LMFDB - Embedded newform 84.4.i.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,4,Mod(25,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("84.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.i (of order $3$, 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:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$-3.22311 - 5.58259i$ of defining polynomial
Character	$\chi$	$=$	84.25
Dual form			84.4.i.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +(-6.22311 - 10.7787i) q^{5} +(15.3924 - 10.2992i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +(-6.22311 - 10.7787i) q^{5} +(15.3924 - 10.2992i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(25.5618 - 44.2743i) q^{11} +37.2311 q^{13} +37.3387 q^{15} +(-11.1076 + 19.2389i) q^{17} +(-27.1693 - 47.0587i) q^{19} +(3.66933 + 55.4395i) q^{21} +(-88.4622 - 153.221i) q^{23} +(-14.9542 + 25.9015i) q^{25} +27.0000 q^{27} +61.0916 q^{29} +(-159.962 + 277.063i) q^{31} +(76.6853 + 132.823i) q^{33} +(-206.801 - 101.818i) q^{35} +(157.540 + 272.867i) q^{37} +(-55.8467 + 96.7293i) q^{39} -206.032 q^{41} +339.661 q^{43} +(-56.0080 + 97.0087i) q^{45} +(-71.0320 - 123.031i) q^{47} +(130.855 - 317.058i) q^{49} +(-33.3227 - 57.7166i) q^{51} +(-155.008 + 268.482i) q^{53} -636.295 q^{55} +163.016 q^{57} +(140.825 - 243.916i) q^{59} +(271.924 + 470.987i) q^{61} +(-149.540 - 73.6260i) q^{63} +(-231.693 - 401.305i) q^{65} +(239.680 - 415.137i) q^{67} +530.773 q^{69} +1105.63 q^{71} +(-119.675 + 207.283i) q^{73} +(-44.8627 - 77.7044i) q^{75} +(-62.5298 - 944.754i) q^{77} +(-580.333 - 1005.17i) q^{79} +(-40.5000 + 70.1481i) q^{81} -2.93158 q^{83} +276.494 q^{85} +(-91.6373 + 158.721i) q^{87} +(639.371 + 1107.42i) q^{89} +(573.078 - 383.449i) q^{91} +(-479.887 - 831.188i) q^{93} +(-338.156 + 585.703i) q^{95} +79.0596 q^{97} -460.112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9	$ 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9} + 5 q^{11} + 10 q^{13} + 66 q^{15} - 100 q^{17} - 67 q^{19} - 27 q^{21} - 76 q^{23} + 93 q^{25} + 108 q^{27} + 550 q^{29} - 362 q^{31} + 15 q^{33} - 466 q^{35} + 5 q^{37} - 15 q^{39} - 324 q^{41} + 1442 q^{43} - 99 q^{45} + 216 q^{47} + 190 q^{49} - 300 q^{51} - 495 q^{53} - 1406 q^{55} + 402 q^{57} - 173 q^{59} + 532 q^{61} + 27 q^{63} - 510 q^{65} - 111 q^{67} + 456 q^{69} + 3200 q^{71} - 1215 q^{73} + 279 q^{75} - 653 q^{77} - 1460 q^{79} - 162 q^{81} - 2818 q^{83} + 328 q^{85} - 825 q^{87} + 1974 q^{89} + 1945 q^{91} - 1086 q^{93} - 658 q^{95} + 1122 q^{97} - 90 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9 + 5 * q^11 + 10 * q^13 + 66 * q^15 - 100 * q^17 - 67 * q^19 - 27 * q^21 - 76 * q^23 + 93 * q^25 + 108 * q^27 + 550 * q^29 - 362 * q^31 + 15 * q^33 - 466 * q^35 + 5 * q^37 - 15 * q^39 - 324 * q^41 + 1442 * q^43 - 99 * q^45 + 216 * q^47 + 190 * q^49 - 300 * q^51 - 495 * q^53 - 1406 * q^55 + 402 * q^57 - 173 * q^59 + 532 * q^61 + 27 * q^63 - 510 * q^65 - 111 * q^67 + 456 * q^69 + 3200 * q^71 - 1215 * q^73 + 279 * q^75 - 653 * q^77 - 1460 * q^79 - 162 * q^81 - 2818 * q^83 + 328 * q^85 - 825 * q^87 + 1974 * q^89 + 1945 * q^91 - 1086 * q^93 - 658 * q^95 + 1122 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			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
$5$	−6.22311	−	10.7787i	−0.556612	−	0.964080i	−0.997776	−	0.0666538i	$-0.978768\pi$
$5$	−6.22311	−	10.7787i	−0.556612	−	0.964080i	0.441164	−	0.897426i	$-0.354566\pi$
$6$		0			0
$7$	15.3924	−	10.2992i	0.831114	−	0.556102i
$7$	15.3924	−	10.2992i	0.831114	−	0.556102i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	25.5618	−	44.2743i	0.700651	−	1.21356i	−0.267587	−	0.963534i	$-0.586226\pi$
