LMFDB - Embedded newform 143.4.g.a.21.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(21,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("143.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.8
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57365 + 2.57365i) q^{2} -0.422811 q^{3} -5.24731i q^{4} +(-8.59350 - 8.59350i) q^{5} +(1.08817 - 1.08817i) q^{6} +(13.9093 + 13.9093i) q^{7} +(-7.08444 - 7.08444i) q^{8} -26.8212 q^{9} +O(q^{10})$	\(q+(-2.57365 + 2.57365i) q^{2} -0.422811 q^{3} -5.24731i q^{4} +(-8.59350 - 8.59350i) q^{5} +(1.08817 - 1.08817i) q^{6} +(13.9093 + 13.9093i) q^{7} +(-7.08444 - 7.08444i) q^{8} -26.8212 q^{9} +44.2333 q^{10} +(14.9033 - 33.3000i) q^{11} +2.21862i q^{12} +(46.6374 + 4.68542i) q^{13} -71.5955 q^{14} +(3.63343 + 3.63343i) q^{15} +78.4442 q^{16} +88.4764 q^{17} +(69.0284 - 69.0284i) q^{18} +(-45.2400 + 45.2400i) q^{19} +(-45.0928 + 45.0928i) q^{20} +(-5.88103 - 5.88103i) q^{21} +(47.3465 + 124.058i) q^{22} -29.5271i q^{23} +(2.99538 + 2.99538i) q^{24} +22.6965i q^{25} +(-132.087 + 107.970i) q^{26} +22.7562 q^{27} +(72.9867 - 72.9867i) q^{28} +235.117i q^{29} -18.7023 q^{30} +(219.465 + 219.465i) q^{31} +(-145.212 + 145.212i) q^{32} +(-6.30130 + 14.0796i) q^{33} +(-227.707 + 227.707i) q^{34} -239.060i q^{35} +140.739i q^{36} +(189.820 - 189.820i) q^{37} -232.863i q^{38} +(-19.7188 - 1.98105i) q^{39} +121.760i q^{40} +(303.124 - 303.124i) q^{41} +30.2714 q^{42} -171.766 q^{43} +(-174.736 - 78.2025i) q^{44} +(230.488 + 230.488i) q^{45} +(75.9922 + 75.9922i) q^{46} +(20.1179 - 20.1179i) q^{47} -33.1671 q^{48} +43.9400i q^{49} +(-58.4128 - 58.4128i) q^{50} -37.4089 q^{51} +(24.5859 - 244.721i) q^{52} +348.269 q^{53} +(-58.5665 + 58.5665i) q^{54} +(-414.235 + 158.092i) q^{55} -197.080i q^{56} +(19.1280 - 19.1280i) q^{57} +(-605.108 - 605.108i) q^{58} +(458.103 - 458.103i) q^{59} +(19.0658 - 19.0658i) q^{60} -181.700i q^{61} -1129.65 q^{62} +(-373.066 - 373.066i) q^{63} -119.896i q^{64} +(-360.514 - 441.043i) q^{65} +(-20.0186 - 52.4533i) q^{66} +(-740.930 - 740.930i) q^{67} -464.264i q^{68} +12.4844i q^{69} +(615.256 + 615.256i) q^{70} +(-223.647 - 223.647i) q^{71} +(190.013 + 190.013i) q^{72} +(454.554 + 454.554i) q^{73} +977.058i q^{74} -9.59634i q^{75} +(237.388 + 237.388i) q^{76} +(670.477 - 255.886i) q^{77} +(55.8478 - 45.6508i) q^{78} +104.394i q^{79} +(-674.110 - 674.110i) q^{80} +714.552 q^{81} +1560.27i q^{82} +(456.654 - 456.654i) q^{83} +(-30.8596 + 30.8596i) q^{84} +(-760.322 - 760.322i) q^{85} +(442.065 - 442.065i) q^{86} -99.4102i q^{87} +(-341.494 + 130.330i) q^{88} +(285.422 - 285.422i) q^{89} -1186.39 q^{90} +(583.525 + 713.867i) q^{91} -154.938 q^{92} +(-92.7922 - 92.7922i) q^{93} +103.553i q^{94} +777.540 q^{95} +(61.3974 - 61.3974i) q^{96} +(799.981 + 799.981i) q^{97} +(-113.086 - 113.086i) q^{98} +(-399.726 + 893.147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−2.57365	+	2.57365i	−0.909922	+	0.909922i	−0.996265	−	0.0863439i	$-0.972482\pi$
$2$	−2.57365	+	2.57365i	−0.909922	+	0.909922i	0.0863439	+	0.996265i	$0.472482\pi$
$3$	−0.422811			−0.0813701			−0.0406851	−	0.999172i	$-0.512954\pi$
$3$	−0.422811			−0.0813701			−0.0406851	+	0.999172i	$0.512954\pi$
$4$		−	5.24731i		−	0.655914i
$5$	−8.59350	−	8.59350i	−0.768626	−	0.768626i	0.209239	−	0.977865i	$-0.432901\pi$
$5$	−8.59350	−	8.59350i	−0.768626	−	0.768626i	−0.977865	+	0.209239i	$0.932901\pi$
$6$	1.08817	−	1.08817i	0.0740404	−	0.0740404i
$7$	13.9093	+	13.9093i	0.751034	+	0.751034i	0.974672	−	0.223638i	$-0.0717933\pi$
$7$	13.9093	+	13.9093i	0.751034	+	0.751034i	−0.223638	+	0.974672i	$0.571793\pi$
$8$	−7.08444	−	7.08444i	−0.313091	−	0.313091i
$9$	−26.8212			−0.993379
$10$	44.2333			1.39878
$11$	14.9033	−	33.3000i	0.408502	−	0.912757i
$11$	14.9033	−	33.3000i	0.408502	−	0.912757i
$12$			2.21862i			0.0533718i
$13$	46.6374	+	4.68542i	0.994991	+	0.0999616i
$13$	46.6374	+	4.68542i	0.994991	+	0.0999616i
$14$	−71.5955			−1.36676
$15$	3.63343	+	3.63343i	0.0625432	+	0.0625432i
$16$	78.4442			1.22569
$17$	88.4764			1.26228			0.631138	−	0.775671i	$-0.282588\pi$
$17$	88.4764			1.26228			0.631138	+	0.775671i	$0.282588\pi$
$18$	69.0284	−	69.0284i	0.903897	−	0.903897i
$19$	−45.2400	+	45.2400i	−0.546251	+	0.546251i	−0.925354	−	0.379104i	$-0.876232\pi$
$19$	−45.2400	+	45.2400i	−0.546251	+	0.546251i	0.379104	+	0.925354i	$0.376232\pi$
$20$	−45.0928	+	45.0928i	−0.504153	+	0.504153i
$21$	−5.88103	−	5.88103i	−0.0611117	−	0.0611117i
$22$	47.3465	+	124.058i	0.458832	+	1.20224i
$23$		−	29.5271i		−	0.267688i	−0.991002	−	0.133844i	$-0.957268\pi$
$23$		−	29.5271i		−	0.267688i	0.991002	−	0.133844i	$-0.0427321\pi$
$24$	2.99538	+	2.99538i	0.0254762	+	0.0254762i
$25$			22.6965i			0.181572i
$26$	−132.087	+	107.970i	−0.996321	+	0.814407i
$27$	22.7562			0.162201
$28$	72.9867	−	72.9867i	0.492614	−	0.492614i
$29$			235.117i			1.50552i	0.658294	+	0.752761i	$0.271279\pi$
$29$			235.117i			1.50552i	−0.658294	+	0.752761i	$0.728721\pi$
$30$	−18.7023			−0.113819
$31$	219.465	+	219.465i	1.27152	+	1.27152i	0.945293	+	0.326224i	$0.105776\pi$
$31$	219.465	+	219.465i	1.27152	+	1.27152i	0.326224	+	0.945293i	$0.394224\pi$
$32$	−145.212	+	145.212i	−0.802191	+	0.802191i
$33$	−6.30130	+	14.0796i	−0.0332399	+	0.0742712i
$34$	−227.707	+	227.707i	−1.14857	+	1.14857i
$35$		−	239.060i		−	1.15453i
$36$			140.739i			0.651571i
$37$	189.820	−	189.820i	0.843410	−	0.843410i	−0.145891	−	0.989301i	$-0.546605\pi$
$37$	189.820	−	189.820i	0.843410	−	0.843410i	0.989301	+	0.145891i	$0.0466048\pi$
$38$		−	232.863i		−	0.994091i
$39$	−19.7188	−	1.98105i	−0.0809625	−	0.00813389i
$40$			121.760i			0.481300i
$41$	303.124	−	303.124i	1.15464	−	1.15464i	0.169023	−	0.985612i	$-0.445939\pi$
$41$	303.124	−	303.124i	1.15464	−	1.15464i	0.985612	−	0.169023i	$-0.0540612\pi$
$42$	30.2714			0.111214
$43$	−171.766			−0.609165			−0.304583	−	0.952486i	$-0.598517\pi$
$43$	−171.766			−0.609165			−0.304583	+	0.952486i	$0.598517\pi$
$44$	−174.736	−	78.2025i	−0.598690	−	0.267943i
$45$	230.488	+	230.488i	0.763537	+	0.763537i
$46$	75.9922	+	75.9922i	0.243575	+	0.243575i
$47$	20.1179	−	20.1179i	0.0624361	−	0.0624361i	−0.675199	−	0.737635i	$-0.735942\pi$
$47$	20.1179	−	20.1179i	0.0624361	−	0.0624361i	0.737635	+	0.675199i	$0.235942\pi$
$48$	−33.1671			−0.0997346
$49$			43.9400i			0.128105i
$50$	−58.4128	−	58.4128i	−0.165216	−	0.165216i
$51$	−37.4089			−0.102712
$52$	24.5859	−	244.721i	0.0655662	−	0.652629i
$53$	348.269			0.902612			0.451306	−	0.892369i	$-0.350958\pi$
$53$	348.269			0.902612			0.451306	+	0.892369i	$0.350958\pi$
$54$	−58.5665	+	58.5665i	−0.147591	+	0.147591i
$55$	−414.235	+	158.092i	−1.01555	+	0.387583i
$56$		−	197.080i		−	0.470284i
$57$	19.1280	−	19.1280i	0.0444485	−	0.0444485i
$58$	−605.108	−	605.108i	−1.36991	−	1.36991i
$59$	458.103	−	458.103i	1.01085	−	1.01085i	0.0109067	−	0.999941i	$-0.496528\pi$
$59$	458.103	−	458.103i	1.01085	−	1.01085i	0.999941	−	0.0109067i	$-0.00347177\pi$
$60$	19.0658	−	19.0658i	0.0410230	−	0.0410230i
$61$		−	181.700i		−	0.381382i	−0.981650	−	0.190691i	$-0.938927\pi$
$61$		−	181.700i		−	0.381382i	0.981650	−	0.190691i	$-0.0610728\pi$
$62$	−1129.65			−2.31396
$63$	−373.066	−	373.066i	−0.746062	−	0.746062i
$64$		−	119.896i		−	0.234172i
$65$	−360.514	−	441.043i	−0.687943	−	0.841609i
$66$	−20.0186	−	52.4533i	−0.0373352	−	0.0978266i
$67$	−740.930	−	740.930i	−1.35103	−	1.35103i	−0.884511	−	0.466519i	$-0.845508\pi$
$67$	−740.930	−	740.930i	−1.35103	−	1.35103i	−0.466519	−	0.884511i	$-0.654492\pi$
$68$		−	464.264i		−	0.827945i
$69$			12.4844i			0.0217818i
$70$	615.256	+	615.256i	1.05053	+	1.05053i
$71$	−223.647	−	223.647i	−0.373832	−	0.373832i	0.495039	−	0.868871i	$-0.335154\pi$
$71$	−223.647	−	223.647i	−0.373832	−	0.373832i	−0.868871	+	0.495039i	$0.835154\pi$
$72$	190.013	+	190.013i	0.311018	+	0.311018i
$73$	454.554	+	454.554i	0.728787	+	0.728787i	0.970378	−	0.241591i	$-0.0776692\pi$
$73$	454.554	+	454.554i	0.728787	+	0.728787i	−0.241591	+	0.970378i	$0.577669\pi$
$74$			977.058i			1.53487i
$75$		−	9.59634i		−	0.0147745i
