.826170	−	0.563421i	$-0.190515\pi$
$977$	717155.	+	414050.i	0.751318	+	0.433774i	−0.0748516	+	0.997195i	$0.523848\pi$
$978$		0			0
$979$	−843013.	+	148646.i	−0.879567	+	0.155091i
$980$		0			0
$981$	−186101.	+	107445.i	−0.193379	+	0.111648i
$982$		0			0
$983$	286986.	+	788487.i	0.296998	+	0.815995i	0.994998	+	0.0998973i	$0.0318514\pi$
$983$	286986.	+	788487.i	0.296998	+	0.815995i	−0.698000	+	0.716098i	$0.745926\pi$
$984$		0			0
$985$	1.42732e6	+	1.19767e6i	1.47113	+	1.23442i
$986$		0			0
$987$			81050.0i			0.0831991i
$988$		0			0
$989$	162483.			0.166118
$990$		0			0
$991$	−423593.	+	504819.i	−0.431322	+	0.514030i	−0.937303	−	0.348515i	$-0.886686\pi$
$991$	−423593.	+	504819.i	−0.431322	+	0.514030i	0.505981	+	0.862545i	$0.331131\pi$
$992$		0			0
$993$	318217.	−	115821.i	0.322719	−	0.117460i
$994$		0			0
$995$	1.27061e6	+	2.20075e6i	1.28341	+	2.22293i
$996$		0			0
$997$	29820.9	+	169122.i	0.0300006	+	0.170142i	0.996127	−	0.0879282i	$-0.0280246\pi$
$997$	29820.9	+	169122.i	0.0300006	+	0.170142i	−0.966126	+	0.258070i	$0.916913\pi$
$998$		0			0
$999$	236684.	−	409948.i	0.237158	−	0.410770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.21.2	✓	42
19.10	odd	18	inner	76.5.j.a.29.2	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.21.2	✓	42	1.1	even	1	trivial
76.5.j.a.29.2	yes	42	19.10	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.77177 + 9.26203i) q^{3} +(42.9478 - 15.6317i) q^{5} +(2.15264 + 3.72849i) q^{7} +(-11.3194 - 64.1954i) q^{9} +O(q^{10})\)	\(q+(-7.77177 + 9.26203i) q^{3} +(42.9478 - 15.6317i) q^{5} +(2.15264 + 3.72849i) q^{7} +(-11.3194 - 64.1954i) q^{9} +(-53.2761 + 92.2769i) q^{11} +(157.331 + 187.500i) q^{13} +(-188.999 + 519.270i) q^{15} +(-15.1100 + 85.6928i) q^{17} +(-115.998 + 341.856i) q^{19} +(-51.2632 - 9.03909i) q^{21} +(55.9483 + 20.3635i) q^{23} +(1121.39 - 940.954i) q^{25} +(-165.590 - 95.6032i) q^{27} +(-226.682 + 39.9702i) q^{29} +(581.855 - 335.934i) q^{31} +(-440.622 - 1210.60i) q^{33} +(150.734 + 126.481i) q^{35} +2475.69i q^{37} -2959.37 q^{39} +(-650.315 + 775.016i) q^{41} +(2564.45 - 933.382i) q^{43} +(-1489.63 - 2580.11i) q^{45} +(-270.376 - 1533.38i) q^{47} +(1191.23 - 2063.27i) q^{49} +(-676.259 - 805.934i) q^{51} +(1048.86 - 2881.73i) q^{53} +(-845.645 + 4795.89i) q^{55} +(-2264.77 - 3731.21i) q^{57} +(4897.42 + 863.548i) q^{59} +(-5548.86 - 2019.62i) q^{61} +(214.985 - 180.394i) q^{63} +(9687.97 + 5593.35i) q^{65} +(698.565 - 123.176i) q^{67} +(-623.424 + 359.934i) q^{69} +(-149.426 - 410.545i) q^{71} +(-4824.78 - 4048.47i) q^{73} +17699.2i q^{75} -458.738 q^{77} +(-5317.06 + 6336.63i) q^{79} +(7134.02 - 2596.57i) q^{81} +(-6604.82 - 11439.9i) q^{83} +(690.587 + 3916.51i) q^{85} +(1391.52 - 2410.18i) q^{87} +(5164.02 + 6154.24i) q^{89} +(-360.414 + 990.228i) q^{91} +(-1410.61 + 7999.97i) q^{93} +(361.918 + 16495.2i) q^{95} +(-14459.8 - 2549.65i) q^{97} +(6526.80 + 2375.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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