LMFDB - Embedded newform 624.4.bv.h.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, degree $2$, not 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:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$3.27897i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.4.bv.h.433.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} -17.5414i q^{5} +(-23.1228 - 13.3499i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} -17.5414i q^{5} +(-23.1228 - 13.3499i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(18.5352 - 10.7013i) q^{11} +(-8.67555 + 46.0623i) q^{13} +(45.5739 - 26.3121i) q^{15} +(41.9815 - 72.7141i) q^{17} +(66.7828 + 38.5571i) q^{19} -80.0997i q^{21} +(-71.0597 - 123.079i) q^{23} -182.701 q^{25} -27.0000 q^{27} +(-67.1115 - 116.241i) q^{29} +122.559i q^{31} +(55.6055 + 32.1039i) q^{33} +(-234.177 + 405.606i) q^{35} +(-192.766 + 111.294i) q^{37} +(-132.687 + 46.5537i) q^{39} +(-171.751 + 99.1604i) q^{41} +(-77.3279 + 133.936i) q^{43} +(136.722 + 78.9363i) q^{45} +78.7956i q^{47} +(184.942 + 320.329i) q^{49} +251.889 q^{51} -477.088 q^{53} +(-187.716 - 325.133i) q^{55} +231.342i q^{57} +(-37.1769 - 21.4641i) q^{59} +(-248.269 + 430.015i) q^{61} +(208.105 - 120.150i) q^{63} +(807.998 + 152.181i) q^{65} +(-419.727 + 242.329i) q^{67} +(213.179 - 369.237i) q^{69} +(-331.196 - 191.216i) q^{71} +193.622i q^{73} +(-274.052 - 474.671i) q^{75} -571.447 q^{77} -1049.60 q^{79} +(-40.5000 - 70.1481i) q^{81} +861.900i q^{83} +(-1275.51 - 736.414i) q^{85} +(201.335 - 348.722i) q^{87} +(838.005 - 483.823i) q^{89} +(815.532 - 949.271i) q^{91} +(-318.418 + 183.839i) q^{93} +(676.345 - 1171.46i) q^{95} +(512.228 + 295.735i) q^{97} +192.623i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$		−	17.5414i		−	1.56895i	−0.620160	−	0.784476i	$-0.712932\pi$
$5$		−	17.5414i		−	1.56895i	0.620160	−	0.784476i	$-0.287068\pi$
$6$		0			0
$7$	−23.1228	−	13.3499i	−1.24851	−	0.720829i	−0.277700	−	0.960668i	$-0.589572\pi$
$7$	−23.1228	−	13.3499i	−1.24851	−	0.720829i	−0.970813	+	0.239838i	$0.922906\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	18.5352	−	10.7013i	0.508051	−	0.293324i	−0.223981	−	0.974594i	$-0.571905\pi$
$11$	18.5352	−	10.7013i	0.508051	−	0.293324i	0.732032	+	0.681270i	$0.238572\pi$
$12$		0			0
$13$	−8.67555	+	46.0623i	−0.185090	+	0.982722i
$13$	−8.67555	+	46.0623i	−0.185090	+	0.982722i
$14$		0			0
$15$	45.5739	−	26.3121i	0.784476	−	0.452917i
$16$		0			0
$17$	41.9815	−	72.7141i	0.598942	−	1.03740i	−0.394036	−	0.919095i	$-0.628922\pi$
$17$	41.9815	−	72.7141i	0.598942	−	1.03740i	0.992978	−	0.118302i	$-0.0377452\pi$
$18$		0			0
$19$	66.7828	+	38.5571i	0.806370	+	0.465558i	0.845694	−	0.533669i	$-0.179187\pi$
$19$	66.7828	+	38.5571i	0.806370	+	0.465558i	−0.0393237	+	0.999227i	$0.512520\pi$
$20$		0			0
$21$		−	80.0997i		−	0.832342i
$22$		0			0
$23$	−71.0597	−	123.079i	−0.644216	−	1.11581i	−0.984482	−	0.175486i	$-0.943850\pi$
$23$	−71.0597	−	123.079i	−0.644216	−	1.11581i	0.340266	−	0.940329i	$-0.389483\pi$
$24$		0			0
$25$	−182.701			−1.46161
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−67.1115	−	116.241i	−0.429734	−	0.744322i	0.567115	−	0.823639i	$-0.308059\pi$
$29$	−67.1115	−	116.241i	−0.429734	−	0.744322i	−0.996849	+	0.0793167i	$0.974726\pi$
$30$		0			0
$31$			122.559i			0.710074i	0.934852	+	0.355037i	$0.115532\pi$
$31$			122.559i			0.710074i	−0.934852	+	0.355037i	$0.884468\pi$
$32$		0			0
$33$	55.6055	+	32.1039i	0.293324	+	0.169350i
$34$		0			0
$35$	−234.177	+	405.606i	−1.13095	+	1.95886i
$36$		0			0
$37$	−192.766	+	111.294i	−0.856502	+	0.494502i	−0.862839	−	0.505478i	$-0.831316\pi$
$37$	−192.766	+	111.294i	−0.856502	+	0.494502i	0.00633725	+	0.999980i	$0.497983\pi$
$38$		0			0
$39$	−132.687	+	46.5537i	−0.544792	+	0.191143i
$40$		0			0
$41$	−171.751	+	99.1604i	−0.654219	+	0.377713i	−0.790071	−	0.613016i	$-0.789956\pi$
$41$	−171.751	+	99.1604i	−0.654219	+	0.377713i	0.135852	+	0.990729i	$0.456623\pi$
$42$		0			0
$43$	−77.3279	+	133.936i	−0.274242	+	0.475000i	−0.969944	−	0.243330i	$-0.921760\pi$
$43$	−77.3279	+	133.936i	−0.274242	+	0.475000i	0.695702	+	0.718331i	$0.255093\pi$
$44$		0			0
$45$	136.722	+	78.9363i	0.452917	+	0.261492i
$46$		0			0
$47$			78.7956i			0.244543i	0.992497	+	0.122271i	$0.0390178\pi$
$47$			78.7956i			0.244543i	−0.992497	+	0.122271i	$0.960982\pi$
$48$		0			0
$49$	184.942	+	320.329i	0.539190	+	0.933905i
$50$		0			0
$51$	251.889			0.691598
$52$		0			0
$53$	−477.088			−1.23647			−0.618237	−	0.785992i	$-0.712153\pi$
$53$	−477.088			−1.23647			−0.618237	+	0.785992i	$0.712153\pi$
$54$		0			0
$55$	−187.716	−	325.133i	−0.460210	−	0.797108i
$56$		0			0
$57$			231.342i			0.537580i
$58$		0			0
$59$	−37.1769	−	21.4641i	−0.0820342	−	0.0473625i	0.458422	−	0.888735i	$-0.348415\pi$
$59$	−37.1769	−	21.4641i	−0.0820342	−	0.0473625i	−0.540456	+	0.841372i	$0.681748\pi$
$60$		0			0
$61$	−248.269	+	430.015i	−0.521109	+	0.902587i	0.478590	+	0.878039i	$0.341148\pi$
$61$	−248.269	+	430.015i	−0.521109	+	0.902587i	−0.999699	+	0.0245485i	$0.992185\pi$
$62$		0			0
$63$	208.105	−	120.150i	0.416171	−	0.240276i
$64$		0			0
$65$	807.998	+	152.181i	1.54184	+	0.290396i
$66$		0			0
$67$	−419.727	+	242.329i	−0.765340	+	0.441869i	−0.831210	−	0.555959i	$-0.812351\pi$
$67$	−419.727	+	242.329i	−0.765340	+	0.441869i	0.0658696	+	0.997828i	$0.479018\pi$
$68$		0			0
$69$	213.179	−	369.237i	0.371938	−	0.644216i
$70$		0			0
$71$	−331.196	−	191.216i	−0.553602	−	0.319622i	0.196971	−	0.980409i	$-0.436889\pi$
$71$	−331.196	−	191.216i	−0.553602	−	0.319622i	−0.750574	+	0.660787i	$0.770223\pi$
$72$		0			0
$73$			193.622i			0.310435i	0.987880	+	0.155217i	$0.0496078\pi$
$73$			193.622i			0.310435i	−0.987880	+	0.155217i	$0.950392\pi$
$74$		0			0
$75$	−274.052	−	474.671i	−0.421930	−	0.730804i
$76$		0			0
$77$	−571.447			−0.845745
$78$		0			0
$79$	−1049.60			−1.49480			−0.747399	−	0.664375i	$-0.768698\pi$
$79$	−1049.60			−1.49480			−0.747399	+	0.664375i	$0.768698\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			861.900i			1.13983i	0.821704	+	0.569914i	$0.193024\pi$
$83$			861.900i			1.13983i	−0.821704	+	0.569914i	$0.806976\pi$
$84$		0			0
$85$	−1275.51	−	736.414i	−1.62763	−	0.939710i
$86$		0			0
$87$	201.335	−	348.722i	0.248107	−	0.429734i
$88$		0			0
$89$	838.005	−	483.823i	0.998072	−	0.576237i	0.0903946	−	0.995906i	$-0.471187\pi$