$76$	237.388	+	237.388i	0.358294	+	0.358294i
$77$	670.477	−	255.886i	0.992311	−	0.378713i
$78$	55.8478	−	45.6508i	0.0810708	−	0.0662684i
$79$			104.394i			0.148675i	0.997233	+	0.0743373i	$0.0236842\pi$
$79$			104.394i			0.148675i	−0.997233	+	0.0743373i	$0.976316\pi$
$80$	−674.110	−	674.110i	−0.942098	−	0.942098i
$81$	714.552			0.980181
$82$			1560.27i			2.10125i
$83$	456.654	−	456.654i	0.603907	−	0.603907i	−0.337440	−	0.941347i	$-0.609561\pi$
$83$	456.654	−	456.654i	0.603907	−	0.603907i	0.941347	+	0.337440i	$0.109561\pi$
$84$	−30.8596	+	30.8596i	−0.0400841	+	0.0400841i
$85$	−760.322	−	760.322i	−0.970218	−	0.970218i
$86$	442.065	−	442.065i	0.554292	−	0.554292i
$87$		−	99.4102i		−	0.122505i
$88$	−341.494	+	130.330i	−0.413675	+	0.157878i
$89$	285.422	−	285.422i	0.339941	−	0.339941i	−0.516404	−	0.856345i	$-0.672730\pi$
$89$	285.422	−	285.422i	0.339941	−	0.339941i	0.856345	+	0.516404i	$0.172730\pi$
$90$	−1186.39			−1.38952
$91$	583.525	+	713.867i	0.672198	+	0.822347i
$92$	−154.938			−0.175580
$93$	−92.7922	−	92.7922i	−0.103463	−	0.103463i
$94$			103.553i			0.113624i
$95$	777.540			0.839725
$96$	61.3974	−	61.3974i	0.0652744	−	0.0652744i
$97$	799.981	+	799.981i	0.837379	+	0.837379i	0.988513	−	0.151135i	$-0.0482927\pi$
$97$	799.981	+	799.981i	0.837379	+	0.837379i	−0.151135	+	0.988513i	$0.548293\pi$
$98$	−113.086	−	113.086i	−0.116565	−	0.116565i
$99$	−399.726	+	893.147i	−0.405798	+	0.906714i
$100$	119.096			0.119096
$101$	−889.235			−0.876062			−0.438031	−	0.898960i	$-0.644324\pi$
$101$	−889.235			−0.876062			−0.438031	+	0.898960i	$0.644324\pi$
$102$	96.2772	−	96.2772i	0.0934594	−	0.0934594i
$103$			1703.93i			1.63003i	0.579441	+	0.815014i	$0.303271\pi$
$103$			1703.93i			1.63003i	−0.579441	+	0.815014i	$0.696729\pi$
$104$	−297.206	−	363.593i	−0.280226	−	0.342820i
$105$			101.077i			0.0939441i
$106$	−896.321	+	896.321i	−0.821306	+	0.821306i
$107$			422.741i			0.381943i	0.981596	+	0.190972i	$0.0611639\pi$
$107$			422.741i			0.381943i	−0.981596	+	0.190972i	$0.938836\pi$
$108$		−	119.409i		−	0.106390i
$109$	1511.59	−	1511.59i	1.32830	−	1.32830i	0.421440	−	0.906856i	$-0.361525\pi$
$109$	1511.59	−	1511.59i	1.32830	−	1.32830i	0.906856	−	0.421440i	$-0.138475\pi$
$110$	659.224	−	1472.97i	0.571405	−	1.27675i
$111$	−80.2580	+	80.2580i	−0.0686284	+	0.0686284i
$112$	1091.11	+	1091.11i	0.920536	+	0.920536i
$113$	−2218.08			−1.84654			−0.923271	−	0.384150i	$-0.874495\pi$
$113$	−2218.08			−1.84654			−0.923271	+	0.384150i	$0.874495\pi$
$114$			98.4573i			0.0808893i
$115$	−253.741	+	253.741i	−0.205752	+	0.205752i
$116$	1233.73			0.987494
$117$	−1250.87	−	125.669i	−0.988403	−	0.0992997i
$118$			2357.99i			1.83958i
$119$	1230.65	+	1230.65i	0.948012	+	0.948012i
$120$		−	51.4816i		−	0.0391634i
$121$	−886.781	−	992.563i	−0.666251	−	0.745727i
$122$	467.631	+	467.631i	0.347027	+	0.347027i
$123$	−128.164	+	128.164i	−0.0939528	+	0.0939528i
$124$	1151.60	−	1151.60i	0.834006	−	0.834006i
$125$	−879.145	+	879.145i	−0.629065	+	0.629065i
$126$	1920.28			1.35771
$127$	1380.16			0.964325			0.482162	−	0.876082i	$-0.339852\pi$
$127$	1380.16			0.964325			0.482162	+	0.876082i	$0.339852\pi$
$128$	−853.128	−	853.128i	−0.589114	−	0.589114i
$129$	72.6247			0.0495678
$130$	2062.92	+	207.251i	1.39177	+	0.139824i
$131$			2551.47i			1.70170i	0.525408	+	0.850850i	$0.323913\pi$
$131$			2551.47i			1.70170i	−0.525408	+	0.850850i	$0.676087\pi$
$132$	73.8802	+	33.0649i	0.0487155	+	0.0218025i
$133$	−1258.52			−0.820506
$134$	3813.79			2.45866
$135$	−195.556	−	195.556i	−0.124672	−	0.124672i
$136$	−626.806	−	626.806i	−0.395207	−	0.395207i
$137$	281.190	−	281.190i	0.175355	−	0.175355i	−0.613972	−	0.789328i	$-0.710429\pi$
$137$	281.190	−	281.190i	0.175355	−	0.175355i	0.789328	+	0.613972i	$0.210429\pi$
$138$	−32.1304	−	32.1304i	−0.0198197	−	0.0198197i
$139$		−	477.956i		−	0.291653i	−0.989310	−	0.145826i	$-0.953416\pi$
$139$		−	477.956i		−	0.291653i	0.989310	−	0.145826i	$-0.0465840\pi$
$140$	−1254.42			−0.757272
$141$	−8.50608	+	8.50608i	−0.00508044	+	0.00508044i
$142$	1151.18			0.680316
$143$	851.078	−	1483.20i	0.497697	−	0.867351i
$144$	−2103.97			−1.21758
$145$	2020.48	−	2020.48i	1.15718	−	1.15718i
$146$	−2339.72			−1.32628
$147$		−	18.5783i		−	0.0104239i
$148$	−996.044	−	996.044i	−0.553205	−	0.553205i
$149$	−634.958	+	634.958i	−0.349113	+	0.349113i	−0.859779	−	0.510666i	$-0.829399\pi$
$149$	−634.958	+	634.958i	−0.349113	+	0.349113i	0.510666	+	0.859779i	$0.329399\pi$
$150$	24.6976	+	24.6976i	0.0134437	+	0.0134437i
$151$	241.247	+	241.247i	0.130016	+	0.130016i	0.769120	−	0.639104i	$-0.220695\pi$
$151$	241.247	+	241.247i	0.130016	+	0.130016i	−0.639104	+	0.769120i	$0.720695\pi$
$152$	641.000			0.342052
$153$	−2373.05			−1.25392
$154$	−1067.01	+	2384.13i	−0.558327	+	1.24752i
$155$		−	3771.94i		−	1.95464i
$156$	−10.3952	+	103.471i	−0.00533513	+	0.0531045i
$157$	−1530.38			−0.777948			−0.388974	−	0.921249i	$-0.627170\pi$
$157$	−1530.38			−0.777948			−0.388974	+	0.921249i	$0.627170\pi$
$158$	−268.675	−	268.675i	−0.135282	−	0.135282i
$159$	−147.252			−0.0734456
$160$	2495.76			1.23317
$161$	410.702	−	410.702i	0.201043	−	0.201043i
$162$	−1839.00	+	1839.00i	−0.891887	+	0.891887i
$163$	1009.89	−	1009.89i	0.485278	−	0.485278i	−0.421534	−	0.906812i	$-0.638508\pi$
$163$	1009.89	−	1009.89i	0.485278	−	0.485278i	0.906812	+	0.421534i	$0.138508\pi$
$164$	−1590.59	−	1590.59i	−0.757342	−	0.757342i
$165$	175.144	−	66.8430i	0.0826358	−	0.0315377i
$166$			2350.53i			1.09902i
$167$	−661.977	−	661.977i	−0.306738	−	0.306738i	0.536905	−	0.843643i	$-0.319594\pi$
$167$	−661.977	−	661.977i	−0.306738	−	0.306738i	−0.843643	+	0.536905i	$0.819594\pi$
$168$			83.3276i			0.0382671i
$169$	2153.09	+	437.031i	0.980015	+	0.198922i
$170$	3913.60			1.76564
$171$	1213.39	−	1213.39i	0.542634	−	0.542634i
$172$			901.311i			0.399560i
$173$	−1773.32			−0.779322			−0.389661	−	0.920958i	$-0.627408\pi$
$173$	−1773.32			−0.779322			−0.389661	+	0.920958i	$0.627408\pi$
$174$	255.847	+	255.847i	0.111470	+	0.111470i
$175$	−315.694	+	315.694i	−0.136367	+	0.136367i
$176$	1169.08	−	2612.19i	0.500698	−	1.11876i
$177$	−193.691	+	193.691i	−0.0822527	+	0.0822527i
$178$			1469.15i			0.618639i
$179$		−	5.85841i		−	0.00244625i	−0.999999	−	0.00122312i	$-0.999611\pi$
$179$		−	5.85841i		−	0.00244625i	0.999999	−	0.00122312i	$-0.000389332\pi$
$180$	1209.44	−	1209.44i	0.500815	−	0.500815i
$181$		−	1486.63i		−	0.610497i	−0.952273	−	0.305249i	$-0.901260\pi$
$181$		−	1486.63i		−	0.610497i	0.952273	−	0.305249i	$-0.0987396\pi$
$182$	−3339.03	−	335.455i	−1.35992	−	0.136624i
$183$			76.8248i			0.0310331i
$184$	−209.183	+	209.183i	−0.0838106	+	0.0838106i
$185$	−3262.43			−1.29653
$186$	477.628			0.188287
$187$	1318.59	−	2946.27i	0.515643	−	1.15215i
$188$	−105.565	−	105.565i	−0.0409528	−	0.0409528i
$189$	316.524	+	316.524i	0.121819	+	0.121819i
$190$	−2001.11	+	2001.11i	−0.764084	+	0.764084i
$191$	4403.25			1.66810			0.834052	−	0.551686i	$-0.186015\pi$
$191$	4403.25			1.66810			0.834052	+	0.551686i	$0.186015\pi$
$192$			50.6933i			0.0190546i
$193$	−932.116	−	932.116i	−0.347643	−	0.347643i	0.511588	−	0.859231i	$-0.329058\pi$
$193$	−932.116	−	932.116i	−0.347643	−	0.347643i	−0.859231	+	0.511588i	$0.829058\pi$
$194$	−4117.73			−1.52390
$195$	152.430	+	186.478i	0.0559780	+	0.0684818i
$196$	230.567			0.0840258
$197$	−1386.13	+	1386.13i	−0.501310	+	0.501310i	−0.911845	−	0.410535i	$-0.865342\pi$
$197$	−1386.13	+	1386.13i	−0.501310	+	0.501310i	0.410535	+	0.911845i	$0.365342\pi$
$198$	−1269.89	−	3327.40i	−0.455794	−	1.19428i
$199$			3304.44i			1.17711i	0.808456	+	0.588556i	$0.200304\pi$
$199$			3304.44i			1.17711i	−0.808456	+	0.588556i	$0.799696\pi$
$200$	160.792	−	160.792i	0.0568486	−	0.0568486i
$201$	313.274	+	313.274i	0.109933	+	0.109933i
$202$	2288.58	−	2288.58i	0.797147	−	0.797147i
$203$	−3270.33	+	3270.33i	−1.13070	+	1.13070i
$204$			196.296i			0.0673700i
$205$	−5209.80			−1.77497
$206$	−4385.30	−	4385.30i	−1.48320	−	1.48320i
$207$			791.952i			0.265915i
$208$	3658.43	+	367.544i	1.21955	+	0.122522i
$209$	832.265	+	2180.72i	0.275450	+	0.721739i