$89$	838.005	−	483.823i	0.998072	−	0.576237i	0.907677	+	0.419669i	$0.137854\pi$
$90$		0			0
$91$	815.532	−	949.271i	0.939461	−	1.09352i
$92$		0			0
$93$	−318.418	+	183.839i	−0.355037	+	0.204981i
$94$		0			0
$95$	676.345	−	1171.46i	0.730438	−	1.26516i
$96$		0			0
$97$	512.228	+	295.735i	0.536174	+	0.309560i	0.743527	−	0.668706i	$-0.233152\pi$
$97$	512.228	+	295.735i	0.536174	+	0.309560i	−0.207353	+	0.978266i	$0.566485\pi$
$98$		0			0
$99$			192.623i			0.195549i
$100$		0			0
$101$	127.555	+	220.932i	0.125665	+	0.217659i	0.921993	−	0.387207i	$-0.126560\pi$
$101$	127.555	+	220.932i	0.125665	+	0.217659i	−0.796328	+	0.604866i	$0.793227\pi$
$102$		0			0
$103$	−247.355			−0.236627			−0.118313	−	0.992976i	$-0.537749\pi$
$103$	−247.355			−0.236627			−0.118313	+	0.992976i	$0.537749\pi$
$104$		0			0
$105$	−1405.06			−1.30590
$106$		0			0
$107$	341.742	+	591.914i	0.308761	+	0.534790i	0.978092	−	0.208175i	$-0.0667523\pi$
$107$	341.742	+	591.914i	0.308761	+	0.534790i	−0.669331	+	0.742965i	$0.733419\pi$
$108$		0			0
$109$		−	1697.76i		−	1.49189i	−0.666006	−	0.745946i	$-0.731998\pi$
$109$		−	1697.76i		−	1.49189i	0.666006	−	0.745946i	$-0.268002\pi$
$110$		0			0
$111$	−578.299	−	333.881i	−0.494502	−	0.285501i
$112$		0			0
$113$	190.354	−	329.703i	0.158469	−	0.274477i	−0.775848	−	0.630920i	$-0.782677\pi$
$113$	190.354	−	329.703i	0.158469	−	0.274477i	0.934317	+	0.356443i	$0.116011\pi$
$114$		0			0
$115$	−2158.98	+	1246.49i	−1.75066	+	1.01074i
$116$		0			0
$117$	−319.980	−	274.900i	−0.252839	−	0.217218i
$118$		0			0
$119$	−1941.46	+	1120.90i	−1.49557	+	0.863469i
$120$		0			0
$121$	−436.465	+	755.979i	−0.327923	+	0.567979i
$122$		0			0
$123$	−515.252	−	297.481i	−0.377713	−	0.218073i
$124$		0			0
$125$			1012.16i			0.724241i
$126$		0			0
$127$	−61.6157	−	106.722i	−0.0430513	−	0.0745670i	0.843697	−	0.536820i	$-0.180375\pi$
$127$	−61.6157	−	106.722i	−0.0430513	−	0.0745670i	−0.886748	+	0.462253i	$0.847041\pi$
$128$		0			0
$129$	−463.967			−0.316667
$130$		0			0
$131$	1218.41			0.812616			0.406308	−	0.913736i	$-0.366816\pi$
$131$	1218.41			0.812616			0.406308	+	0.913736i	$0.366816\pi$
$132$		0			0
$133$	−1029.47	−	1783.09i	−0.671176	−	1.16251i
$134$		0			0
$135$			473.618i			0.301945i
$136$		0			0
$137$	−2363.24	−	1364.41i	−1.47376	−	0.850875i	−0.474194	−	0.880420i	$-0.657261\pi$
$137$	−2363.24	−	1364.41i	−1.47376	−	0.850875i	−0.999563	+	0.0295456i	$0.990594\pi$
$138$		0			0
$139$	1556.39	−	2695.75i	0.949722	−	1.64497i	0.203713	−	0.979031i	$-0.434699\pi$
$139$	1556.39	−	2695.75i	0.949722	−	1.64497i	0.746009	−	0.665936i	$-0.231968\pi$
$140$		0			0
$141$	−204.717	+	118.193i	−0.122271	+	0.0705934i
$142$		0			0
$143$	332.123	+	946.612i	0.194220	+	0.553564i
$144$		0			0
$145$	−2039.02	+	1177.23i	−1.16780	+	0.674232i
$146$		0			0
$147$	−554.827	+	960.988i	−0.311302	+	0.539190i
$148$		0			0
$149$	1186.95	+	685.286i	0.652609	+	0.376784i	0.789455	−	0.613809i	$-0.210363\pi$
$149$	1186.95	+	685.286i	0.652609	+	0.376784i	−0.136846	+	0.990592i	$0.543697\pi$
$150$		0			0
$151$			2847.56i			1.53464i	0.641263	+	0.767321i	$0.278411\pi$
$151$			2847.56i			1.53464i	−0.641263	+	0.767321i	$0.721589\pi$
$152$		0			0
$153$	377.833	+	654.427i	0.199647	+	0.345799i
$154$		0			0
$155$	2149.86			1.11407
$156$		0			0
$157$	3354.00			1.70496			0.852479	−	0.522761i	$-0.175098\pi$
$157$	3354.00			1.70496			0.852479	+	0.522761i	$0.175098\pi$
$158$		0			0
$159$	−715.632	−	1239.51i	−0.356939	−	0.618237i
$160$		0			0
$161$			3794.57i			1.85748i
$162$		0			0
$163$	−1901.95	−	1098.09i	−0.913941	−	0.527664i	−0.0322438	−	0.999480i	$-0.510265\pi$
$163$	−1901.95	−	1098.09i	−0.913941	−	0.527664i	−0.881697	+	0.471816i	$0.843599\pi$
$164$		0			0
$165$	563.147	−	975.399i	0.265703	−	0.460210i
$166$		0			0
$167$	−790.279	+	456.268i	−0.366189	+	0.211419i	−0.671792	−	0.740740i	$-0.734475\pi$
$167$	−790.279	+	456.268i	−0.366189	+	0.211419i	0.305603	+	0.952159i	$0.401142\pi$
$168$		0			0
$169$	−2046.47	−	799.231i	−0.931484	−	0.363783i
$170$		0			0
$171$	−601.045	+	347.014i	−0.268790	+	0.155186i
$172$		0			0
$173$	449.818	−	779.108i	0.197682	−	0.342396i	−0.750094	−	0.661331i	$-0.769992\pi$
$173$	449.818	−	779.108i	0.197682	−	0.342396i	0.947777	+	0.318935i	$0.103325\pi$
$174$		0			0
$175$	4224.56	+	2439.05i	1.82484	+	1.05357i
$176$		0			0
$177$		−	128.784i		−	0.0546895i
$178$		0			0
$179$	−156.639	−	271.307i	−0.0654064	−	0.113287i	0.831468	−	0.555573i	$-0.187501\pi$
$179$	−156.639	−	271.307i	−0.0654064	−	0.113287i	−0.896874	+	0.442286i	$0.854168\pi$
$180$		0			0
$181$	2745.06			1.12728			0.563642	−	0.826019i	$-0.309400\pi$
$181$	2745.06			1.12728			0.563642	+	0.826019i	$0.309400\pi$
$182$		0			0
$183$	−1489.62			−0.601725
$184$		0			0
$185$	1952.25	+	3381.39i	0.775849	+	1.34381i
$186$		0			0
$187$		−	1797.02i		−	0.702735i
$188$		0			0
$189$	624.315	+	360.449i	0.240276	+	0.138724i
$190$		0			0
$191$	44.9340	−	77.8279i	0.0170226	−	0.0294839i	−0.857389	−	0.514670i	$-0.827915\pi$
$191$	44.9340	−	77.8279i	0.0170226	−	0.0294839i	0.874411	+	0.485186i	$0.161248\pi$
$192$		0			0
$193$	735.215	−	424.477i	0.274207	−	0.158314i	−0.356591	−	0.934261i	$-0.616061\pi$
$193$	735.215	−	424.477i	0.274207	−	0.158314i	0.630798	+	0.775947i	$0.282728\pi$
$194$		0			0
$195$	816.618	+	2327.51i	0.299893	+	0.854751i
$196$		0			0
$197$	−3761.90	+	2171.93i	−1.36053	+	0.785501i	−0.989694	−	0.143198i	$-0.954261\pi$
$197$	−3761.90	+	2171.93i	−1.36053	+	0.785501i	−0.370834	+	0.928699i	$0.620928\pi$
$198$		0			0
$199$	1664.20	−	2882.48i	0.592825	−	1.02680i	−0.401024	−	0.916067i	$-0.631346\pi$
$199$	1664.20	−	2882.48i	0.592825	−	1.02680i	0.993850	−	0.110736i	$-0.0353209\pi$
$200$		0			0
$201$	−1259.18	−	726.988i	−0.441869	−	0.255113i
$202$		0			0
$203$			3583.74i			1.23906i
$204$		0			0
$205$	1739.41	+	3012.75i	0.592614	+	1.02644i
$206$		0			0
$207$	1279.07			0.429477
$208$		0			0
$209$	1650.44			0.546236
$210$		0			0
$211$	−2299.94	−	3983.62i	−0.750401	−	1.29973i	−0.947629	−	0.319375i	$-0.896527\pi$
$211$	−2299.94	−	3983.62i	−0.750401	−	1.29973i	0.197228	−	0.980358i	$-0.436806\pi$
$212$		0			0
$213$		−	1147.30i		−	0.369068i
$214$		0			0
$215$	2349.42	+	1356.44i	0.745253	+	0.430272i
$216$		0			0
$217$	1636.16	−	2833.91i	0.511842	−	0.886537i
$218$		0			0
$219$	−503.045	+	290.433i	−0.155217	+	0.0896148i
$220$		0			0
$221$	2985.16	+	2564.60i	0.908615	+	0.780604i
$222$		0			0
$223$	−2190.68	+	1264.79i	−0.657842	+	0.379806i	−0.791454	−	0.611228i	$-0.790676\pi$
$223$	−2190.68	+	1264.79i	−0.657842	+	0.379806i	0.133612	+	0.991034i	$0.457342\pi$
$224$		0			0
$225$	822.155	−	1424.01i	0.243601	−	0.421930i
$226$		0			0
$227$	−32.2742	−	18.6335i	−0.00943661	−	0.00544823i	0.495274	−	0.868737i	$-0.335068\pi$
$227$	−32.2742	−	18.6335i	−0.00943661	−	0.00544823i	−0.504711	+	0.863288i	$0.668401\pi$
$228$		0			0
$229$		−	4094.45i		−	1.18152i	−0.806846	−	0.590762i	$-0.798827\pi$
$229$		−	4094.45i		−	1.18152i	0.806846	−	0.590762i	$-0.201173\pi$
$230$		0			0
$231$	−857.170	−	1484.66i	−0.244146	−	0.422873i
$232$		0			0
$233$	−1466.04			−0.412205			−0.206103	−	0.978530i	$-0.566078\pi$
$233$	−1466.04			−0.412205			−0.206103	+	0.978530i	$0.566078\pi$
$234$		0			0
$235$	1382.19			0.383676
$236$		0			0
$237$	−1574.40	−	2726.94i	−0.431511	−	0.747399i
$238$		0			0
$239$		−	5520.53i		−	1.49412i	−0.664759	−	0.747058i	$-0.731466\pi$
$239$		−	5520.53i		−	1.49412i	0.664759	−	0.747058i	$-0.268534\pi$
$240$		0			0
$241$	−2308.50	−	1332.81i	−0.617028	−	0.356241i	0.158683	−	0.987330i	$-0.449275\pi$
$241$	−2308.50	−	1332.81i	−0.617028	−	0.356241i	−0.775711	+	0.631088i	$0.782609\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	5619.03	−	3244.15i	1.46525	−	0.845963i
$246$		0			0
$247$	−2355.40	+	2741.67i	−0.606764	+	0.706267i
$248$		0			0
$249$	−2239.28	+	1292.85i	−0.569914	+	0.329040i
$250$		0			0
$251$	−789.605	+	1367.64i	−0.198564	+	0.343922i	−0.948063	−	0.318083i	$-0.896961\pi$
$251$	−789.605	+	1367.64i	−0.198564	+	0.343922i	0.749499	+	0.662005i	$0.230294\pi$
$252$		0			0
$253$	−2634.21	−	1520.86i	−0.654590	−	0.377927i
$254$		0			0
$255$		−	4418.49i		−	1.08508i
$256$		0			0
$257$	−1331.96	−	2307.01i	−0.323288	−	0.559952i	0.657876	−	0.753126i	$-0.271455\pi$
$257$	−1331.96	−	2307.01i	−0.323288	−	0.559952i	−0.981164	+	0.193174i	$0.938122\pi$
$258$		0			0
$259$	5943.06			1.42581
$260$		0			0
$261$	1208.01			0.286490
$262$		0			0
$263$	−1218.47	−	2110.45i	−0.285680	−	0.494812i	0.687094	−	0.726569i	$-0.258886\pi$
$263$	−1218.47	−	2110.45i	−0.285680	−	0.494812i	−0.972774	+	0.231756i	$0.925553\pi$
$264$		0			0
$265$			8368.80i			1.93997i
$266$		0			0
$267$	2514.02	+	1451.47i	0.576237	+	0.332691i
$268$		0			0
$269$	1341.59	−	2323.70i	0.304083	−	0.526687i	−0.672974	−	0.739666i	$-0.734983\pi$
$269$	1341.59	−	2323.70i	0.304083	−	0.526687i	0.977057	+	0.212980i	$0.0683168\pi$
$270$		0			0
$271$	3340.38	−	1928.57i	0.748759	−	0.432296i	−0.0764866	−	0.997071i	$-0.524370\pi$
$271$	3340.38	−	1928.57i	0.748759	−	0.432296i	0.825245	+	0.564775i	$0.191037\pi$
$272$		0			0
$273$	3689.58	+	694.909i	0.817961	+	0.154058i
$274$		0			0
$275$	−3386.40	+	1955.14i	−0.742572	+	0.428724i
$276$		0			0
$277$	552.453	−	956.877i	0.119833	−	0.207557i	−0.799868	−	0.600175i	$-0.795097\pi$
$277$	552.453	−	956.877i	0.119833	−	0.207557i	0.919701	+	0.392619i	$0.128431\pi$
$278$		0			0
$279$	−955.255	−	551.517i	−0.204981	−	0.118346i
$280$		0			0
$281$			4982.58i			1.05778i	0.848691	+	0.528890i	$0.177391\pi$
$281$			4982.58i			1.05778i	−0.848691	+	0.528890i	$0.822609\pi$
$282$		0			0
$283$	−1292.43	−	2238.55i	−0.271473	−	0.470205i	0.697766	−	0.716326i	$-0.254178\pi$
$283$	−1292.43	−	2238.55i	−0.271473	−	0.470205i	−0.969239	+	0.246120i	$0.920844\pi$
$284$		0			0
$285$	4058.07			0.843437
$286$		0			0
$287$	5295.14			1.08907
$288$		0			0
$289$	−1068.39	−	1850.51i	−0.217462	−	0.376655i
$290$		0			0
$291$			1774.41i			0.357449i
$292$		0			0
$293$	80.1491	+	46.2741i	0.0159807	+	0.00922649i	0.507969	−	0.861375i	$-0.330396\pi$
$293$	80.1491	+	46.2741i	0.0159807	+	0.00922649i	−0.491988	+	0.870602i	$0.663730\pi$
$294$		0			0
$295$	−376.510	+	652.135i	−0.0743094	+	0.128708i
$296$		0			0
$297$	−500.450	+	288.935i	−0.0977745	+	0.0564502i
$298$		0			0
$299$	6285.78	−	2205.39i	1.21577	−	0.426559i
$300$		0			0
$301$	3576.07	−	2064.65i	0.684789	−	0.395363i
$302$		0			0
$303$	−382.665	+	662.795i	−0.0725529	+	0.125665i
$304$		0			0
$305$	7543.07	+	4355.00i	1.41612	+	0.817595i
$306$		0			0
$307$			3979.46i			0.739803i	0.929071	+	0.369901i	$0.120609\pi$
$307$			3979.46i			0.739803i	−0.929071	+	0.369901i	$0.879391\pi$
$308$		0			0
$309$	−371.032	−	642.646i	−0.0683083	−	0.118313i
$310$		0			0
$311$	3450.91			0.629207			0.314604	−	0.949223i	$-0.398128\pi$
$311$	3450.91			0.629207			0.314604	+	0.949223i	$0.398128\pi$
$312$		0			0
$313$	−6189.03			−1.11765			−0.558825	−	0.829285i	$-0.688748\pi$
$313$	−6189.03			−1.11765			−0.558825	+	0.829285i	$0.688748\pi$
$314$		0			0
$315$	−2107.59	−	3650.46i	−0.376982	−	0.652952i
$316$		0			0
$317$		−	5437.78i		−	0.963459i	−0.876320	−	0.481729i	$-0.840009\pi$
$317$		−	5437.78i		−	0.963459i	0.876320	−	0.481729i	$-0.159991\pi$
$318$		0			0
$319$	−2487.85	−	1436.36i	−0.436654	−	0.252102i
$320$		0			0
$321$	−1025.23	+	1775.74i	−0.178263	+	0.308761i
$322$		0			0
$323$	5607.28	−	3237.37i	0.965937	−	0.557684i
$324$		0			0
$325$	1585.03	−	8415.63i	0.270528	−	1.43635i
$326$		0			0
$327$	4410.92	−	2546.64i	0.745946	−	0.430672i
$328$		0			0
$329$	1051.92	−	1821.97i	0.176274	−	0.305315i
$330$		0			0
$331$	−5738.84	−	3313.32i	−0.952976	−	0.550201i	−0.0589722	−	0.998260i	$-0.518782\pi$
$331$	−5738.84	−	3313.32i	−0.952976	−	0.550201i	−0.894004	+	0.448058i	$0.852116\pi$
$332$		0			0
$333$		−	2003.29i		−	0.329668i
$334$		0			0
$335$	4250.80	+	7362.60i	0.693271	+	1.20078i
$336$		0			0
$337$	5538.63			0.895277			0.447638	−	0.894215i	$-0.352265\pi$
$337$	5538.63			0.895277			0.447638	+	0.894215i	$0.352265\pi$
$338$		0			0
$339$	1142.13			0.182985
$340$		0			0
$341$	1311.54	+	2271.66i	0.208281	+	0.360754i
$342$		0			0
$343$		−	717.813i		−	0.112998i
$344$		0			0
$345$	−6476.94	−	3739.46i	−1.01074	−	0.583553i
$346$		0			0
$347$	4699.47	−	8139.72i	0.727034	−	1.25926i	−0.231098	−	0.972931i	$-0.574232\pi$
$347$	4699.47	−	8139.72i	0.727034	−	1.25926i	0.958131	−	0.286329i	$-0.0924350\pi$
$348$		0			0
$349$	4985.99	−	2878.66i	0.764739	−	0.441522i	−0.0662555	−	0.997803i	$-0.521105\pi$
$349$	4985.99	−	2878.66i	0.764739	−	0.441522i	0.830995	+	0.556280i	$0.187772\pi$
$350$		0			0
$351$	234.240	−	1243.68i	0.0356205	−	0.189125i
$352$		0			0