$210$	−260.137	−	260.137i	−0.0854818	−	0.0854818i
$211$			735.975i			0.240126i	0.992766	+	0.120063i	$0.0383097\pi$
$211$			735.975i			0.240126i	−0.992766	+	0.120063i	$0.961690\pi$
$212$		−	1827.48i		−	0.592036i
$213$	94.5607	+	94.5607i	0.0304188	+	0.0304188i
$214$	−1087.99	−	1087.99i	−0.347538	−	0.347538i
$215$	1476.07	+	1476.07i	0.468220	+	0.468220i
$216$	−161.215	−	161.215i	−0.0507838	−	0.0507838i
$217$			6105.22i			1.90990i
$218$			7780.61i			2.41729i
$219$	−192.190	−	192.190i	−0.0593015	−	0.0593015i
$220$	829.557	+	2173.62i	0.254221	+	0.666117i
$221$	4126.31	+	414.549i	1.25595	+	0.126179i
$222$		−	413.111i		−	0.124893i
$223$	1223.47	+	1223.47i	0.367398	+	0.367398i	0.866527	−	0.499130i	$-0.166347\pi$
$223$	1223.47	+	1223.47i	0.367398	+	0.367398i	−0.499130	+	0.866527i	$0.666347\pi$
$224$	−4039.61			−1.20495
$225$		−	608.748i		−	0.180370i
$226$	5708.55	−	5708.55i	1.68021	−	1.68021i
$227$	−642.601	+	642.601i	−0.187890	+	0.187890i	−0.794783	−	0.606894i	$-0.792415\pi$
$227$	−642.601	+	642.601i	−0.187890	+	0.187890i	0.606894	+	0.794783i	$0.292415\pi$
$228$	−100.371	−	100.371i	−0.0291544	−	0.0291544i
$229$	1653.69	−	1653.69i	0.477201	−	0.477201i	−0.427034	−	0.904235i	$-0.640442\pi$
$229$	1653.69	−	1653.69i	0.477201	−	0.477201i	0.904235	+	0.427034i	$0.140442\pi$
$230$		−	1306.08i		−	0.374436i
$231$	−283.485	+	108.191i	−0.0807445	+	0.0308159i
$232$	1665.67	−	1665.67i	0.471366	−	0.471366i
$233$	−3075.76			−0.864806			−0.432403	−	0.901681i	$-0.642334\pi$
$233$	−3075.76			−0.864806			−0.432403	+	0.901681i	$0.642334\pi$
$234$	3542.73	−	2895.88i	0.989724	−	0.809015i
$235$	−345.766			−0.0959801
$236$	−2403.81	−	2403.81i	−0.663029	−	0.663029i
$237$		−	44.1392i		−	0.0120977i
$238$	−6334.51			−1.72523
$239$	−2875.89	+	2875.89i	−0.778351	+	0.778351i	−0.979550	−	0.201200i	$-0.935516\pi$
$239$	−2875.89	+	2875.89i	−0.778351	+	0.778351i	0.201200	+	0.979550i	$0.435516\pi$
$240$	285.022	+	285.022i	0.0766586	+	0.0766586i
$241$	1174.93	+	1174.93i	0.314041	+	0.314041i	0.846473	−	0.532432i	$-0.178722\pi$
$241$	1174.93	+	1174.93i	0.314041	+	0.314041i	−0.532432	+	0.846473i	$0.678722\pi$
$242$	4836.77	+	272.246i	1.28479	+	0.0723166i
$243$	−916.539			−0.241959
$244$	−953.436			−0.250154
$245$	377.598	−	377.598i	0.0984647	−	0.0984647i
$246$		−	659.700i		−	0.170979i
$247$	−2321.84	+	1897.91i	−0.598119	+	0.488911i
$248$		−	3109.57i		−	0.796201i
$249$	−193.079	+	193.079i	−0.0491400	+	0.0491400i
$250$		−	4525.22i		−	1.14480i
$251$		−	3153.29i		−	0.792964i	−0.918043	−	0.396482i	$-0.870231\pi$
$251$		−	3153.29i		−	0.792964i	0.918043	−	0.396482i	$-0.129769\pi$
$252$	−1957.59	+	1957.59i	−0.489352	+	0.489352i
$253$	−983.251	−	440.052i	−0.244334	−	0.109351i
$254$	−3552.04	+	3552.04i	−0.877460	+	0.877460i
$255$	321.473	+	321.473i	0.0789467	+	0.0789467i
$256$	5350.46			1.30627
$257$		−	3181.77i		−	0.772271i	−0.922442	−	0.386135i	$-0.873810\pi$
$257$		−	3181.77i		−	0.772271i	0.922442	−	0.386135i	$-0.126190\pi$
$258$	−186.910	+	186.910i	−0.0451028	+	0.0451028i
$259$	5280.54			1.26686
$260$	−2314.29	+	1891.73i	−0.552024	+	0.451232i
$261$		−	6306.13i		−	1.49555i
$262$	−6566.58	−	6566.58i	−1.54841	−	1.54841i
$263$			3246.06i			0.761066i	0.924767	+	0.380533i	$0.124259\pi$
$263$			3246.06i			0.761066i	−0.924767	+	0.380533i	$0.875741\pi$
$264$	144.387	−	55.1050i	0.0336607	−	0.0128465i
$265$	−2992.85	−	2992.85i	−0.693771	−	0.693771i
$266$	3238.98	−	3238.98i	0.746596	−	0.746596i
$267$	−120.680	+	120.680i	−0.0276610	+	0.0276610i
$268$	−3887.89	+	3887.89i	−0.886160	+	0.886160i
$269$	5786.01			1.31145			0.655724	−	0.755001i	$-0.272364\pi$
$269$	5786.01			1.31145			0.655724	+	0.755001i	$0.272364\pi$
$270$	1006.58			0.226884
$271$	4948.65	+	4948.65i	1.10926	+	1.10926i	0.993248	+	0.116011i	$0.0370109\pi$
$271$	4948.65	+	4948.65i	1.10926	+	1.10926i	0.116011	+	0.993248i	$0.462989\pi$
$272$	6940.46			1.54716
$273$	−246.721	−	301.831i	−0.0546968	−	0.0669145i
$274$			1447.37i			0.319119i
$275$	755.794	+	338.254i	0.165731	+	0.0741726i
$276$	65.5095			0.0142870
$277$	−2024.15			−0.439059			−0.219529	−	0.975606i	$-0.570452\pi$
$277$	−2024.15			−0.439059			−0.219529	+	0.975606i	$0.570452\pi$
$278$	1230.09	+	1230.09i	0.265381	+	0.265381i
$279$	−5886.31	−	5886.31i	−1.26310	−	1.26310i
$280$	−1693.61	+	1693.61i	−0.361473	+	0.361473i
$281$	2646.37	+	2646.37i	0.561812	+	0.561812i	0.929822	−	0.368010i	$-0.119961\pi$
$281$	2646.37	+	2646.37i	0.561812	+	0.561812i	−0.368010	+	0.929822i	$0.619961\pi$
$282$		−	43.7833i		−	0.00924559i
$283$	3710.33			0.779351			0.389675	−	0.920952i	$-0.372587\pi$
$283$	3710.33			0.779351			0.389675	+	0.920952i	$0.372587\pi$
$284$	−1173.55	+	1173.55i	−0.245202	+	0.245202i
$285$	−328.753			−0.0683285
$286$	1626.85	+	6007.60i	0.336356	+	1.24209i
$287$	8432.52			1.73434
$288$	3894.77	−	3894.77i	0.796880	−	0.796880i
$289$	2915.08			0.593340
$290$			10400.0i			2.10589i
$291$	−338.241	−	338.241i	−0.0681376	−	0.0681376i
$292$	2385.19	−	2385.19i	0.478022	−	0.478022i
$293$	−21.6331	−	21.6331i	−0.00431338	−	0.00431338i	0.704947	−	0.709260i	$-0.250971\pi$
$293$	−21.6331	−	21.6331i	−0.00431338	−	0.00431338i	−0.709260	+	0.704947i	$0.750971\pi$
$294$	47.8140	+	47.8140i	0.00948494	+	0.00948494i
$295$	−7873.42			−1.55393
$296$	−2689.53			−0.528128
$297$	339.144	−	757.783i	0.0662597	−	0.148051i
$298$		−	3268.31i		−	0.635330i
$299$	138.347	−	1377.07i	0.0267585	−	0.266347i
$300$	−50.3550			−0.00969083
$301$	−2389.16	−	2389.16i	−0.457504	−	0.457504i
$302$	−1241.77			−0.236609
$303$	375.979			0.0712852
$304$	−3548.81	+	3548.81i	−0.669534	+	0.669534i
$305$	−1561.44	+	1561.44i	−0.293140	+	0.293140i
$306$	6107.38	−	6107.38i	1.14097	−	1.14097i
$307$	−4990.80	−	4990.80i	−0.927817	−	0.927817i	0.0697478	−	0.997565i	$-0.477781\pi$
$307$	−4990.80	−	4990.80i	−0.927817	−	0.927817i	−0.997565	+	0.0697478i	$0.977781\pi$
$308$	−1342.71	−	3518.20i	−0.248403	−	0.650871i
$309$		−	720.440i		−	0.132636i
$310$	9707.64	+	9707.64i	1.77857	+	1.77857i
$311$		−	853.537i		−	0.155626i	−0.996968	−	0.0778129i	$-0.975206\pi$
$311$		−	853.537i		−	0.155626i	0.996968	−	0.0778129i	$-0.0247937\pi$
$312$	125.662	+	153.731i	0.0228020	+	0.0278953i
$313$	1540.65			0.278220			0.139110	−	0.990277i	$-0.455576\pi$
$313$	1540.65			0.278220			0.139110	+	0.990277i	$0.455576\pi$
$314$	3938.66	−	3938.66i	0.707871	−	0.707871i
$315$			6411.88i			1.14688i
$316$	547.791			0.0975178
$317$	−560.984	−	560.984i	−0.0993942	−	0.0993942i	0.655661	−	0.755055i	$-0.272390\pi$
$317$	−560.984	−	560.984i	−0.0993942	−	0.0993942i	−0.755055	+	0.655661i	$0.772390\pi$
$318$	378.975	−	378.975i	0.0668297	−	0.0668297i
$319$	7829.40	+	3504.03i	1.37418	+	0.615010i
$320$	−1030.33	+	1030.33i	−0.179990	+	0.179990i
$321$		−	178.740i		−	0.0310788i
$322$			2114.00i			0.365866i
$323$	−4002.67	+	4002.67i	−0.689519	+	0.689519i
$324$		−	3749.48i		−	0.642914i
$325$	−106.343	+	1058.51i	−0.0181502	+	0.180663i
$326$			5198.18i			0.883130i
$327$	−639.119	+	639.119i	−0.108084	+	0.108084i
$328$	−4294.93			−0.723012
$329$	559.654			0.0937834
$330$	−278.727	+	622.788i	−0.0464952	+	0.103889i
$331$	4096.97	+	4096.97i	0.680332	+	0.680332i	0.960075	−	0.279743i	$-0.0902492\pi$
$331$	4096.97	+	4096.97i	0.680332	+	0.680332i	−0.279743	+	0.960075i	$0.590249\pi$
$332$	−2396.21	−	2396.21i	−0.396111	−	0.396111i
$333$	−5091.20	+	5091.20i	−0.837826	+	0.837826i
$334$	3407.39			0.558216
$335$			12734.4i			2.07687i
$336$	−461.333	−	461.333i	−0.0749041	−	0.0749041i
$337$	−2283.10			−0.369046			−0.184523	−	0.982828i	$-0.559074\pi$
$337$	−2283.10			−0.369046			−0.184523	+	0.982828i	$0.559074\pi$
$338$	−6666.07	+	4416.54i	−1.07274	+	0.710734i
$339$	937.829			0.150253
$340$	−3989.65	+	3989.65i	−0.636380	+	0.636380i
$341$	10578.9	−	4037.42i	1.68000	−	0.641168i
$342$			6245.68i			0.987509i
$343$	4159.73	−	4159.73i	0.654823	−	0.654823i
$344$	1216.87	+	1216.87i	0.190724	+	0.190724i
$345$	107.285	−	107.285i	0.0167420	−	0.0167420i
$346$	4563.89	−	4563.89i	0.709122	−	0.709122i
$347$			4040.42i			0.625076i	0.949905	+	0.312538i	$0.101179\pi$
$347$			4040.42i			0.625076i	−0.949905	+	0.312538i	$0.898821\pi$