$353$	−2994.56	+	1728.91i	−0.451514	+	0.260682i	−0.708470	−	0.705741i	$-0.750614\pi$
$353$	−2994.56	+	1728.91i	−0.451514	+	0.260682i	0.256955	+	0.966423i	$0.417281\pi$
$354$		0			0
$355$	−3354.20	+	5809.65i	−0.501472	+	0.868575i
$356$		0			0
$357$	−5824.37	−	3362.70i	−0.863469	−	0.498524i
$358$		0			0
$359$			7168.96i			1.05394i	0.849885	+	0.526968i	$0.176671\pi$
$359$			7168.96i			1.05394i	−0.849885	+	0.526968i	$0.823329\pi$
$360$		0			0
$361$	−456.203	−	790.167i	−0.0665116	−	0.115202i
$362$		0			0
$363$	−2618.79			−0.378652
$364$		0			0
$365$	3396.40			0.487057
$366$		0			0
$367$	1955.05	+	3386.25i	0.278073	+	0.481637i	0.970906	−	0.239461i	$-0.0769708\pi$
$367$	1955.05	+	3386.25i	0.278073	+	0.481637i	−0.692832	+	0.721099i	$0.743637\pi$
$368$		0			0
$369$		−	1784.89i		−	0.251809i
$370$		0			0
$371$	11031.6	+	6369.10i	1.54375	+	0.891286i
$372$		0			0
$373$	−5688.80	+	9853.28i	−0.789691	+	1.36778i	0.136466	+	0.990645i	$0.456426\pi$
$373$	−5688.80	+	9853.28i	−0.789691	+	1.36778i	−0.926156	+	0.377140i	$0.876908\pi$
$374$		0			0
$375$	−2629.66	+	1518.24i	−0.362120	+	0.209070i
$376$		0			0
$377$	5936.54	−	2082.86i	0.811001	−	0.284543i
$378$		0			0
$379$	−3492.00	+	2016.11i	−0.473278	+	0.273247i	−0.717611	−	0.696444i	$-0.754764\pi$
$379$	−3492.00	+	2016.11i	−0.473278	+	0.273247i	0.244333	+	0.969691i	$0.421431\pi$
$380$		0			0
$381$	184.847	−	320.165i	0.0248557	−	0.0430513i
$382$		0			0
$383$	1724.22	+	995.480i	0.230035	+	0.132811i	0.610588	−	0.791948i	$-0.290933\pi$
$383$	1724.22	+	995.480i	0.230035	+	0.132811i	−0.380553	+	0.924759i	$0.624266\pi$
$384$		0			0
$385$			10024.0i			1.32693i
$386$		0			0
$387$	−695.951	−	1205.42i	−0.0914139	−	0.158333i
$388$		0			0
$389$	11122.4			1.44969			0.724846	−	0.688911i	$-0.241911\pi$
$389$	11122.4			1.44969			0.724846	+	0.688911i	$0.241911\pi$
$390$		0			0
$391$	−11932.8			−1.54339
$392$		0			0
$393$	1827.61	+	3165.51i	0.234582	+	0.406308i
$394$		0			0
$395$			18411.4i			2.34527i
$396$		0			0
$397$	−9334.12	−	5389.06i	−1.18002	−	0.681282i	−0.223997	−	0.974590i	$-0.571911\pi$
$397$	−9334.12	−	5389.06i	−1.18002	−	0.681282i	−0.956018	+	0.293308i	$0.905244\pi$
$398$		0			0
$399$	3088.41	−	5349.28i	0.387503	−	0.671176i
$400$		0			0
$401$	−4080.35	+	2355.79i	−0.508137	+	0.293373i	−0.732067	−	0.681232i	$-0.761444\pi$
$401$	−4080.35	+	2355.79i	−0.508137	+	0.293373i	0.223931	+	0.974605i	$0.428111\pi$
$402$		0			0
$403$	−5645.36	−	1063.27i	−0.697805	−	0.131427i
$404$		0			0
$405$	−1230.50	+	710.427i	−0.150972	+	0.0871640i
$406$		0			0
$407$	−2381.97	+	4125.69i	−0.290098	+	0.502465i
$408$		0			0
$409$	1026.05	+	592.388i	0.124046	+	0.0716179i	0.560739	−	0.827993i	$-0.310517\pi$
$409$	1026.05	+	592.388i	0.124046	+	0.0716179i	−0.436693	+	0.899611i	$0.643850\pi$
$410$		0			0
$411$		−	8186.49i		−	0.982505i
$412$		0			0
$413$	573.089	+	992.619i	0.0682805	+	0.118265i
$414$		0			0
$415$	15118.9			1.78834
$416$		0			0
$417$	9338.35			1.09664
$418$		0			0
$419$	−3084.15	−	5341.91i	−0.359596	−	0.622838i	0.628298	−	0.777973i	$-0.283752\pi$
$419$	−3084.15	−	5341.91i	−0.359596	−	0.622838i	−0.987893	+	0.155135i	$0.950419\pi$
$420$		0			0
$421$			10328.8i			1.19571i	0.801603	+	0.597857i	$0.203981\pi$
$421$			10328.8i			1.19571i	−0.801603	+	0.597857i	$0.796019\pi$
$422$		0			0
$423$	−614.151	−	354.580i	−0.0705934	−	0.0407571i
$424$		0			0
$425$	−7670.06	+	13284.9i	−0.875418	+	1.51627i
$426$		0			0
$427$	11481.4	−	6628.77i	1.30122	−	0.751261i
$428$		0			0
$429$	−1961.19	+	2282.80i	−0.220715	+	0.256910i
$430$		0			0
$431$	−9796.87	+	5656.23i	−1.09489	+	0.632137i	−0.934875	−	0.354977i	$-0.884489\pi$
$431$	−9796.87	+	5656.23i	−1.09489	+	0.632137i	−0.160018	+	0.987114i	$0.551155\pi$
$432$		0			0
$433$	−5237.87	+	9072.27i	−0.581331	+	1.00689i	0.413991	+	0.910281i	$0.364134\pi$
$433$	−5237.87	+	9072.27i	−0.581331	+	1.00689i	−0.995322	+	0.0966135i	$0.969199\pi$
$434$		0			0
$435$	−6117.07	−	3531.69i	−0.674232	−	0.389268i
$436$		0			0
$437$		−	10959.4i		−	1.19968i
$438$		0			0
$439$	1020.31	+	1767.23i	0.110926	+	0.192130i	0.916144	−	0.400849i	$-0.131285\pi$
$439$	1020.31	+	1767.23i	0.110926	+	0.192130i	−0.805218	+	0.592979i	$0.797952\pi$
$440$		0			0
$441$	−3328.96			−0.359460
$442$		0			0
$443$	4089.28			0.438572			0.219286	−	0.975661i	$-0.429627\pi$
$443$	4089.28			0.438572			0.219286	+	0.975661i	$0.429627\pi$
$444$		0			0
$445$	−8486.93	−	14699.8i	−0.904088	−	1.56593i
$446$		0			0
$447$			4111.71i			0.435072i
$448$		0			0
$449$	13179.1	+	7608.96i	1.38521	+	0.799753i	0.992771	−	0.120025i	$-0.0382973\pi$
$449$	13179.1	+	7608.96i	1.38521	+	0.799753i	0.392441	+	0.919777i	$0.371631\pi$
$450$		0			0
$451$	−2122.29	+	3675.91i	−0.221585	+	0.383796i
$452$		0			0
$453$	−7398.17	+	4271.34i	−0.767321	+	0.443013i
$454$		0			0
$455$	−16651.5	−	14305.6i	−1.71568	−	1.47397i
$456$		0			0
$457$	−758.912	+	438.158i	−0.0776814	+	0.0448494i	−0.538338	−	0.842729i	$-0.680947\pi$
$457$	−758.912	+	438.158i	−0.0776814	+	0.0448494i	0.460656	+	0.887579i	$0.347614\pi$
$458$		0			0
$459$	−1133.50	+	1963.28i	−0.115266	+	0.199647i
$460$		0			0
$461$	−14110.5	−	8146.69i	−1.42558	−	0.823057i	−0.428808	−	0.903396i	$-0.641066\pi$
$461$	−14110.5	−	8146.69i	−1.42558	−	0.823057i	−0.996768	+	0.0803390i	$0.974400\pi$
$462$		0			0
$463$		−	11704.8i		−	1.17488i	−0.809269	−	0.587438i	$-0.800137\pi$
$463$		−	11704.8i		−	1.17488i	0.809269	−	0.587438i	$-0.199863\pi$
$464$		0			0
$465$	3224.79	+	5585.50i	0.321605	+	0.557036i
$466$		0			0
$467$	−15616.1			−1.54738			−0.773688	−	0.633567i	$-0.781590\pi$
$467$	−15616.1			−1.54738			−0.773688	+	0.633567i	$0.781590\pi$
$468$		0			0
$469$	12940.3			1.27405
$470$		0			0
$471$	5031.00	+	8713.95i	0.492179	+	0.852479i
$472$		0			0
$473$			3310.03i			0.321766i
$474$		0			0
$475$	−12201.3	−	7044.42i	−1.17860	−	0.680463i
$476$		0			0
$477$	2146.90	−	3718.53i	0.206079	−	0.356939i
$478$		0			0
$479$	−8985.90	+	5188.01i	−0.857153	+	0.494877i	−0.863058	−	0.505105i	$-0.831454\pi$
$479$	−8985.90	+	5188.01i	−0.857153	+	0.494877i	0.00590498	+	0.999983i	$0.498120\pi$
$480$		0			0
$481$	−3454.09	−	9844.79i	−0.327428	−	0.933230i
$482$		0			0
$483$	−9858.59	+	5691.86i	−0.928740	+	0.536208i
$484$		0			0
$485$	5187.61	−	8985.20i	0.485685	−	0.841231i
$486$		0			0
$487$	3459.14	+	1997.13i	0.321865	+	0.185829i	0.652224	−	0.758027i	$-0.273836\pi$
$487$	3459.14	+	1997.13i	0.321865	+	0.185829i	−0.330358	+	0.943856i	$0.607170\pi$
$488$		0			0
$489$		−	6588.55i		−	0.609294i
$490$		0			0
$491$	−6133.65	−	10623.8i	−0.563763	−	0.976467i	−0.997164	−	0.0752653i	$-0.976020\pi$
$491$	−6133.65	−	10623.8i	−0.563763	−	0.976467i	0.433400	−	0.901202i	$-0.357314\pi$
$492$		0			0
$493$	−11269.8			−1.02954
$494$		0			0
$495$	3378.88			0.306807
$496$		0			0
$497$	5105.45	+	8842.90i	0.460786	+	0.798105i
$498$		0			0
$499$		−	3578.76i		−	0.321056i	−0.987031	−	0.160528i	$-0.948680\pi$
$499$		−	3578.76i		−	0.321056i	0.987031	−	0.160528i	$-0.0513198\pi$
$500$		0			0
$501$	−2370.84	−	1368.80i	−0.211419	−	0.122063i
$502$		0			0
$503$	−648.409	+	1123.08i	−0.0574774	+	0.0995537i	−0.893332	−	0.449397i	$-0.851639\pi$
$503$	−648.409	+	1123.08i	−0.0574774	+	0.0995537i	0.835855	+	0.548950i	$0.184972\pi$
$504$		0			0
$505$	3875.45	−	2237.49i	0.341496	−	0.197163i
$506$		0			0
$507$	−993.241	−	6515.73i	−0.0870047	−	0.570757i
$508$		0			0
$509$	−4095.09	+	2364.30i	−0.356604	+	0.205886i	−0.667590	−	0.744529i	$-0.732674\pi$
$509$	−4095.09	+	2364.30i	−0.356604	+	0.205886i	0.310986	+	0.950415i	$0.399341\pi$
$510$		0			0
$511$	2584.84	−	4477.08i	0.223771	−	0.387582i
$512$		0			0
$513$	−1803.14	−	1041.04i	−0.155186	−	0.0895967i
$514$		0			0
$515$			4338.95i			0.371256i
$516$		0			0
$517$	843.214	+	1460.49i	0.0717302	+	0.124240i
$518$		0			0
$519$	2698.91			0.228264
$520$		0			0
$521$	−9220.74			−0.775370			−0.387685	−	0.921792i	$-0.626725\pi$
$521$	−9220.74			−0.775370			−0.387685	+	0.921792i	$0.626725\pi$
$522$		0			0
$523$	−6051.33	−	10481.2i	−0.505939	−	0.876313i	−0.999976	−	0.00687187i	$-0.997813\pi$
$523$	−6051.33	−	10481.2i	−0.505939	−	0.876313i	0.494037	−	0.869441i	$-0.335521\pi$
$524$		0			0
$525$			14634.3i			1.21656i
$526$		0			0
$527$	8911.78	+	5145.22i	0.736629	+	0.425293i
$528$		0			0
$529$	−4015.45	+	6954.97i	−0.330028	+	0.571626i
$530$		0			0
$531$	334.592	−	193.177i	0.0273447	−	0.0157875i
$532$		0			0
$533$	−3077.52	−	8771.51i	−0.250098	−	0.712826i
$534$		0			0
$535$	10383.0	−	5994.63i	0.839059	−	0.484431i
$536$		0			0
$537$	469.917	−	813.920i	0.0377624	−	0.0654064i
$538$		0			0
$539$	6855.87	+	3958.24i	0.547873	+	0.316314i
$540$		0			0
$541$		−	12801.3i		−	1.01732i	−0.860968	−	0.508659i	$-0.830141\pi$
$541$		−	12801.3i		−	1.01732i	0.860968	−	0.508659i	$-0.169859\pi$
$542$		0			0
$543$	4117.59	+	7131.87i	0.325419	+	0.563642i
$544$		0			0
$545$	−29781.2			−2.34071
$546$		0			0
$547$	−400.693			−0.0313207			−0.0156603	−	0.999877i	$-0.504985\pi$
$547$	−400.693			−0.0313207			−0.0156603	+	0.999877i	$0.504985\pi$
$548$		0			0
$549$	−2234.43	−	3870.14i	−0.173703	−	0.300862i
$550$		0			0
$551$		−	10350.5i		−	0.800265i
$552$		0			0
$553$	24269.7	+	14012.1i	1.86628	+	1.07750i
$554$		0			0
$555$	−5856.74	+	10144.2i	−0.447937	+	0.775849i
$556$		0			0
$557$	−12536.2	+	7237.77i	−0.953636	+	0.550582i	−0.894209	−	0.447650i	$-0.852261\pi$
$557$	−12536.2	+	7237.77i	−0.953636	+	0.550582i	−0.0594277	+	0.998233i	$0.518928\pi$
$558$		0			0
$559$	−5498.53	−	4723.87i	−0.416034	−	0.357421i
$560$		0			0
$561$	4668.80	−	2695.54i	0.351367	−	0.202862i
$562$		0			0
$563$	7388.18	−	12796.7i	0.553063	−	0.957934i	−0.444988	−	0.895536i	$-0.646792\pi$
$563$	7388.18	−	12796.7i	0.553063	−	0.957934i	0.998051	−	0.0623972i	$-0.0198746\pi$
$564$		0			0
$565$	−5783.46	−	3339.08i	−0.430641	−	0.248631i
$566$		0			0
$567$			2162.69i			0.160184i
$568$		0			0
$569$	−3434.44	−	5948.63i	−0.253039	−	0.438277i	0.711322	−	0.702866i	$-0.248097\pi$
$569$	−3434.44	−	5948.63i	−0.253039	−	0.438277i	−0.964361	+	0.264590i	$0.914763\pi$
$570$		0			0
$571$	3011.00			0.220677			0.110338	−	0.993894i	$-0.464807\pi$
$571$	3011.00			0.220677			0.110338	+	0.993894i	$0.464807\pi$
$572$		0			0
$573$	269.604			0.0196559
$574$		0			0
$575$	12982.7	+	22486.7i	0.941591	+	1.63088i
$576$		0			0
$577$		−	23106.6i		−	1.66714i	−0.552411	−	0.833572i	$-0.686292\pi$
$577$		−	23106.6i		−	1.66714i	0.552411	−	0.833572i	$-0.313708\pi$
$578$		0			0
$579$	2205.65	+	1273.43i	0.158314	+	0.0914023i
$580$		0			0
$581$	11506.3	−	19929.5i	0.821622	−	1.42309i
$582$		0			0
$583$	−8842.91	+	5105.46i	−0.628192	+	0.362687i
$584$		0			0
$585$	−4822.12	+	5612.90i	−0.340804	+	0.396692i
$586$		0			0
$587$	−2619.56	+	1512.40i	−0.184192	+	0.106343i	−0.589261	−	0.807943i	$-0.700581\pi$
$587$	−2619.56	+	1512.40i	−0.184192	+	0.106343i	0.405069	+	0.914286i	$0.367248\pi$
$588$		0			0
$589$	−4725.53	+	8184.85i	−0.330580	+	0.572582i
$590$		0			0
$591$	−11285.7	−	6515.80i	−0.785501	−	0.453509i
$592$		0			0
$593$			6396.07i			0.442926i	0.975169	+	0.221463i	$0.0710832\pi$
$593$			6396.07i			0.442926i	−0.975169	+	0.221463i	$0.928917\pi$
$594$		0			0
$595$	19662.2	+	34055.9i	1.35474	+	2.34648i
$596$		0			0
$597$	9985.22			0.684536
$598$		0			0
$599$	−12095.9			−0.825084			−0.412542	−	0.910939i	$-0.635359\pi$
$599$	−12095.9			−0.825084			−0.412542	+	0.910939i	$0.635359\pi$
$600$		0			0
$601$	5908.25	+	10233.4i	0.401003	+	0.694557i	0.993847	−	0.110760i	$-0.0353285\pi$
$601$	5908.25	+	10233.4i	0.401003	+	0.694557i	−0.592845	+	0.805317i	$0.701995\pi$
$602$		0			0
$603$		−	4361.93i		−	0.294580i
$604$		0			0
$605$	13260.9	+	7656.21i	0.891131	+	0.514495i
$606$		0			0
$607$	−12582.0	+	21792.6i	−0.841329	+	1.45722i	0.0474421	+	0.998874i	$0.484893\pi$
$607$	−12582.0	+	21792.6i	−0.841329	+	1.45722i	−0.888771	+	0.458351i	$0.848440\pi$
$608$		0			0
$609$	−9310.83	+	5375.61i	−0.619530	+	0.357686i
$610$		0			0
$611$	−3629.50	−	683.595i	−0.240318	−	0.0452623i
$612$		0			0
$613$	16959.4	−	9791.51i	1.11743	−	0.645148i	0.176685	−	0.984267i	$-0.443462\pi$
$613$	16959.4	−	9791.51i	1.11743	−	0.645148i	0.940743	+	0.339120i	$0.110129\pi$
$614$		0			0
$615$	−5218.24	+	9038.25i	−0.342146	+	0.592614i
$616$		0			0
$617$	−17040.8	−	9838.54i	−1.11189	−	0.641952i	−0.172575	−	0.984996i	$-0.555209\pi$
$617$	−17040.8	−	9838.54i	−1.11189	−	0.641952i	−0.939319	+	0.343044i	$0.888542\pi$
$618$		0			0
$619$		−	4394.05i		−	0.285318i	−0.989772	−	0.142659i	$-0.954435\pi$
$619$		−	4394.05i		−	0.285318i	0.989772	−	0.142659i	$-0.0455652\pi$
$620$		0			0
$621$	1918.61	+	3323.13i	0.123979	+	0.214739i
$622$		0			0
$623$	−25836.0			−1.66147
$624$		0			0
$625$	−5082.96			−0.325310
$626$		0			0