$348$	−521.637			−0.0803525
$349$	−7206.02	−	7206.02i	−1.10524	−	1.10524i	−0.993767	−	0.111475i	$-0.964443\pi$
$349$	−7206.02	−	7206.02i	−1.10524	−	1.10524i	−0.111475	−	0.993767i	$-0.535557\pi$
$350$		−	1624.97i		−	0.248166i
$351$	1061.29	+	106.622i	0.161389	+	0.0162139i
$352$	2671.42	+	6999.71i	0.404509	+	1.05990i
$353$	−4706.04	−	4706.04i	−0.709568	−	0.709568i	0.256876	−	0.966444i	$-0.417307\pi$
$353$	−4706.04	−	4706.04i	−0.709568	−	0.709568i	−0.966444	+	0.256876i	$0.917307\pi$
$354$		−	996.986i		−	0.149687i
$355$			3843.83i			0.574674i
$356$	−1497.70	−	1497.70i	−0.222972	−	0.222972i
$357$	−520.333	−	520.333i	−0.0771399	−	0.0771399i
$358$	15.0775	+	15.0775i	0.00222589	+	0.00222589i
$359$	−8194.36	−	8194.36i	−1.20469	−	1.20469i	−0.972725	−	0.231960i	$-0.925486\pi$
$359$	−8194.36	−	8194.36i	−1.20469	−	1.20469i	−0.231960	−	0.972725i	$-0.574514\pi$
$360$		−	3265.76i		−	0.478113i
$361$			2765.69i			0.403220i
$362$	3826.05	+	3826.05i	0.555505	+	0.555505i
$363$	374.941	+	419.667i	0.0542130	+	0.0606799i
$364$	3745.88	−	3061.94i	0.539389	−	0.440904i
$365$		−	7812.41i		−	1.12033i
$366$	−197.720	−	197.720i	−0.0282377	−	0.0282377i
$367$	−7115.38			−1.01204			−0.506021	−	0.862521i	$-0.668884\pi$
$367$	−7115.38			−1.01204			−0.506021	+	0.862521i	$0.668884\pi$
$368$		−	2316.23i		−	0.328102i
$369$	−8130.16	+	8130.16i	−1.14699	+	1.14699i
$370$	8396.35	−	8396.35i	1.17974	−	1.17974i
$371$	4844.19	+	4844.19i	0.677892	+	0.677892i
$372$	−486.910	+	486.910i	−0.0678631	+	0.0678631i
$373$		−	5757.94i		−	0.799289i	−0.916670	−	0.399645i	$-0.869134\pi$
$373$		−	5757.94i		−	0.799289i	0.916670	−	0.399645i	$-0.130866\pi$
$374$	4189.05	+	10976.2i	0.579173	+	1.51756i
$375$	371.713	−	371.713i	0.0511871	−	0.0511871i
$376$	−285.048			−0.0390964
$377$	−1101.62	+	10965.3i	−0.150494	+	1.49798i
$378$	−1629.24			−0.221691
$379$	−2150.77	−	2150.77i	−0.291498	−	0.291498i	0.546174	−	0.837672i	$-0.316084\pi$
$379$	−2150.77	−	2150.77i	−0.291498	−	0.291498i	−0.837672	+	0.546174i	$0.816084\pi$
$380$		−	4079.99i		−	0.550788i
$381$	−583.547			−0.0784672
$382$	−11332.4	+	11332.4i	−1.51784	+	1.51784i
$383$	−2746.89	−	2746.89i	−0.366474	−	0.366474i	0.499715	−	0.866190i	$-0.333438\pi$
$383$	−2746.89	−	2746.89i	−0.366474	−	0.366474i	−0.866190	+	0.499715i	$0.833438\pi$
$384$	360.712	+	360.712i	0.0479362	+	0.0479362i
$385$	−7960.70	−	3562.79i	−1.05380	−	0.471628i
$386$	4797.87			0.632656
$387$	4606.98			0.605132
$388$	4197.75	−	4197.75i	0.549249	−	0.549249i
$389$		−	4982.59i		−	0.649428i	−0.945812	−	0.324714i	$-0.894732\pi$
$389$		−	4982.59i		−	0.649428i	0.945812	−	0.324714i	$-0.105268\pi$
$390$	−872.228	−	87.6282i	−0.113249	−	0.0113775i
$391$		−	2612.45i		−	0.337896i
$392$	311.290	−	311.290i	0.0401085	−	0.0401085i
$393$		−	1078.79i		−	0.138468i
$394$		−	7134.84i		−	0.912305i
$395$	897.114	−	897.114i	0.114275	−	0.114275i
$396$	4686.62	+	2097.49i	0.594727	+	0.266169i
$397$	5500.24	−	5500.24i	0.695338	−	0.695338i	−0.268063	−	0.963401i	$-0.586384\pi$
$397$	5500.24	−	5500.24i	0.695338	−	0.695338i	0.963401	+	0.268063i	$0.0863836\pi$
$398$	−8504.46	−	8504.46i	−1.07108	−	1.07108i
$399$	532.116			0.0667647
$400$			1780.41i			0.222551i
$401$	−1803.57	+	1803.57i	−0.224604	+	0.224604i	−0.810434	−	0.585830i	$-0.800769\pi$
$401$	−1803.57	+	1803.57i	−0.224604	+	0.224604i	0.585830	+	0.810434i	$0.300769\pi$
$402$	−1612.51			−0.200062
$403$	9206.97	+	11263.5i	1.13804	+	1.39225i
$404$			4666.10i			0.574621i
$405$	−6140.50	−	6140.50i	−0.753392	−	0.753392i
$406$		−	16833.3i		−	2.05769i
$407$	−3492.05	−	9149.95i	−0.425293	−	1.11436i
$408$	265.021	+	265.021i	0.0321581	+	0.0321581i
$409$	−7331.03	+	7331.03i	−0.886298	+	0.886298i	−0.994165	−	0.107867i	$-0.965598\pi$
$409$	−7331.03	+	7331.03i	−0.886298	+	0.886298i	0.107867	+	0.994165i	$0.465598\pi$
$410$	13408.2	−	13408.2i	1.61508	−	1.61508i
$411$	−118.890	+	118.890i	−0.0142687	+	0.0142687i
$412$	8941.04			1.06916
$413$	12743.8			1.51836
$414$	−2038.20	−	2038.20i	−0.241962	−	0.241962i
$415$	−7848.51			−0.928357
$416$	−7452.70	+	6091.94i	−0.878362	+	0.717985i
$417$			202.085i			0.0237318i
$418$	−7754.35	−	3470.44i	−0.907363	−	0.406088i
$419$	118.470			0.0138130			0.00690651	−	0.999976i	$-0.497802\pi$
$419$	118.470			0.0138130			0.00690651	+	0.999976i	$0.497802\pi$
$420$	530.384			0.0616193
$421$	5238.69	+	5238.69i	0.606456	+	0.606456i	0.942018	−	0.335562i	$-0.108926\pi$
$421$	5238.69	+	5238.69i	0.606456	+	0.606456i	−0.335562	+	0.942018i	$0.608926\pi$
$422$	−1894.14	−	1894.14i	−0.218496	−	0.218496i
$423$	−539.587	+	539.587i	−0.0620227	+	0.0620227i
$424$	−2467.29	−	2467.29i	−0.282600	−	0.282600i
$425$			2008.11i			0.229194i
$426$	−486.732			−0.0553574
$427$	2527.33	−	2527.33i	0.286431	−	0.286431i
$428$	2218.26			0.250522
$429$	−359.845	+	627.113i	−0.0404977	+	0.0705764i
$430$	−7597.78			−0.852087
$431$	1294.93	−	1294.93i	0.144721	−	0.144721i	−0.631034	−	0.775755i	$-0.717369\pi$
$431$	1294.93	−	1294.93i	0.144721	−	0.144721i	0.775755	+	0.631034i	$0.217369\pi$
$432$	1785.09			0.198809
$433$		−	9846.07i		−	1.09278i	−0.837532	−	0.546388i	$-0.816002\pi$
$433$		−	9846.07i		−	1.09278i	0.837532	−	0.546388i	$-0.183998\pi$
$434$	−15712.7	−	15712.7i	−1.73786	−	1.73786i
$435$	−854.282	+	854.282i	−0.0941602	+	0.0941602i
$436$	−7931.80	−	7931.80i	−0.871248	−	0.871248i
$437$	1335.80	+	1335.80i	0.146225	+	0.146225i
$438$	989.261			0.107919
$439$	−5379.12			−0.584810			−0.292405	−	0.956295i	$-0.594456\pi$
$439$	−5379.12			−0.584810			−0.292405	+	0.956295i	$0.594456\pi$
$440$	4054.62	+	1814.64i	0.439310	+	0.196612i
$441$		−	1178.52i		−	0.127257i
$442$	−11686.6	+	9552.76i	−1.25763	+	1.02801i
$443$	7084.07			0.759762			0.379881	−	0.925035i	$-0.375965\pi$
$443$	7084.07			0.759762			0.379881	+	0.925035i	$0.375965\pi$
$444$	421.139	+	421.139i	0.0450143	+	0.0450143i
$445$	−4905.56			−0.522574
$446$	−6297.56			−0.668606
$447$	268.467	−	268.467i	0.0284073	−	0.0284073i
$448$	1667.67	−	1667.67i	0.175871	−	0.175871i
$449$	−12056.4	+	12056.4i	−1.26721	+	1.26721i	−0.319691	+	0.947522i	$0.603579\pi$
$449$	−12056.4	+	12056.4i	−1.26721	+	1.26721i	−0.947522	+	0.319691i	$0.896421\pi$
$450$	1566.70	+	1566.70i	0.164122	+	0.164122i
$451$	−5576.47	−	14611.6i	−0.582230	−	1.52557i
$452$			11638.9i			1.21117i
$453$	−102.002	−	102.002i	−0.0105794	−	0.0105794i
$454$		−	3307.66i		−	0.341930i
$455$	1120.10	−	11149.1i	0.115409	−	1.14875i
$456$	−271.022			−0.0278328
$457$	1868.50	−	1868.50i	0.191258	−	0.191258i	−0.604982	−	0.796239i	$-0.706820\pi$
$457$	1868.50	−	1868.50i	0.191258	−	0.191258i	0.796239	+	0.604982i	$0.206820\pi$
$458$			8512.04i			0.868431i
$459$	2013.39			0.204743
$460$	1331.46	+	1331.46i	0.134956	+	0.134956i
$461$	5438.91	−	5438.91i	0.549491	−	0.549491i	−0.376802	−	0.926294i	$-0.622976\pi$
$461$	5438.91	−	5438.91i	0.549491	−	0.549491i	0.926294	+	0.376802i	$0.122976\pi$
$462$	451.145	−	1008.04i	0.0454311	−	0.101511i
$463$	−4158.04	+	4158.04i	−0.417366	+	0.417366i	−0.884295	−	0.466929i	$-0.845360\pi$
$463$	−4158.04	+	4158.04i	−0.417366	+	0.417366i	0.466929	+	0.884295i	$0.345360\pi$
$464$			18443.6i			1.84531i
$465$			1594.82i			0.159049i
$466$	7915.92	−	7915.92i	0.786905	−	0.786905i
$467$			7334.69i			0.726786i	0.931636	+	0.363393i	$0.118382\pi$
$467$			7334.69i			0.726786i	−0.931636	+	0.363393i	$0.881618\pi$
$468$	−659.423	+	6563.72i	−0.0651321	+	0.648308i
$469$		−	20611.7i		−	2.02934i
$470$	889.881	−	889.881i	0.0873343	−	0.0873343i
$471$	647.063			0.0633017
$472$	−6490.81			−0.632974
$473$	−2559.89	+	5719.81i	−0.248845	+	0.556020i
$474$	113.599	+	113.599i	0.0110079	+	0.0110079i
$475$	−1026.79	−	1026.79i	−0.0991838	−	0.0991838i
$476$	6457.61	−	6457.61i	0.621815	−	0.621815i
$477$	−9341.00			−0.896635
$478$		−	14803.0i		−	1.41648i
$479$	4522.70	+	4522.70i	0.431414	+	0.431414i	0.889109	−	0.457695i	$-0.151325\pi$
$479$	4522.70	+	4522.70i	0.431414	+	0.431414i	−0.457695	+	0.889109i	$0.651325\pi$
$480$	−1055.24			−0.100343
$481$	9742.08	−	7963.31i	0.923494	−	0.754877i
$482$	−6047.71			−0.571506
$483$	−173.650	+	173.650i	−0.0163589	+	0.0163589i