$627$	2475.66	+	4287.97i	0.157685	+	0.273118i
$628$		0			0
$629$			18689.1i			1.18471i
$630$		0			0
$631$	20687.3	+	11943.8i	1.30515	+	0.753529i	0.981282	−	0.192574i	$-0.0616835\pi$
$631$	20687.3	+	11943.8i	1.30515	+	0.753529i	0.323867	+	0.946102i	$0.395017\pi$
$632$		0			0
$633$	6899.83	−	11950.9i	0.433244	−	0.750401i
$634$		0			0
$635$	−1872.05	+	1080.83i	−0.116992	+	0.0675453i
$636$		0			0
$637$	−16359.6	+	5739.83i	−1.01757	+	0.357018i
$638$		0			0
$639$	2980.77	−	1720.95i	0.184534	−	0.106541i
$640$		0			0
$641$	−2721.81	+	4714.31i	−0.167714	+	0.290490i	−0.937616	−	0.347673i	$-0.886972\pi$
$641$	−2721.81	+	4714.31i	−0.167714	+	0.290490i	0.769901	+	0.638163i	$0.220305\pi$
$642$		0			0
$643$	5056.73	+	2919.50i	0.310137	+	0.179057i	0.646988	−	0.762501i	$-0.276029\pi$
$643$	5056.73	+	2919.50i	0.310137	+	0.179057i	−0.336851	+	0.941558i	$0.609362\pi$
$644$		0			0
$645$			8138.64i			0.496835i
$646$		0			0
$647$	−4354.43	−	7542.09i	−0.264591	−	0.458285i	0.702866	−	0.711323i	$-0.251904\pi$
$647$	−4354.43	−	7542.09i	−0.264591	−	0.458285i	−0.967456	+	0.253038i	$0.918570\pi$
$648$		0			0
$649$	−918.773			−0.0555701
$650$		0			0
$651$	9816.96			0.591024
$652$		0			0
$653$	−1397.47	−	2420.48i	−0.0837475	−	0.145055i	0.821109	−	0.570771i	$-0.193356\pi$
$653$	−1397.47	−	2420.48i	−0.0837475	−	0.145055i	−0.904857	+	0.425716i	$0.860022\pi$
$654$		0			0
$655$		−	21372.6i		−	1.27495i
$656$		0			0
$657$	−1509.13	−	871.299i	−0.0896148	−	0.0517391i
$658$		0			0
$659$	15695.0	−	27184.5i	0.927752	−	1.60691i	0.140678	−	0.990055i	$-0.455072\pi$
$659$	15695.0	−	27184.5i	0.927752	−	1.60691i	0.787074	−	0.616859i	$-0.211595\pi$
$660$		0			0
$661$	17837.7	−	10298.6i	1.04963	−	0.606005i	0.127085	−	0.991892i	$-0.459438\pi$
$661$	17837.7	−	10298.6i	1.04963	−	0.606005i	0.922546	+	0.385887i	$0.126104\pi$
$662$		0			0
$663$	−2185.27	+	11602.6i	−0.128008	+	0.679648i
$664$		0			0
$665$	−31278.0	+	18058.4i	−1.82392	+	1.05304i
$666$		0			0
$667$	−9537.85	+	16520.0i	−0.553684	+	0.959008i
$668$		0			0
$669$	−6572.04	−	3794.37i	−0.379806	−	0.219281i
$670$		0			0
$671$			10627.2i			0.611414i
$672$		0			0
$673$	−8967.89	−	15532.8i	−0.513651	−	0.889669i	−0.999875	−	0.0158347i	$-0.994959\pi$
$673$	−8967.89	−	15532.8i	−0.513651	−	0.889669i	0.486224	−	0.873834i	$-0.338374\pi$
$674$		0			0
$675$	4932.93			0.281287
$676$		0			0
$677$	−24104.0			−1.36838			−0.684188	−	0.729305i	$-0.739843\pi$
$677$	−24104.0			−1.36838			−0.684188	+	0.729305i	$0.739843\pi$
$678$		0			0
$679$	−7896.09	−	13676.4i	−0.446280	−	0.772980i
$680$		0			0
$681$		−	111.801i		−	0.00629107i
$682$		0			0
$683$	−5840.69	−	3372.12i	−0.327215	−	0.188918i	0.327389	−	0.944890i	$-0.393831\pi$
$683$	−5840.69	−	3372.12i	−0.327215	−	0.188918i	−0.654604	+	0.755972i	$0.727165\pi$
$684$		0			0
$685$	−23933.8	+	41454.5i	−1.33498	+	2.31225i
$686$		0			0
$687$	10637.7	−	6141.67i	0.590762	−	0.341076i
$688$		0			0
$689$	4139.00	−	21975.8i	0.228858	−	1.21511i
$690$		0			0
$691$	−26712.1	+	15422.2i	−1.47059	+	0.849043i	−0.999455	−	0.0330199i	$-0.989488\pi$
$691$	−26712.1	+	15422.2i	−1.47059	+	0.849043i	−0.471131	+	0.882063i	$0.656154\pi$
$692$		0			0
$693$	2571.51	−	4453.98i	0.140958	−	0.244146i
$694$		0			0
$695$	−47287.2	−	27301.3i	−2.58087	−	1.49007i
$696$		0			0
$697$			16651.6i			0.904913i
$698$		0			0
$699$	−2199.07	−	3808.90i	−0.118993	−	0.206103i
$700$		0			0
$701$	21007.6			1.13188			0.565940	−	0.824447i	$-0.308514\pi$
$701$	21007.6			1.13188			0.565940	+	0.824447i	$0.308514\pi$
$702$		0			0
$703$	−17164.6			−0.920877
$704$		0			0
$705$	2073.28	+	3591.02i	0.110758	+	0.191838i
$706$		0			0
$707$		−	6811.41i		−	0.362333i
$708$		0			0
$709$	12785.5	+	7381.68i	0.677246	+	0.391008i	0.798817	−	0.601574i	$-0.205460\pi$
$709$	12785.5	+	7381.68i	0.677246	+	0.391008i	−0.121570	+	0.992583i	$0.538793\pi$
$710$		0			0
$711$	4723.20	−	8180.81i	0.249133	−	0.431511i
$712$		0			0
$713$	15084.5	−	8709.02i	0.792311	−	0.457441i
$714$		0			0
$715$	16604.9	−	5825.91i	0.868515	−	0.304722i
$716$		0			0
$717$	14342.8	−	8280.80i	0.747058	−	0.431314i
$718$		0			0
$719$	13093.1	−	22678.0i	0.679126	−	1.17628i	−0.296119	−	0.955151i	$-0.595692\pi$
$719$	13093.1	−	22678.0i	0.679126	−	1.17628i	0.975245	−	0.221129i	$-0.0709742\pi$
$720$		0			0
$721$	5719.53	+	3302.17i	0.295432	+	0.170568i
$722$		0			0
$723$		−	7996.89i		−	0.411352i
$724$		0			0
$725$	12261.3	+	21237.3i	0.628103	+	1.08791i
$726$		0			0
$727$	20044.0			1.02254			0.511272	−	0.859419i	$-0.329175\pi$
$727$	20044.0			1.02254			0.511272	+	0.859419i	$0.329175\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	6492.68	+	11245.6i	0.328509	+	0.568995i
$732$		0			0
$733$		−	25555.5i		−	1.28774i	−0.765134	−	0.643871i	$-0.777327\pi$
$733$		−	25555.5i		−	1.28774i	0.765134	−	0.643871i	$-0.222673\pi$
$734$		0			0
$735$	16857.1	+	9732.44i	0.845963	+	0.488417i
$736$		0			0
$737$	−5186.47	+	8983.23i	−0.259221	+	0.448985i
$738$		0			0
$739$	−9620.24	+	5554.25i	−0.478872	+	0.276477i	−0.719946	−	0.694030i	$-0.755834\pi$
$739$	−9620.24	+	5554.25i	−0.478872	+	0.276477i	0.241074	+	0.970507i	$0.422500\pi$
$740$		0			0
$741$	−10656.2	−	2007.02i	−0.528291	−	0.0995004i
$742$		0			0
$743$	24411.7	−	14094.1i	1.20535	−	0.695911i	0.243612	−	0.969873i	$-0.421667\pi$
$743$	24411.7	−	14094.1i	1.20535	−	0.695911i	0.961741	+	0.273962i	$0.0883342\pi$
$744$		0			0
$745$	12020.9	−	20820.8i	0.591155	−	1.02391i
$746$		0			0
$747$	−6717.84	−	3878.55i	−0.329040	−	0.189971i
$748$		0			0
$749$		−	18248.9i		−	0.890256i
$750$		0			0
$751$	−8588.28	−	14875.3i	−0.417298	−	0.722782i	0.578369	−	0.815776i	$-0.303690\pi$
$751$	−8588.28	−	14875.3i	−0.417298	−	0.722782i	−0.995667	+	0.0929941i	$0.970356\pi$
$752$		0			0
$753$	−4737.63			−0.229281
$754$		0			0
$755$	49950.2			2.40778
$756$		0			0
$757$	2204.98	+	3819.14i	0.105867	+	0.183367i	0.914092	−	0.405507i	$-0.132905\pi$
$757$	2204.98	+	3819.14i	0.105867	+	0.183367i	−0.808225	+	0.588874i	$0.799572\pi$
$758$		0			0
$759$		−	9125.16i		−	0.436393i
$760$		0			0
$761$	28097.0	+	16221.8i	1.33839	+	0.772721i	0.986569	−	0.163346i	$-0.0522286\pi$
$761$	28097.0	+	16221.8i	1.33839	+	0.772721i	0.351823	+	0.936067i	$0.385562\pi$
$762$		0			0
$763$	−22665.1	+	39257.0i	−1.07540	+	1.86265i
$764$		0			0
$765$	11479.6	−	6627.73i	0.542542	−	0.313237i
$766$		0			0
$767$	1311.21	−	1526.24i	0.0617278	−	0.0718505i
$768$		0			0
$769$	−27707.7	+	15997.1i	−1.29931	+	0.750155i	−0.980284	−	0.197593i	$-0.936688\pi$
$769$	−27707.7	+	15997.1i	−1.29931	+	0.750155i	−0.319022	+	0.947747i	$0.603354\pi$
$770$		0			0
$771$	3995.87	−	6921.04i	0.186651	−	0.323288i
$772$		0			0
$773$	7776.38	+	4489.70i	0.361833	+	0.208904i	0.669885	−	0.742465i	$-0.266344\pi$
$773$	7776.38	+	4489.70i	0.361833	+	0.208904i	−0.308051	+	0.951370i	$0.599677\pi$
$774$		0			0
$775$		−	22391.7i		−	1.03785i
$776$		0			0
$777$	8914.59	+	15440.5i	0.411595	+	0.712903i
$778$		0			0
$779$	−15293.3			−0.703390
$780$		0			0
$781$	−8185.04			−0.375011
$782$		0			0
$783$	1812.01	+	3138.50i	0.0827024	+	0.143245i
$784$		0			0
$785$		−	58833.9i		−	2.67500i
$786$		0			0
$787$	10886.4	+	6285.27i	0.493086	+	0.284683i	0.725854	−	0.687849i	$-0.241445\pi$
$787$	10886.4	+	6285.27i	0.493086	+	0.284683i	−0.232768	+	0.972532i	$0.574778\pi$
$788$		0			0
$789$	3655.40	−	6331.34i	0.164937	−	0.285680i
$790$		0			0
$791$	−8803.05	+	5082.44i	−0.395702	+	0.228459i
$792$		0			0
$793$	−17653.6	−	15166.5i	−0.790540	−	0.679165i
$794$		0			0
$795$	−21742.8	+	12553.2i	−0.969983	+	0.560020i
$796$		0			0
$797$	18931.7	−	32790.6i	0.841398	−	1.45734i	−0.0473148	−	0.998880i	$-0.515066\pi$
$797$	18931.7	−	32790.6i	0.841398	−	1.45734i	0.888713	−	0.458464i	$-0.151600\pi$
$798$		0			0
$799$	5729.55	+	3307.96i	0.253688	+	0.146467i
$800$		0			0
$801$			8708.81i			0.384158i
$802$		0			0
$803$	2072.00	+	3588.82i	0.0910578	+	0.157717i
$804$		0			0
$805$	66562.1			2.91429
$806$		0			0
$807$	8049.54			0.351124
$808$		0			0
$809$	−1251.90	−	2168.35i	−0.0544058	−	0.0942336i	0.837540	−	0.546376i	$-0.183993\pi$
$809$	−1251.90	−	2168.35i	−0.0544058	−	0.0942336i	−0.891946	+	0.452143i	$0.850660\pi$
$810$		0			0
$811$			5409.55i			0.234223i	0.993119	+	0.117112i	$0.0373635\pi$
$811$			5409.55i			0.234223i	−0.993119	+	0.117112i	$0.962636\pi$
$812$		0			0
$813$	10021.1	+	5785.71i	0.432296	+	0.249586i
$814$		0			0
$815$	−19262.1	+	33362.9i	−0.827879	+	1.43393i
$816$		0			0
$817$	−10328.3	+	5963.07i	−0.442280	+	0.255351i
$818$		0			0
$819$	3728.94	+	10628.2i	0.159096	+	0.453453i
$820$		0			0
$821$	−27177.3	+	15690.8i	−1.15529	+	0.667007i	−0.950171	−	0.311730i	$-0.899092\pi$
$821$	−27177.3	+	15690.8i	−1.15529	+	0.667007i	−0.205119	+	0.978737i	$0.565758\pi$
$822$		0			0
$823$	16523.1	−	28618.8i	0.699827	−	1.21214i	−0.268699	−	0.963224i	$-0.586594\pi$
$823$	16523.1	−	28618.8i	0.699827	−	1.21214i	0.968526	−	0.248912i	$-0.0800730\pi$
$824$		0			0
$825$	−10159.2	−	5865.41i	−0.428724	−	0.247524i
$826$		0			0
$827$		−	33653.7i		−	1.41506i	−0.706684	−	0.707529i	$-0.749810\pi$
$827$		−	33653.7i		−	1.41506i	0.706684	−	0.707529i	$-0.250190\pi$
$828$		0			0
$829$	6449.25	+	11170.4i	0.270195	+	0.467992i	0.968912	−	0.247407i	$-0.0795784\pi$
$829$	6449.25	+	11170.4i	0.270195	+	0.467992i	−0.698716	+	0.715399i	$0.746245\pi$
$830$		0			0
$831$	3314.72			0.138371
$832$		0			0
$833$	31056.6			1.29177
$834$		0			0
$835$	8003.58	+	13862.6i	0.331707	+	0.574533i
$836$		0			0
$837$		−	3309.10i		−	0.136654i
$838$		0			0
$839$	342.798	+	197.915i	0.0141057	+	0.00814395i	0.507036	−	0.861925i	$-0.330741\pi$
$839$	342.798	+	197.915i	0.0141057	+	0.00814395i	−0.492931	+	0.870069i	$0.664074\pi$
$840$		0			0
$841$	3186.59	−	5519.33i	0.130657	−	0.226304i
$842$		0			0
$843$	−12945.1	+	7473.87i	−0.528890	+	0.305355i
$844$		0			0
$845$	−14019.6	+	35898.0i	−0.570758	+	1.46145i
$846$		0			0
$847$	20184.6	−	11653.6i	0.818831	−	0.472752i
$848$		0			0
$849$	3877.29	−	6715.66i	0.156735	−	0.271473i
$850$		0			0
$851$	27395.8	+	15817.0i	1.10354	+	0.637132i
$852$		0			0
$853$			21248.9i			0.852930i	0.904504	+	0.426465i	$0.140241\pi$
$853$			21248.9i			0.852930i	−0.904504	+	0.426465i	$0.859759\pi$
$854$		0			0
$855$	6087.11	+	10543.2i	0.243479	+	0.421718i
$856$		0			0
$857$	9920.37			0.395418			0.197709	−	0.980261i	$-0.436650\pi$
$857$	9920.37			0.395418			0.197709	+	0.980261i	$0.436650\pi$
$858$		0			0
$859$	−20946.3			−0.831990			−0.415995	−	0.909367i	$-0.636567\pi$
$859$	−20946.3			−0.831990			−0.415995	+	0.909367i	$0.636567\pi$
$860$		0			0
$861$	7942.72	+	13757.2i	0.314387	+	0.544534i
$862$		0			0
$863$			11271.4i			0.444594i	0.974979	+	0.222297i	$0.0713554\pi$
$863$			11271.4i			0.444594i	−0.974979	+	0.222297i	$0.928645\pi$
$864$		0			0
$865$	−13666.6	−	7890.44i	−0.537202	−	0.310154i
$866$		0			0
$867$	3205.17	−	5551.52i	0.125552	−	0.217462i
$868$		0			0
$869$	−19454.5	+	11232.1i	−0.759435	+	0.438460i
$870$		0			0
$871$	−7520.89	−	21435.9i	−0.292578	−	0.833902i
$872$		0			0
$873$	−4610.05	+	2661.61i	−0.178725	+	0.103187i
$874$		0			0
$875$	13512.2	−	23403.9i	0.522054	−	0.904224i
$876$		0			0
$877$	8172.12	+	4718.18i	0.314656	+	0.181667i	0.649008	−	0.760782i	$-0.275184\pi$
$877$	8172.12	+	4718.18i	0.314656	+	0.181667i	−0.334352	+	0.942448i	$0.608518\pi$
$878$		0			0
$879$			277.645i			0.0106538i
$880$		0			0
$881$	−10171.5	−	17617.6i	−0.388974	−	0.673723i	0.603337	−	0.797486i	$-0.293837\pi$
$881$	−10171.5	−	17617.6i	−0.388974	−	0.673723i	−0.992312	+	0.123763i	$0.960504\pi$
$882$		0			0
$883$	46521.9			1.77303			0.886515	−	0.462699i	$-0.153119\pi$
$883$	46521.9			1.77303			0.886515	+	0.462699i	$0.153119\pi$
$884$		0			0
$885$	−2259.06			−0.0858051
$886$		0			0
$887$	−9977.53	−	17281.6i	−0.377692	−	0.654181i	0.613034	−	0.790056i	$-0.289949\pi$
$887$	−9977.53	−	17281.6i	−0.377692	−	0.654181i	−0.990726	+	0.135875i	$0.956615\pi$
$888$		0			0
$889$			3290.27i			0.124130i
$890$		0			0
$891$	−1501.35	−	866.804i	−0.0564502	−	0.0325915i
$892$		0			0
$893$	−3038.13	+	5262.19i	−0.113849	+	0.197192i
$894$		0			0
$895$	−4759.10	+	2747.67i	−0.177742	+	0.102619i
$896$		0			0
$897$	15158.5	+	13022.8i	0.564243	+	0.484749i
$898$		0			0
$899$	14246.4	−	8225.14i	0.528523	−	0.305143i
$900$		0			0
$901$	−20028.9	+	34691.0i	−0.740575	+	1.28271i
$902$		0			0
$903$	10728.2	+	6193.94i	0.395363	+	0.228263i
$904$		0			0
$905$		−	48152.2i		−	1.76866i
$906$		0			0
$907$	1326.97	+	2298.39i	0.0485793	+	0.0841419i	0.889293	−	0.457339i	$-0.151197\pi$
$907$	1326.97	+	2298.39i	0.0485793	+	0.0841419i	−0.840713	+	0.541481i	$0.817864\pi$
$908$		0			0
$909$	−2295.99			−0.0837769
$910$		0			0
$911$	−1797.50			−0.0653720			−0.0326860	−	0.999466i	$-0.510406\pi$