$484$	−5208.29	+	4653.22i	−0.489133	+	0.437004i
$485$		−	13749.3i		−	1.28726i
$486$	2358.85	−	2358.85i	0.220164	−	0.220164i
$487$	−1104.91	−	1104.91i	−0.102810	−	0.102810i	0.653831	−	0.756641i	$-0.273161\pi$
$487$	−1104.91	−	1104.91i	−0.102810	−	0.102810i	−0.756641	+	0.653831i	$0.773161\pi$
$488$	−1287.24	+	1287.24i	−0.119407	+	0.119407i
$489$	−426.991	+	426.991i	−0.0394871	+	0.0394871i
$490$			1943.61i			0.179190i
$491$	−2399.35			−0.220531			−0.110266	−	0.993902i	$-0.535170\pi$
$491$	−2399.35			−0.220531			−0.110266	+	0.993902i	$0.535170\pi$
$492$	672.519	+	672.519i	0.0616250	+	0.0616250i
$493$			20802.3i			1.90038i
$494$	1091.06	−	10860.1i	0.0993709	−	0.989112i
$495$	11110.3	−	4240.21i	1.00883	−	0.385017i
$496$	17215.7	+	17215.7i	1.55849	+	1.55849i
$497$		−	6221.58i		−	0.561521i
$498$		−	993.832i		−	0.0894271i
$499$	13609.7	+	13609.7i	1.22095	+	1.22095i	0.967294	+	0.253658i	$0.0816338\pi$
$499$	13609.7	+	13609.7i	1.22095	+	1.22095i	0.253658	+	0.967294i	$0.418366\pi$
$500$	4613.15	+	4613.15i	0.412613	+	0.412613i
$501$	279.891	+	279.891i	0.0249593	+	0.0249593i
$502$	8115.45	+	8115.45i	0.721535	+	0.721535i
$503$		−	3373.74i		−	0.299061i	−0.988757	−	0.149530i	$-0.952224\pi$
$503$		−	3373.74i		−	0.299061i	0.988757	−	0.149530i	$-0.0477762\pi$
$504$			5285.93i			0.467170i
$505$	7641.64	+	7641.64i	0.673364	+	0.673364i
$506$	3663.08	−	1398.00i	0.321826	−	0.122824i
$507$	−910.353	−	184.782i	−0.0797440	−	0.0161863i
$508$		−	7242.12i		−	0.632514i
$509$	−1408.52	−	1408.52i	−0.122655	−	0.122655i	0.643115	−	0.765770i	$-0.277642\pi$
$509$	−1408.52	−	1408.52i	−0.122655	−	0.122655i	−0.765770	+	0.643115i	$0.777642\pi$
$510$	−1654.72			−0.143671
$511$			12645.1i			1.09469i
$512$	−6945.19	+	6945.19i	−0.599486	+	0.599486i
$513$	−1029.49	+	1029.49i	−0.0886027	+	0.0886027i
$514$	8188.76	+	8188.76i	0.702706	+	0.702706i
$515$	14642.7	−	14642.7i	1.25288	−	1.25288i
$516$		−	381.085i		−	0.0325122i
$517$	−370.102	−	969.751i	−0.0314837	−	0.0824944i
$518$	−13590.2	+	13590.2i	−1.15274	+	1.15274i
$519$	749.779			0.0634135
$520$	−570.498	+	5678.58i	−0.0481115	+	0.478889i
$521$	239.632			0.0201506			0.0100753	−	0.999949i	$-0.496793\pi$
$521$	239.632			0.0201506			0.0100753	+	0.999949i	$0.496793\pi$
$522$	16229.8	+	16229.8i	1.36084	+	1.36084i
$523$		−	11603.9i		−	0.970179i	−0.874464	−	0.485090i	$-0.838787\pi$
$523$		−	11603.9i		−	0.970179i	0.874464	−	0.485090i	$-0.161213\pi$
$524$	13388.4			1.11617
$525$	133.479	−	133.479i	0.0110962	−	0.0110962i
$526$	−8354.20	−	8354.20i	−0.692510	−	0.692510i
$527$	19417.4	+	19417.4i	1.60500	+	1.60500i
$528$	−494.301	+	1104.46i	−0.0407418	+	0.0910335i
$529$	11295.2			0.928343
$530$	15405.1			1.26255
$531$	−12286.9	+	12286.9i	−1.00415	+	1.00415i
$532$			6603.84i			0.538182i
$533$	15557.2	−	12716.7i	1.26427	−	1.03343i
$534$		−	621.175i		−	0.0503387i
$535$	3632.83	−	3632.83i	0.293572	−	0.293572i
$536$			10498.2i			0.845991i
$537$			2.47700i			0.000199051i
$538$	−14891.1	+	14891.1i	−1.19331	+	1.19331i
$539$	1463.20	+	654.852i	0.116929	+	0.0523311i
$540$	−1026.14	+	1026.14i	−0.0817743	+	0.0817743i
$541$	2155.91	+	2155.91i	0.171330	+	0.171330i	0.787564	−	0.616233i	$-0.211342\pi$
$541$	2155.91	+	2155.91i	0.171330	+	0.171330i	−0.616233	+	0.787564i	$0.711342\pi$
$542$	−25472.2			−2.01868
$543$			628.562i			0.0496762i
$544$	−12847.9	+	12847.9i	−1.01259	+	1.01259i
$545$	−25979.7			−2.04193
$546$	1411.78	+	141.834i	0.110657	+	0.0111171i
$547$			2033.53i			0.158953i	0.996837	+	0.0794767i	$0.0253249\pi$
$547$			2033.53i			0.158953i	−0.996837	+	0.0794767i	$0.974675\pi$
$548$	−1475.49	−	1475.49i	−0.115018	−	0.115018i
$549$			4873.41i			0.378857i
$550$	−2815.69	+	1074.60i	−0.218294	+	0.0833111i
$551$	−10636.7	−	10636.7i	−0.822393	−	0.822393i
$552$	88.4448	−	88.4448i	0.00681968	−	0.00681968i
$553$	−1452.06	+	1452.06i	−0.111660	+	0.111660i
$554$	5209.44	−	5209.44i	0.399509	−	0.399509i
$555$	1379.39			0.105499
$556$	−2507.99			−0.191299
$557$	−10006.4	−	10006.4i	−0.761197	−	0.761197i	0.215342	−	0.976539i	$-0.430913\pi$
$557$	−10006.4	−	10006.4i	−0.761197	−	0.761197i	−0.976539	+	0.215342i	$0.930913\pi$
$558$	30298.6			2.29864
$559$	−8010.73	−	804.796i	−0.606114	−	0.0608931i
$560$		−	18752.9i		−	1.41510i
$561$	−557.517	+	1245.72i	−0.0419579	+	0.0937507i
$562$	−13621.6			−1.02241
$563$	−10803.8			−0.808750			−0.404375	−	0.914593i	$-0.632511\pi$
$563$	−10803.8			−0.808750			−0.404375	+	0.914593i	$0.632511\pi$
$564$	44.6341	+	44.6341i	0.00333233	+	0.00333233i
$565$	19061.0	+	19061.0i	1.41930	+	1.41930i
$566$	−9549.08	+	9549.08i	−0.709148	+	0.709148i
$567$	9938.95	+	9938.95i	0.736149	+	0.736149i
$568$			3168.83i			0.234087i
$569$	1070.61			0.0788790			0.0394395	−	0.999222i	$-0.487443\pi$
$569$	1070.61			0.0788790			0.0394395	+	0.999222i	$0.487443\pi$
$570$	846.093	−	846.093i	0.0621736	−	0.0621736i
$571$	6554.92			0.480411			0.240206	−	0.970722i	$-0.422785\pi$
$571$	6554.92			0.480411			0.240206	+	0.970722i	$0.422785\pi$
$572$	−7782.80	−	4465.87i	−0.568908	−	0.326447i
$573$	−1861.74			−0.135734
$574$	−21702.3	+	21702.3i	−1.57811	+	1.57811i
$575$	670.161			0.0486046
$576$			3215.75i			0.232621i
$577$	−15953.9	−	15953.9i	−1.15107	−	1.15107i	−0.986338	−	0.164733i	$-0.947324\pi$
$577$	−15953.9	−	15953.9i	−1.15107	−	1.15107i	−0.164733	−	0.986338i	$-0.552676\pi$
$578$	−7502.39	+	7502.39i	−0.539893	+	0.539893i
$579$	394.109	+	394.109i	0.0282878	+	0.0282878i
$580$	−10602.1	−	10602.1i	−0.759013	−	0.759013i
$581$	12703.5			0.907110
$582$	1741.03			0.124000
$583$	5190.37	−	11597.4i	0.368719	−	0.823865i
$584$		−	6440.52i		−	0.456354i
$585$	9669.44	+	11829.3i	0.683388	+	0.836037i
$586$	111.352			0.00784968
$587$	−7097.96	−	7097.96i	−0.499087	−	0.499087i	0.412067	−	0.911154i	$-0.364807\pi$
$587$	−7097.96	−	7097.96i	−0.499087	−	0.499087i	−0.911154	+	0.412067i	$0.864807\pi$
$588$	−97.4863			−0.00683719
$589$	−19857.2			−1.38913
$590$	20263.4	−	20263.4i	1.41395	−	1.41395i
$591$	586.074	−	586.074i	0.0407916	−	0.0407916i
$592$	14890.3	−	14890.3i	1.03376	−	1.03376i
$593$	12520.7	+	12520.7i	0.867055	+	0.867055i	0.992145	−	0.125090i	$-0.0399220\pi$
$593$	12520.7	+	12520.7i	0.867055	+	0.867055i	−0.125090	+	0.992145i	$0.539922\pi$
$594$	1077.43	+	2823.10i	0.0744233	+	0.195005i
$595$		−	21151.2i		−	1.45733i
$596$	3331.82	+	3331.82i	0.228988	+	0.228988i
$597$		−	1397.15i		−	0.0957818i
$598$	3188.02	+	3900.13i	0.218007	+	0.266703i
$599$	13385.8			0.913067			0.456533	−	0.889706i	$-0.349091\pi$
$599$	13385.8			0.913067			0.456533	+	0.889706i	$0.349091\pi$
$600$	−67.9847	+	67.9847i	−0.00462577	+	0.00462577i
$601$			745.527i			0.0506001i	0.999680	+	0.0253001i	$0.00805412\pi$
$601$			745.527i			0.0506001i	−0.999680	+	0.0253001i	$0.991946\pi$
$602$	12297.7			0.832585
$603$	19872.7	+	19872.7i	1.34209	+	1.34209i
$604$	1265.90	−	1265.90i	0.0852793	−	0.0852793i
$605$	−909.039	+	16150.1i	−0.0610871	+	1.08528i
$606$	−967.637	+	967.637i	−0.0648640	+	0.0648640i
$607$		−	15993.4i		−	1.06944i	−0.845029	−	0.534721i	$-0.820417\pi$
$607$		−	15993.4i		−	1.06944i	0.845029	−	0.534721i	$-0.179583\pi$
$608$		−	13138.8i		−	0.876395i
$609$	1382.73	−	1382.73i	0.0920051	−	0.0920051i
$610$		−	8037.18i		−	0.533469i
$611$	1032.51	−	843.986i	0.0683646	−	0.0558822i
$612$			12452.1i			0.822463i
$613$	12735.0	−	12735.0i	0.839092	−	0.839092i	−0.149647	−	0.988739i	$-0.547814\pi$
$613$	12735.0	−	12735.0i	0.839092	−	0.839092i	0.988739	+	0.149647i	$0.0478138\pi$
$614$	25689.1			1.68848
$615$	2202.76			0.144429
$616$	−6562.76	−	2937.15i	−0.429255	−	0.192112i
$617$	−2046.56	−	2046.56i	−0.133536	−	0.133536i	0.637180	−	0.770715i	$-0.280101\pi$
$617$	−2046.56	−	2046.56i	−0.133536	−	0.133536i	−0.770715	+	0.637180i	$0.780101\pi$
$618$	1854.16	+	1854.16i	0.120688	+	0.120688i
$619$	−18132.6	+	18132.6i	−1.17740	+	1.17740i	−0.196996	+	0.980404i	$0.563118\pi$
$619$	−18132.6	+	18132.6i	−1.17740	+	1.17740i	−0.980404	+	0.196996i	$0.936882\pi$
$620$	−19792.5			−1.28208
$621$		−	671.925i		−	0.0434193i
$622$	2196.70	+	2196.70i	0.141607	+	0.141607i
$623$	7940.08			0.510614
$624$	−1546.83	−	155.402i	−0.0992350	−	0.00996963i