$911$	−1797.50			−0.0653720			−0.0326860	+	0.999466i	$0.510406\pi$
$912$		0			0
$913$	9223.43	+	15975.5i	0.334339	+	0.579091i
$914$		0			0
$915$			26130.0i			0.944077i
$916$		0			0
$917$	−28173.0	−	16265.7i	−1.01456	−	0.585757i
$918$		0			0
$919$	−24321.0	+	42125.2i	−0.872987	+	1.51206i	−0.0140961	+	0.999901i	$0.504487\pi$
$919$	−24321.0	+	42125.2i	−0.872987	+	1.51206i	−0.858891	+	0.512158i	$0.828846\pi$
$920$		0			0
$921$	−10338.9	+	5969.18i	−0.369901	+	0.213563i
$922$		0			0
$923$	11681.2	−	13596.7i	0.416566	−	0.484878i
$924$		0			0
$925$	35218.6	−	20333.5i	1.25187	−	0.722768i
$926$		0			0
$927$	1113.10	−	1927.94i	0.0394378	−	0.0683083i
$928$		0			0
$929$	32688.3	+	18872.6i	1.15443	+	0.666513i	0.949964	−	0.312359i	$-0.101119\pi$
$929$	32688.3	+	18872.6i	1.15443	+	0.666513i	0.204471	+	0.978873i	$0.434453\pi$
$930$		0			0
$931$			28523.3i			1.00410i
$932$		0			0
$933$	5176.37	+	8965.74i	0.181636	+	0.314604i
$934$		0			0
$935$	−31522.3			−1.10256
$936$		0			0
$937$	2705.50			0.0943273			0.0471637	−	0.998887i	$-0.484982\pi$
$937$	2705.50			0.0943273			0.0471637	+	0.998887i	$0.484982\pi$
$938$		0			0
$939$	−9283.55	−	16079.6i	−0.322638	−	0.558825i
$940$		0			0
$941$		−	5189.27i		−	0.179772i	−0.995952	−	0.0898860i	$-0.971350\pi$
$941$		−	5189.27i		−	0.179772i	0.995952	−	0.0898860i	$-0.0286503\pi$
$942$		0			0
$943$	24409.1	+	14092.6i	0.842916	+	0.486658i
$944$		0			0
$945$	6322.78	−	10951.4i	0.217651	−	0.376982i
$946$		0			0
$947$	62.5886	−	36.1356i	0.00214768	−	0.00123997i	−0.498926	−	0.866645i	$-0.666272\pi$
$947$	62.5886	−	36.1356i	0.00214768	−	0.00123997i	0.501073	+	0.865405i	$0.332939\pi$
$948$		0			0
$949$	−8918.67	−	1679.78i	−0.305071	−	0.0574582i
$950$		0			0
$951$	14127.8	−	8156.68i	0.481729	−	0.278127i
$952$		0			0
$953$	22347.5	−	38707.1i	0.759609	−	1.31568i	−0.183441	−	0.983031i	$-0.558724\pi$
$953$	22347.5	−	38707.1i	0.759609	−	1.31568i	0.943050	−	0.332651i	$-0.107943\pi$
$954$		0			0
$955$	−1365.21	−	788.205i	−0.0462588	−	0.0267076i
$956$		0			0
$957$		−	8618.16i		−	0.291103i
$958$		0			0
$959$	36429.7	+	63098.1i	1.22667	+	2.12466i
$960$		0			0
$961$	14770.2			0.495795
$962$		0			0
$963$	−6151.35			−0.205841
$964$		0			0
$965$	−7445.92	−	12896.7i	−0.248386	−	0.430217i
$966$		0			0
$967$		−	17936.9i		−	0.596496i	−0.954488	−	0.298248i	$-0.903598\pi$
$967$		−	17936.9i		−	0.596496i	0.954488	−	0.298248i	$-0.0964022\pi$
$968$		0			0
$969$	16821.9	+	9712.10i	0.557684	+	0.321979i
$970$		0			0
$971$	−20457.3	+	35433.1i	−0.676113	+	1.17106i	0.300029	+	0.953930i	$0.403004\pi$
$971$	−20457.3	+	35433.1i	−0.676113	+	1.17106i	−0.976142	+	0.217132i	$0.930330\pi$
$972$		0			0
$973$	−71976.2	+	41555.5i	−2.37148	+	1.36918i
$974$		0			0
$975$	24242.0	−	8505.41i	0.796272	−	0.279376i
$976$		0			0
$977$	−20886.8	+	12059.0i	−0.683961	+	0.394885i	−0.801346	−	0.598202i	$-0.795882\pi$
$977$	−20886.8	+	12059.0i	−0.683961	+	0.394885i	0.117385	+	0.993086i	$0.462549\pi$
$978$		0			0
$979$	10355.1	−	17935.5i	0.338048	−	0.585516i
$980$		0			0
$981$	13232.8	+	7639.93i	0.430672	+	0.248649i
$982$		0			0
$983$			2928.61i			0.0950235i	0.998871	+	0.0475118i	$0.0151292\pi$
$983$			2928.61i			0.0950235i	−0.998871	+	0.0475118i	$0.984871\pi$
$984$		0			0
$985$	38098.7	+	65989.0i	1.23241	+	2.13460i
$986$		0			0
$987$	6311.50			0.203543
$988$		0			0
$989$	21979.6			0.706683
$990$		0			0
$991$	24904.9	+	43136.6i	0.798317	+	1.38272i	0.920712	+	0.390244i	$0.127609\pi$
$991$	24904.9	+	43136.6i	0.798317	+	1.38272i	−0.122395	+	0.992481i	$0.539057\pi$
$992$		0			0
$993$		−	19879.9i		−	0.635318i
$994$		0			0
$995$	−50562.8	−	29192.5i	−1.61100	−	0.930114i
$996$		0			0
$997$	20575.8	−	35638.4i	0.653604	−	1.13208i	−0.328638	−	0.944456i	$-0.606589\pi$
$997$	20575.8	−	35638.4i	0.653604	−	1.13208i	0.982242	−	0.187620i	$-0.0600772\pi$
$998$		0			0
$999$	5204.69	−	3004.93i	0.164834	−	0.0951669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bv.h.49.1		10
4.3	odd	2		39.4.j.c.10.4	yes	10
12.11	even	2		117.4.q.e.10.2		10
13.4	even	6	inner	624.4.bv.h.433.5		10
52.3	odd	6		507.4.b.i.337.8		10
52.11	even	12		507.4.a.r.1.3		10
52.15	even	12		507.4.a.r.1.8		10
52.23	odd	6		507.4.b.i.337.3		10
52.43	odd	6		39.4.j.c.4.4	✓	10
156.11	odd	12		1521.4.a.bk.1.8		10
156.95	even	6		117.4.q.e.82.2		10
156.119	odd	12		1521.4.a.bk.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.4	✓	10	52.43	odd	6
39.4.j.c.10.4	yes	10	4.3	odd	2
117.4.q.e.10.2		10	12.11	even	2
117.4.q.e.82.2		10	156.95	even	6
507.4.a.r.1.3		10	52.11	even	12
507.4.a.r.1.8		10	52.15	even	12
507.4.b.i.337.3		10	52.23	odd	6
507.4.b.i.337.8		10	52.3	odd	6
624.4.bv.h.49.1		10	1.1	even	1	trivial
624.4.bv.h.433.5		10	13.4	even	6	inner
1521.4.a.bk.1.3		10	156.119	odd	12
1521.4.a.bk.1.8		10	156.11	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} -17.5414i q^{5} +(-23.1228 - 13.3499i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} -17.5414i q^{5} +(-23.1228 - 13.3499i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(18.5352 - 10.7013i) q^{11} +(-8.67555 + 46.0623i) q^{13} +(45.5739 - 26.3121i) q^{15} +(41.9815 - 72.7141i) q^{17} +(66.7828 + 38.5571i) q^{19} -80.0997i q^{21} +(-71.0597 - 123.079i) q^{23} -182.701 q^{25} -27.0000 q^{27} +(-67.1115 - 116.241i) q^{29} +122.559i q^{31} +(55.6055 + 32.1039i) q^{33} +(-234.177 + 405.606i) q^{35} +(-192.766 + 111.294i) q^{37} +(-132.687 + 46.5537i) q^{39} +(-171.751 + 99.1604i) q^{41} +(-77.3279 + 133.936i) q^{43} +(136.722 + 78.9363i) q^{45} +78.7956i q^{47} +(184.942 + 320.329i) q^{49} +251.889 q^{51} -477.088 q^{53} +(-187.716 - 325.133i) q^{55} +231.342i q^{57} +(-37.1769 - 21.4641i) q^{59} +(-248.269 + 430.015i) q^{61} +(208.105 - 120.150i) q^{63} +(807.998 + 152.181i) q^{65} +(-419.727 + 242.329i) q^{67} +(213.179 - 369.237i) q^{69} +(-331.196 - 191.216i) q^{71} +193.622i q^{73} +(-274.052 - 474.671i) q^{75} -571.447 q^{77} -1049.60 q^{79} +(-40.5000 - 70.1481i) q^{81} +861.900i q^{83} +(-1275.51 - 736.414i) q^{85} +(201.335 - 348.722i) q^{87} +(838.005 - 483.823i) q^{89} +(815.532 - 949.271i) q^{91} +(-318.418 + 183.839i) q^{93} +(676.345 - 1171.46i) q^{95} +(512.228 + 295.735i) q^{97} +192.623i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Introduction

L-functions

Modular forms

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