$625$	17946.9			1.14860
$626$	−3965.10	+	3965.10i	−0.253158	+	0.253158i
$627$	−351.891	−	922.033i	−0.0224134	−	0.0587280i
$628$			8030.39i			0.510267i
$629$	16794.6	−	16794.6i	1.06462	−	1.06462i
$630$	−16501.9	−	16501.9i	−1.04358	−	1.04358i
$631$	−5086.05	+	5086.05i	−0.320876	+	0.320876i	−0.849103	−	0.528227i	$-0.822857\pi$
$631$	−5086.05	+	5086.05i	−0.320876	+	0.320876i	0.528227	+	0.849103i	$0.322857\pi$
$632$	739.577	−	739.577i	0.0465487	−	0.0465487i
$633$		−	311.179i		−	0.0195391i
$634$	2887.55			0.180882
$635$	−11860.4	−	11860.4i	−0.741205	−	0.741205i
$636$			772.678i			0.0481740i
$637$	−205.877	+	2049.25i	−0.0128056	+	0.127463i
$638$	−29168.3	+	11132.0i	−1.81000	+	0.690782i
$639$	5998.50	+	5998.50i	0.371357	+	0.371357i
$640$			14662.7i			0.905616i
$641$		−	11851.9i		−	0.730297i	−0.930949	−	0.365149i	$-0.881018\pi$
$641$		−	11851.9i		−	0.730297i	0.930949	−	0.365149i	$-0.118982\pi$
$642$	460.013	+	460.013i	0.0282792	+	0.0282792i
$643$	−6643.67	−	6643.67i	−0.407466	−	0.407466i	0.473388	−	0.880854i	$-0.343031\pi$
$643$	−6643.67	−	6643.67i	−0.407466	−	0.407466i	−0.880854	+	0.473388i	$0.843031\pi$
$644$	−2155.08	−	2155.08i	−0.131867	−	0.131867i
$645$	−624.101	−	624.101i	−0.0380991	−	0.0380991i
$646$		−	20602.9i		−	1.25482i
$647$		−	11820.0i		−	0.718226i	−0.933294	−	0.359113i	$-0.883079\pi$
$647$		−	11820.0i		−	0.718226i	0.933294	−	0.359113i	$-0.116921\pi$
$648$	−5062.20	−	5062.20i	−0.306886	−	0.306886i
$649$	−8427.57	−	22082.1i	−0.509725	−	1.33559i
$650$	−2450.53	−	2997.91i	−0.147873	−	0.180904i
$651$		−	2581.36i		−	0.155409i
$652$	−5299.19	−	5299.19i	−0.318301	−	0.318301i
$653$	−3264.27			−0.195622			−0.0978108	−	0.995205i	$-0.531184\pi$
$653$	−3264.27			−0.195622			−0.0978108	+	0.995205i	$0.531184\pi$
$654$		−	3289.73i		−	0.196695i
$655$	21926.0	−	21926.0i	1.30797	−	1.30797i
$656$	23778.3	−	23778.3i	1.41523	−	1.41523i
$657$	−12191.7	−	12191.7i	−0.723962	−	0.723962i
$658$	−1440.35	+	1440.35i	−0.0853355	+	0.0853355i
$659$			24183.7i			1.42954i	0.699361	+	0.714769i	$0.253468\pi$
$659$			24183.7i			1.42954i	−0.699361	+	0.714769i	$0.746532\pi$
$660$	−350.746	−	919.033i	−0.0206860	−	0.0542020i
$661$	7674.09	−	7674.09i	0.451569	−	0.451569i	−0.444306	−	0.895875i	$-0.646550\pi$
$661$	7674.09	−	7674.09i	0.451569	−	0.451569i	0.895875	+	0.444306i	$0.146550\pi$
$662$	−21088.3			−1.23810
$663$	−1744.65	−	175.276i	−0.102197	−	0.0102672i
$664$	−6470.28			−0.378156
$665$	10815.1	+	10815.1i	0.630662	+	0.630662i
$666$		−	26205.9i		−	1.52471i
$667$	6942.32			0.403010
$668$	−3473.60	+	3473.60i	−0.201194	+	0.201194i
$669$	−517.298	−	517.298i	−0.0298952	−	0.0298952i
$670$	−32773.8	−	32773.8i	−1.88979	−	1.88979i
$671$	−6050.61	−	2707.94i	−0.348109	−	0.155795i
$672$	1707.99			0.0980466
$673$	−22552.2			−1.29172			−0.645858	−	0.763458i	$-0.723500\pi$
$673$	−22552.2			−1.29172			−0.645858	+	0.763458i	$0.723500\pi$
$674$	5875.90	−	5875.90i	0.335803	−	0.335803i
$675$			516.487i			0.0294512i
$676$	2293.24	−	11298.0i	0.130476	−	0.642806i
$677$			21179.8i			1.20237i	0.799109	+	0.601186i	$0.205305\pi$
$677$			21179.8i			1.20237i	−0.799109	+	0.601186i	$0.794695\pi$
$678$	−2413.64	+	2413.64i	−0.136719	+	0.136719i
$679$			22254.4i			1.25780i
$680$			10772.9i			0.607533i
$681$	271.699	−	271.699i	0.0152886	−	0.0152886i
$682$	−16835.5	+	37617.3i	−0.945258	+	2.11208i
$683$	−2681.42	+	2681.42i	−0.150222	+	0.150222i	−0.778217	−	0.627995i	$-0.783876\pi$
$683$	−2681.42	+	2681.42i	−0.150222	+	0.150222i	0.627995	+	0.778217i	$0.283876\pi$
$684$	−6367.05	−	6367.05i	−0.355921	−	0.355921i
$685$	−4832.81			−0.269565
$686$			21411.4i			1.19168i
$687$	−699.200	+	699.200i	−0.0388299	+	0.0388299i
$688$	−13474.1			−0.746648
$689$	16242.4	+	1631.78i	0.898091	+	0.0902265i
$690$			552.225i			0.0304679i
$691$	782.287	+	782.287i	0.0430674	+	0.0430674i	0.728313	−	0.685245i	$-0.240305\pi$
$691$	782.287	+	782.287i	0.0430674	+	0.0430674i	−0.685245	+	0.728313i	$0.740305\pi$
$692$			9305.15i			0.511169i
$693$	−17983.0	+	6863.17i	−0.985741	+	0.376205i
$694$	−10398.6	−	10398.6i	−0.568770	−	0.568770i
$695$	−4107.32	+	4107.32i	−0.224172	+	0.224172i
$696$	−704.266	+	704.266i	−0.0383551	+	0.0383551i
$697$	26819.3	−	26819.3i	1.45747	−	1.45747i
$698$	37091.5			2.01137
$699$	1300.47			0.0703693
$700$	1656.54	+	1656.54i	0.0894449	+	0.0894449i
$701$	5160.32			0.278035			0.139018	−	0.990290i	$-0.455606\pi$
$701$	5160.32			0.278035			0.139018	+	0.990290i	$0.455606\pi$
$702$	−3005.80	+	2456.98i	−0.161605	+	0.132098i
$703$			17174.9i			0.921427i
$704$	−3992.53	−	1786.85i	−0.213742	−	0.0956597i
$705$	146.194			0.00780991
$706$	24223.4			1.29130
$707$	−12368.7	−	12368.7i	−0.657952	−	0.657952i
$708$	1016.36	+	1016.36i	0.0539507	+	0.0539507i
$709$	−15503.6	+	15503.6i	−0.821229	+	0.821229i	−0.986284	−	0.165055i	$-0.947220\pi$
$709$	−15503.6	+	15503.6i	−0.821229	+	0.821229i	0.165055	+	0.986284i	$0.447220\pi$
$710$	−9892.66	−	9892.66i	−0.522908	−	0.522908i
$711$		−	2799.99i		−	0.147690i
$712$	−4044.12			−0.212865
$713$	6480.14	−	6480.14i	0.340369	−	0.340369i
$714$	2678.31			0.140382
$715$	−20059.6	+	5432.12i	−1.04921	+	0.284126i
$716$	−30.7409			−0.00160453
$717$	1215.96	−	1215.96i	0.0633345	−	0.0633345i
$718$	42178.8			2.19234
$719$			9303.09i			0.482541i	0.970458	+	0.241270i	$0.0775640\pi$
$719$			9303.09i			0.482541i	−0.970458	+	0.241270i	$0.922436\pi$
$720$	18080.5	+	18080.5i	0.935860	+	0.935860i
$721$	−23700.5	+	23700.5i	−1.22421	+	1.22421i
$722$	−7117.90	−	7117.90i	−0.366899	−	0.366899i
$723$	−496.774	−	496.774i	−0.0255536	−	0.0255536i
$724$	−7800.79			−0.400434
$725$	−5336.34			−0.273361
$726$	−2045.04	−	115.109i	−0.104543	−	0.00588441i
$727$			14106.4i			0.719636i	0.933022	+	0.359818i	$0.117161\pi$
$727$			14106.4i			0.719636i	−0.933022	+	0.359818i	$0.882839\pi$
$728$	923.401	−	9191.29i	0.0470103	−	0.467929i
$729$	−18905.4			−0.960492
$730$	20106.4	+	20106.4i	1.01941	+	1.01941i
$731$	−15197.3			−0.768934
$732$	403.124			0.0203550
$733$	−15858.7	+	15858.7i	−0.799119	+	0.799119i	−0.982957	−	0.183837i	$-0.941148\pi$
$733$	−15858.7	+	15858.7i	−0.799119	+	0.799119i	0.183837	+	0.982957i	$0.441148\pi$
$734$	18312.5	−	18312.5i	0.920879	−	0.920879i
$735$	−159.653	+	159.653i	−0.00801209	+	0.00801209i
$736$	4287.69	+	4287.69i	0.214737	+	0.214737i
$737$	−35715.3	+	13630.6i	−1.78506	+	0.681263i
$738$		−	41848.3i		−	2.08734i
$739$	−4747.62	−	4747.62i	−0.236325	−	0.236325i	0.579002	−	0.815326i	$-0.303442\pi$
$739$	−4747.62	−	4747.62i	−0.236325	−	0.236325i	−0.815326	+	0.579002i	$0.803442\pi$
$740$			17119.0i			0.850415i
$741$	981.702	−	802.457i	0.0486690	−	0.0397827i
$742$	−24934.5			−1.23366
$743$	−18812.8	+	18812.8i	−0.928903	+	0.928903i	−0.997635	−	0.0687319i	$-0.978105\pi$
$743$	−18812.8	+	18812.8i	−0.928903	+	0.928903i	0.0687319	+	0.997635i	$0.478105\pi$
$744$			1314.76i			0.0647869i
$745$	10913.0			0.536674
$746$	14818.9	+	14818.9i	0.727290	+	0.727290i
$747$	−12248.0	+	12248.0i	−0.599909	+	0.599909i
$748$	−15460.0	−	6919.08i	−0.755713	−	0.338217i
$749$	−5880.05	+	5880.05i	−0.286852	+	0.286852i
$750$			1913.31i			0.0931525i
$751$		−	23226.0i		−	1.12853i	−0.825593	−	0.564266i	$-0.809159\pi$
$751$		−	23226.0i		−	1.12853i	0.825593	−	0.564266i	$-0.190841\pi$
$752$	1578.13	−	1578.13i	0.0765274	−	0.0765274i
$753$			1333.25i			0.0645235i
$754$	−25385.5	−	31055.9i	−1.22611	−	1.49998i
$755$		−	4146.31i		−	0.199867i
$756$	1660.90	−	1660.90i	0.0799027	−	0.0799027i
$757$	−12426.3			−0.596621			−0.298310	−	0.954469i	$-0.596423\pi$
$757$	−12426.3			−0.596621			−0.298310	+	0.954469i	$0.596423\pi$
$758$	11070.7			0.530481
$759$	415.730	+	186.059i	0.0198815	+	0.00889791i
$760$	−5508.43	−	5508.43i	−0.262910	−	0.262910i
$761$	−18465.2	−	18465.2i	−0.879584	−	0.879584i	0.113907	−	0.993491i	$-0.463663\pi$
$761$	−18465.2	−	18465.2i	−0.879584	−	0.879584i	−0.993491	+	0.113907i	$0.963663\pi$
$762$	1501.84	−	1501.84i	0.0713990	−	0.0713990i
$763$	42050.5			1.99519
$764$		−	23105.2i		−	1.09413i
$765$	20392.8	+	20392.8i	0.963794	+	0.963794i
$766$	14139.1			0.666925
$767$	23511.2	−	19218.3i	1.10683	−	0.904738i
$768$	−2262.24			−0.106291
$769$	22363.4	−	22363.4i	1.04869	−	1.04869i	0.0499389	−	0.998752i	$-0.484097\pi$
$769$	22363.4	−	22363.4i	1.04869	−	1.04869i	0.998752	−	0.0499389i	$-0.0159026\pi$
$770$	29657.4	−	11318.7i	1.38802	−	0.529735i
$771$			1345.29i			0.0628398i
$772$	−4891.10	+	4891.10i	−0.228024	+	0.228024i
$773$	17783.0	+	17783.0i	0.827437	+	0.827437i	0.987162	−	0.159725i	$-0.0510607\pi$
$773$	17783.0	+	17783.0i	0.827437	+	0.827437i	−0.159725	+	0.987162i	$0.551061\pi$
$774$	−11856.7	+	11856.7i	−0.550622	+	0.550622i
$775$	−4981.08	+	4981.08i	−0.230872	+	0.230872i
$776$		−	11334.8i		−	0.524351i
$777$	−2232.67			−0.103084
$778$	12823.4	+	12823.4i	0.590928	+	0.590928i
$779$			27426.7i			1.26144i
$780$	978.508	−	799.846i	0.0449182	−	0.0367168i
$781$	−10780.6	+	4114.37i	−0.493929	+	0.188507i
$782$	6723.52	+	6723.52i	0.307459	+	0.307459i
$783$			5350.38i			0.244198i
$784$			3446.84i			0.157017i
$785$	13151.3	+	13151.3i	0.597951	+	0.597951i
$786$	2776.42	+	2776.42i	0.125995	+	0.125995i
$787$	−3687.79	−	3687.79i	−0.167034	−	0.167034i	0.618641	−	0.785674i	$-0.287684\pi$
$787$	−3687.79	−	3687.79i	−0.167034	−	0.167034i	−0.785674	+	0.618641i	$0.787684\pi$
$788$	7273.49	+	7273.49i	0.328816	+	0.328816i
$789$		−	1372.47i		−	0.0619280i
$790$			4617.71i			0.207963i
$791$	−30852.0	−	30852.0i	−1.38682	−	1.38682i
$792$	9159.28	−	3495.61i	0.410936	−	0.156832i
$793$	851.340	−	8474.01i	0.0381235	−	0.379472i
$794$			28311.4i			1.26541i
$795$	1265.41	+	1265.41i	0.0564522	+	0.0564522i
$796$	17339.4			0.772085
$797$			20272.4i			0.900984i	0.892780	+	0.450492i	$0.148751\pi$
$797$			20272.4i			0.900984i	−0.892780	+	0.450492i	$0.851249\pi$
$798$	−1369.48	+	1369.48i	−0.0607506	+	0.0607506i
$799$	1779.96	−	1779.96i	0.0788116	−	0.0788116i
$800$	−3295.81	−	3295.81i	−0.145655	−	0.145655i
$801$	−7655.38	+	7655.38i	−0.337690	+	0.337690i
$802$		−	9283.53i		−	0.408744i
$803$	21911.0	−	8362.27i	0.962917	−	0.367495i
$804$	1643.85	−	1643.85i	0.0721069	−	0.0721069i
$805$	−7058.74			−0.309053
$806$	−52683.9	−	5292.87i	−2.30237	−	0.231307i
$807$	−2446.39			−0.106713
$808$	6299.73	+	6299.73i	0.274287	+	0.274287i
$809$			22863.7i			0.993629i	0.867857	+	0.496815i	$0.165497\pi$
$809$			22863.7i			0.993629i	−0.867857	+	0.496815i	$0.834503\pi$
$810$	31607.0			1.37106
$811$	11252.4	−	11252.4i	0.487206	−	0.487206i	−0.420218	−	0.907423i	$-0.638046\pi$
$811$	11252.4	−	11252.4i	0.487206	−	0.487206i	0.907423	+	0.420218i	$0.138046\pi$
$812$	17160.4	+	17160.4i	0.741642	+	0.741642i
$813$	−2092.35	−	2092.35i	−0.0902605	−	0.0902605i
$814$	32536.0	+	14561.4i	1.40097	+	0.627000i
$815$	−17356.9			−0.745995
$816$	−2934.51			−0.125893
$817$	7770.70	−	7770.70i	0.332757	−	0.332757i
$818$		−	37734.9i		−	1.61292i
$819$	−15650.9	−	19146.8i	−0.667747	−	0.816902i
$820$			27337.4i			1.16423i
$821$	12718.0	−	12718.0i	0.540635	−	0.540635i	−0.383080	−	0.923715i	$-0.625137\pi$
$821$	12718.0	−	12718.0i	0.540635	−	0.540635i	0.923715	+	0.383080i	$0.125137\pi$
$822$		−	611.963i		−	0.0259668i
$823$		−	4349.76i		−	0.184232i	−0.995748	−	0.0921161i	$-0.970637\pi$
$823$		−	4349.76i		−	0.184232i	0.995748	−	0.0921161i	$-0.0293631\pi$
$824$	12071.4	−	12071.4i	0.510347	−	0.510347i
$825$	−319.558	−	143.018i	−0.0134856	−	0.00603543i
$826$	−32798.1	+	32798.1i	−1.38159	+	1.38159i
$827$	8237.45	+	8237.45i	0.346365	+	0.346365i	0.858754	−	0.512389i	$-0.171239\pi$
$827$	8237.45	+	8237.45i	0.346365	+	0.346365i	−0.512389	+	0.858754i	$0.671239\pi$
$828$	4155.62			0.174418
$829$		−	23250.3i		−	0.974086i	−0.873378	−	0.487043i	$-0.838076\pi$
$829$		−	23250.3i		−	0.974086i	0.873378	−	0.487043i	$-0.161924\pi$
$830$	20199.3	−	20199.3i	0.844732	−	0.844732i
$831$	855.833			0.0357262
$832$	561.762	−	5591.63i	0.0234082	−	0.232999i
$833$			3887.65i			0.161704i
$834$	−520.096	−	520.096i	−0.0215941	−	0.0215941i
$835$			11377.4i			0.471534i
$836$	11442.9	−	4367.15i	0.473399	−	0.180671i
$837$	4994.19	+	4994.19i	0.206242	+	0.206242i
$838$	−304.901	+	304.901i	−0.0125688	+	0.0125688i
$839$	−3365.21	+	3365.21i	−0.138474	+	0.138474i	−0.772946	−	0.634472i	$-0.781218\pi$
$839$	−3365.21	+	3365.21i	−0.138474	+	0.138474i	0.634472	+	0.772946i	$0.281218\pi$
$840$	716.076	−	716.076i	0.0294131	−	0.0294131i
$841$	−30891.1			−1.26660
$842$	−26965.1			−1.10365
$843$	−1118.91	−	1118.91i	−0.0457147	−	0.0457147i
$844$	3861.89			0.157502
$845$	−14747.0	−	22258.2i	−0.600369	−	0.906162i
$846$		−	2777.41i		−	0.112872i
$847$	1471.36	−	26140.4i	0.0596889	−	1.06044i
$848$	27319.7			1.10632
$849$	−1568.77			−0.0634159
$850$	−5168.15	−	5168.15i	−0.208549	−	0.208549i
$851$	−5604.82	−	5604.82i	−0.225770	−	0.225770i
$852$	496.190	−	496.190i	0.0199521	−	0.0199521i
$853$	26115.9	+	26115.9i	1.04829	+	1.04829i	0.998773	+	0.0495176i	$0.0157684\pi$
$853$	26115.9	+	26115.9i	1.04829	+	1.04829i	0.0495176	+	0.998773i	$0.484232\pi$
$854$			13008.9i			0.521259i
$855$	−20854.6			−0.834165
$856$	2994.88	−	2994.88i	0.119583	−	0.119583i
$857$	−5545.60			−0.221043			−0.110522	−	0.993874i	$-0.535252\pi$
$857$	−5545.60			−0.221043			−0.110522	+	0.993874i	$0.535252\pi$
$858$	−687.852	−	2540.08i	−0.0273693	−	0.101069i
$859$	1801.80			0.0715677			0.0357838	−	0.999360i	$-0.488607\pi$
$859$	1801.80			0.0715677			0.0357838	+	0.999360i	$0.488607\pi$
$860$	7745.42	−	7745.42i	0.307112	−	0.307112i
$861$	−3565.37			−0.141124
$862$			6665.40i			0.263369i
$863$	16055.3	+	16055.3i	0.633288	+	0.633288i	0.948891	−	0.315603i	$-0.102207\pi$
$863$	16055.3	+	16055.3i	0.633288	+	0.633288i	−0.315603	+	0.948891i	$0.602207\pi$
$864$	−3304.48	+	3304.48i	−0.130117	+	0.130117i
$865$	15239.0	+	15239.0i	0.599007	+	0.599007i
$866$	25340.3	+	25340.3i	0.994340	+	0.994340i
$867$	−1232.53			−0.0482802
$868$	32036.0			1.25273
$869$	3476.34	+	1555.83i	0.135704	+	0.0607340i
$870$		−	4397.24i		−	0.171357i
$871$	−31083.5	−	38026.6i	−1.20921	−	1.47931i
$872$	−21417.6			−0.831755
$873$	−21456.5	−	21456.5i	−0.831834	−	0.831834i
$874$	−6875.77			−0.266106
$875$	−24456.7			−0.944899
$876$	−1008.48	+	1008.48i	−0.0388967	+	0.0388967i
$877$	25760.1	−	25760.1i	0.991856	−	0.991856i	−0.00811081	−	0.999967i	$-0.502582\pi$
$877$	25760.1	−	25760.1i	0.991856	−	0.991856i	0.999967	+	0.00811081i	$0.00258178\pi$
$878$	13844.0	−	13844.0i	0.532131	−	0.532131i
$879$	9.14673	+	9.14673i	0.000350980	+	0.000350980i
$880$	−32494.4	+	12401.4i	−1.24476	+	0.475057i
$881$			22288.3i			0.852342i	0.904643	+	0.426171i	$0.140138\pi$
$881$			22288.3i			0.852342i	−0.904643	+	0.426171i	$0.859862\pi$
$882$	3033.10	+	3033.10i	0.115794	+	0.115794i
$883$			17198.4i			0.655462i	0.944771	+	0.327731i	$0.106284\pi$
$883$			17198.4i			0.655462i	−0.944771	+	0.327731i	$0.893716\pi$
$884$	2175.27	−	21652.1i	0.0827627	−	0.823798i
$885$	3328.97			0.126443
$886$	−18231.9	+	18231.9i	−0.691324	+	0.691324i
$887$			44851.8i			1.69783i	0.528528	+	0.848916i	$0.322744\pi$
$887$			44851.8i			1.69783i	−0.528528	+	0.848916i	$0.677256\pi$
$888$	1137.17			0.0429738
$889$	19197.1	+	19197.1i	0.724241	+	0.724241i
$890$	12625.2	−	12625.2i	0.475502	−	0.475502i
$891$	10649.2	−	23794.6i	0.400406	−	0.894667i
$892$	6419.94	−	6419.94i	0.240981	−	0.240981i
$893$			1820.27i			0.0682116i
$894$			1381.88i			0.0516969i
$895$	−50.3443	+	50.3443i	−0.00188025	+	0.00188025i
$896$		−	23732.9i		−	0.884889i
$897$	−58.4945	+	582.239i	−0.00217734	+	0.0216727i
$898$		−	62058.0i		−	2.30613i
$899$	−51599.9	+	51599.9i	−1.91430	+	1.91430i
$900$	−3194.29			−0.118307
$901$	30813.6			1.13934
$902$	51957.0	+	23253.2i	1.91794	+	0.858368i
$903$	1010.16	+	1010.16i	0.0372271	+	0.0372271i
$904$	15713.8	+	15713.8i	0.578135	+	0.578135i
$905$	−12775.3	+	12775.3i	−0.469244	+	0.469244i
$906$	525.034			0.0192529
$907$		−	35264.3i		−	1.29100i	−0.763762	−	0.645498i	$-0.776650\pi$
$907$		−	35264.3i		−	1.29100i	0.763762	−	0.645498i	$-0.223350\pi$
$908$	3371.93	+	3371.93i	0.123239	+	0.123239i
$909$	23850.4			0.870261
$910$	25811.2	+	31576.7i	0.940256	+	1.15028i
$911$	−17.7508			−0.000645565			−0.000322783	−	1.00000i	$-0.500103\pi$
$911$	−17.7508			−0.000645565			−0.000322783		1.00000i	$0.500103\pi$
$912$	1500.48	−	1500.48i	0.0544801	−	0.0544801i
$913$	−8400.91	−	22012.3i	−0.304523	−	0.797918i
$914$			9617.72i			0.348059i
$915$	660.194	−	660.194i	0.0238528	−	0.0238528i
$916$	−8677.44	−	8677.44i	−0.313003	−	0.313003i
$917$	−35489.3	+	35489.3i	−1.27804	+	1.27804i
$918$	−5181.76	+	5181.76i	−0.186300	+	0.186300i
$919$			12016.6i			0.431328i	0.976468	+	0.215664i	$0.0691915\pi$
$919$			12016.6i			0.431328i	−0.976468	+	0.215664i	$0.930808\pi$
$920$	3595.22			0.128838
$921$	2110.17	+	2110.17i	0.0754966	+	0.0754966i
$922$			27995.7i			0.999988i
$923$	−9382.46	−	11478.2i	−0.334591	−	0.409328i
$924$	567.714	+	1487.54i	0.0202126	+	0.0529615i
$925$	4308.24	+	4308.24i	0.153140	+	0.153140i
$926$		−	21402.6i		−	0.759540i
$927$		−	45701.4i		−	1.61924i
$928$	−34141.9	−	34141.9i	−1.20772	−	1.20772i
$929$	14485.6	+	14485.6i	0.511579	+	0.511579i	0.915010	−	0.403431i	$-0.132182\pi$
$929$	14485.6	+	14485.6i	0.511579	+	0.511579i	−0.403431	+	0.915010i	$0.632182\pi$
$930$	−4104.50	−	4104.50i	−0.144722	−	0.144722i
$931$	−1987.84	−	1987.84i	−0.0699774	−	0.0699774i
$932$			16139.5i			0.567238i
$933$			360.885i			0.0126633i
$934$	−18876.9	−	18876.9i	−0.661318	−	0.661318i
$935$	−36650.1	+	13987.4i	−1.28191	+	0.489237i
$936$	7971.44	+	9752.02i	0.278370	+	0.340550i
$937$			23093.2i			0.805148i	0.915388	+	0.402574i	$0.131884\pi$
$937$			23093.2i			0.805148i	−0.915388	+	0.402574i	$0.868116\pi$
$938$	53047.3	+	53047.3i	1.84654	+	1.84654i
$939$	−651.406			−0.0226388
$940$			1814.35i			0.0629547i
$941$	15665.7	−	15665.7i	0.542706	−	0.542706i	−0.381616	−	0.924321i	$-0.624632\pi$
$941$	15665.7	−	15665.7i	0.542706	−	0.542706i	0.924321	+	0.381616i	$0.124632\pi$
$942$	−1665.31	+	1665.31i	−0.0575996	+	0.0575996i
$943$	−8950.36	−	8950.36i	−0.309082	−	0.309082i
$944$	35935.6	−	35935.6i	1.23899	−	1.23899i
$945$		−	5440.11i		−	0.187266i
$946$	−8132.53	−	21309.0i	−0.279505	−	0.732364i
$947$	−32337.2	+	32337.2i	−1.10963	+	1.10963i	−0.116430	+	0.993199i	$0.537145\pi$
$947$	−32337.2	+	32337.2i	−1.10963	+	1.10963i	−0.993199	+	0.116430i	$0.962855\pi$
$948$	−231.612			−0.00793504
$949$	19069.4	+	23329.0i	0.652286	+	0.797988i
$950$	5285.19			0.180499
$951$	237.190	+	237.190i	0.00808772	+	0.00808772i
$952$		−	17436.9i		−	0.593628i
$953$	41305.7			1.40401			0.702005	−	0.712172i	$-0.252288\pi$
$953$	41305.7			1.40401			0.702005	+	0.712172i	$0.252288\pi$
$954$	24040.4	−	24040.4i	0.815868	−	0.815868i
$955$	−37839.3	−	37839.3i	−1.28215	−	1.28215i
$956$	15090.7	+	15090.7i	0.510531	+	0.510531i
$957$	−3310.36	−	1481.54i	−0.111817	−	0.0500434i
$958$	−23279.7			−0.785106
$959$	7822.34			0.263396
$960$	435.633	−	435.633i	0.0146458	−	0.0146458i
$961$			66538.4i			2.23351i
$962$	−4577.92	+	45567.4i	−0.153428	+	1.52719i
$963$		−	11338.4i		−	0.379414i
$964$	6165.23	−	6165.23i	0.205984	−	0.205984i
$965$			16020.3i			0.534415i
$966$		−	893.825i		−	0.0297706i
$967$	13220.7	−	13220.7i	0.439657	−	0.439657i	−0.452240	−	0.891897i	$-0.649375\pi$
$967$	13220.7	−	13220.7i	0.439657	−	0.439657i	0.891897	+	0.452240i	$0.149375\pi$
$968$	−749.407	+	13314.1i	−0.0248831	+	0.442078i
$969$	1692.38	−	1692.38i	0.0561062	−	0.0561062i
$970$	35385.8	+	35385.8i	1.17131	+	1.17131i
$971$	3737.27			0.123517			0.0617583	−	0.998091i	$-0.480329\pi$
$971$	3737.27			0.123517			0.0617583	+	0.998091i	$0.480329\pi$
$972$			4809.37i			0.158704i
$973$	6648.06	−	6648.06i	0.219041	−	0.219041i
$974$	5687.32			0.187098
$975$	44.9629	−	447.548i	0.00147689	−	0.0147005i
$976$		−	14253.3i		−	0.467456i
$977$	−10188.1	−	10188.1i	−0.333621	−	0.333621i	0.520339	−	0.853960i	$-0.325806\pi$
$977$	−10188.1	−	10188.1i	−0.333621	−	0.333621i	−0.853960	+	0.520339i	$0.825806\pi$
$978$		−	2197.85i		−	0.0718604i
$979$	−5250.82	−	13758.3i	−0.171417	−	0.449150i
$980$	−1981.38	−	1981.38i	−0.0645844	−	0.0645844i
$981$	−40542.8	+	40542.8i	−1.31950	+	1.31950i
$982$	6175.07	−	6175.07i	0.200666	−	0.200666i
$983$	−639.701	+	639.701i	−0.0207561	+	0.0207561i	−0.717409	−	0.696653i	$-0.754672\pi$
$983$	−639.701	+	639.701i	−0.0207561	+	0.0207561i	0.696653	+	0.717409i	$0.254672\pi$
$984$	1815.95			0.0588315
$985$	23823.5			0.770639
$986$	−53537.8	−	53537.8i	−1.72920	−	1.72920i
$987$	−236.628			−0.00763116
$988$	9958.91	+	12183.4i	0.320683	+	0.392315i
$989$			5071.75i			0.163066i
$990$	−17681.2	+	39506.8i	−0.567621	+	1.26829i
$991$	31922.0			1.02325			0.511623	−	0.859210i	$-0.329044\pi$
$991$	31922.0			1.02325			0.511623	+	0.859210i	$0.329044\pi$
$992$	−63737.9			−2.04000
$993$	−1732.25	−	1732.25i	−0.0553587	−	0.0553587i
$994$	16012.2	+	16012.2i	0.510940	+	0.510940i
$995$	28396.7	−	28396.7i	0.904760	−	0.904760i
$996$	1013.14	+	1013.14i	0.0322316	+	0.0322316i
$997$		−	5231.74i		−	0.166189i	−0.996542	−	0.0830947i	$-0.973520\pi$
$997$		−	5231.74i		−	0.166189i	0.996542	−	0.0830947i	$-0.0264804\pi$
$998$	−70053.3			−2.22194
$999$	4319.58	−	4319.58i	0.136802	−	0.136802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.8	✓	80
11.10	odd	2	inner	143.4.g.a.21.33	yes	80
13.5	odd	4	inner	143.4.g.a.109.33	yes	80
143.109	even	4	inner	143.4.g.a.109.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.8	✓	80	1.1	even	1	trivial
143.4.g.a.21.33	yes	80	11.10	odd	2	inner
143.4.g.a.109.8	yes	80	143.109	even	4	inner
143.4.g.a.109.33	yes	80	13.5	odd	4	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57365 + 2.57365i) q^{2} -0.422811 q^{3} -5.24731i q^{4} +(-8.59350 - 8.59350i) q^{5} +(1.08817 - 1.08817i) q^{6} +(13.9093 + 13.9093i) q^{7} +(-7.08444 - 7.08444i) q^{8} -26.8212 q^{9} +O(q^{10})\)	\(q+(-2.57365 + 2.57365i) q^{2} -0.422811 q^{3} -5.24731i q^{4} +(-8.59350 - 8.59350i) q^{5} +(1.08817 - 1.08817i) q^{6} +(13.9093 + 13.9093i) q^{7} +(-7.08444 - 7.08444i) q^{8} -26.8212 q^{9} +44.2333 q^{10} +(14.9033 - 33.3000i) q^{11} +2.21862i q^{12} +(46.6374 + 4.68542i) q^{13} -71.5955 q^{14} +(3.63343 + 3.63343i) q^{15} +78.4442 q^{16} +88.4764 q^{17} +(69.0284 - 69.0284i) q^{18} +(-45.2400 + 45.2400i) q^{19} +(-45.0928 + 45.0928i) q^{20} +(-5.88103 - 5.88103i) q^{21} +(47.3465 + 124.058i) q^{22} -29.5271i q^{23} +(2.99538 + 2.99538i) q^{24} +22.6965i q^{25} +(-132.087 + 107.970i) q^{26} +22.7562 q^{27} +(72.9867 - 72.9867i) q^{28} +235.117i q^{29} -18.7023 q^{30} +(219.465 + 219.465i) q^{31} +(-145.212 + 145.212i) q^{32} +(-6.30130 + 14.0796i) q^{33} +(-227.707 + 227.707i) q^{34} -239.060i q^{35} +140.739i q^{36} +(189.820 - 189.820i) q^{37} -232.863i q^{38} +(-19.7188 - 1.98105i) q^{39} +121.760i q^{40} +(303.124 - 303.124i) q^{41} +30.2714 q^{42} -171.766 q^{43} +(-174.736 - 78.2025i) q^{44} +(230.488 + 230.488i) q^{45} +(75.9922 + 75.9922i) q^{46} +(20.1179 - 20.1179i) q^{47} -33.1671 q^{48} +43.9400i q^{49} +(-58.4128 - 58.4128i) q^{50} -37.4089 q^{51} +(24.5859 - 244.721i) q^{52} +348.269 q^{53} +(-58.5665 + 58.5665i) q^{54} +(-414.235 + 158.092i) q^{55} -197.080i q^{56} +(19.1280 - 19.1280i) q^{57} +(-605.108 - 605.108i) q^{58} +(458.103 - 458.103i) q^{59} +(19.0658 - 19.0658i) q^{60} -181.700i q^{61} -1129.65 q^{62} +(-373.066 - 373.066i) q^{63} -119.896i q^{64} +(-360.514 - 441.043i) q^{65} +(-20.0186 - 52.4533i) q^{66} +(-740.930 - 740.930i) q^{67} -464.264i q^{68} +12.4844i q^{69} +(615.256 + 615.256i) q^{70} +(-223.647 - 223.647i) q^{71} +(190.013 + 190.013i) q^{72} +(454.554 + 454.554i) q^{73} +977.058i q^{74} -9.59634i q^{75} +(237.388 + 237.388i) q^{76} +(670.477 - 255.886i) q^{77} +(55.8478 - 45.6508i) q^{78} +104.394i q^{79} +(-674.110 - 674.110i) q^{80} +714.552 q^{81} +1560.27i q^{82} +(456.654 - 456.654i) q^{83} +(-30.8596 + 30.8596i) q^{84} +(-760.322 - 760.322i) q^{85} +(442.065 - 442.065i) q^{86} -99.4102i q^{87} +(-341.494 + 130.330i) q^{88} +(285.422 - 285.422i) q^{89} -1186.39 q^{90} +(583.525 + 713.867i) q^{91} -154.938 q^{92} +(-92.7922 - 92.7922i) q^{93} +103.553i q^{94} +777.540 q^{95} +(61.3974 - 61.3974i) q^{96} +(799.981 + 799.981i) q^{97} +(-113.086 - 113.086i) q^{98} +(-399.726 + 893.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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