$11$	25.5618	−	44.2743i	0.700651	−	1.21356i	0.968238	−	0.250030i	$-0.0804405\pi$
$12$		0			0
$13$	37.2311			0.794312			0.397156	−	0.917751i	$-0.369997\pi$
$13$	37.2311			0.794312			0.397156	+	0.917751i	$0.369997\pi$
$14$		0			0
$15$	37.3387			0.642720
$16$		0			0
$17$	−11.1076	+	19.2389i	−0.158469	+	0.274477i	−0.934317	−	0.356444i	$-0.883989\pi$
$17$	−11.1076	+	19.2389i	−0.158469	+	0.274477i	0.775848	+	0.630920i	$0.217323\pi$
$18$		0			0
$19$	−27.1693	−	47.0587i	−0.328056	−	0.568210i	0.654070	−	0.756434i	$-0.273060\pi$
$19$	−27.1693	−	47.0587i	−0.328056	−	0.568210i	−0.982126	+	0.188224i	$0.939727\pi$
$20$		0			0
$21$	3.66933	+	55.4395i	0.0381292	+	0.576090i
$22$		0			0
$23$	−88.4622	−	153.221i	−0.801985	−	1.38908i	−0.918308	−	0.395867i	$-0.870444\pi$
$23$	−88.4622	−	153.221i	−0.801985	−	1.38908i	0.116323	−	0.993211i	$-0.462889\pi$
$24$		0			0
$25$	−14.9542	+	25.9015i	−0.119634	+	0.207212i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	61.0916			0.391187			0.195593	−	0.980685i	$-0.437337\pi$
$29$	61.0916			0.391187			0.195593	+	0.980685i	$0.437337\pi$
$30$		0			0
$31$	−159.962	+	277.063i	−0.926776	+	1.60522i	−0.138097	+	0.990419i	$0.544099\pi$
$31$	−159.962	+	277.063i	−0.926776	+	1.60522i	−0.788679	+	0.614805i	$0.789235\pi$
$32$		0			0
$33$	76.6853	+	132.823i	0.404521	+	0.700651i
$34$		0			0
$35$	−206.801	−	101.818i	−0.998735	−	0.491727i
$36$		0			0
$37$	157.540	+	272.867i	0.699984	+	1.21241i	0.968471	+	0.249125i	$0.0801430\pi$
$37$	157.540	+	272.867i	0.699984	+	1.21241i	−0.268487	+	0.963283i	$0.586524\pi$
$38$		0			0
$39$	−55.8467	+	96.7293i	−0.229298	+	0.397156i
$40$		0			0
$41$	−206.032			−0.784800			−0.392400	−	0.919795i	$-0.628355\pi$
$41$	−206.032			−0.784800			−0.392400	+	0.919795i	$0.628355\pi$
$42$		0			0
$43$	339.661			1.20460			0.602301	−	0.798269i	$-0.294251\pi$
$43$	339.661			1.20460			0.602301	+	0.798269i	$0.294251\pi$
$44$		0			0
$45$	−56.0080	+	97.0087i	−0.185537	+	0.321360i
$46$		0			0
$47$	−71.0320	−	123.031i	−0.220449	−	0.381828i	0.734496	−	0.678613i	$-0.237419\pi$
$47$	−71.0320	−	123.031i	−0.220449	−	0.381828i	−0.954944	+	0.296785i	$0.904085\pi$
$48$		0			0
$49$	130.855	−	317.058i	0.381500	−	0.924369i
$50$		0			0
$51$	−33.3227	−	57.7166i	−0.0914923	−	0.158469i
$52$		0			0
$53$	−155.008	+	268.482i	−0.401736	+	0.695826i	−0.993936	−	0.109965i	$-0.964926\pi$
$53$	−155.008	+	268.482i	−0.401736	+	0.695826i	0.592200	+	0.805791i	$0.298260\pi$
$54$		0			0
$55$	−636.295			−1.55996
$56$		0			0
$57$	163.016			0.378807
$58$		0			0
$59$	140.825	−	243.916i	0.310743	−	0.538223i	−0.667780	−	0.744358i	$-0.732755\pi$
$59$	140.825	−	243.916i	0.310743	−	0.538223i	0.978523	+	0.206136i	$0.0660888\pi$
$60$		0			0
$61$	271.924	+	470.987i	0.570760	+	0.988585i	0.996488	+	0.0837341i	$0.0266846\pi$
$61$	271.924	+	470.987i	0.570760	+	0.988585i	−0.425728	+	0.904851i	$0.639982\pi$
$62$		0			0
$63$	−149.540	−	73.6260i	−0.299052	−	0.147238i
$64$		0			0
$65$	−231.693	−	401.305i	−0.442123	−	0.765780i
$66$		0			0
$67$	239.680	−	415.137i	0.437038	−	0.756971i	−0.560422	−	0.828207i	$-0.689361\pi$
$67$	239.680	−	415.137i	0.437038	−	0.756971i	0.997459	+	0.0712360i	$0.0226943\pi$
$68$		0			0
$69$	530.773			0.926052
$70$		0			0
$71$	1105.63			1.84809			0.924046	−	0.382280i	$-0.124861\pi$
$71$	1105.63			1.84809			0.924046	+	0.382280i	$0.124861\pi$
$72$		0			0
$73$	−119.675	+	207.283i	−0.191876	+	0.332338i	−0.945872	−	0.324541i	$-0.894790\pi$
$73$	−119.675	+	207.283i	−0.191876	+	0.332338i	0.753996	+	0.656879i	$0.228124\pi$
$74$		0			0
$75$	−44.8627	−	77.7044i	−0.0690706	−	0.119634i
$76$		0			0
$77$	−62.5298	−	944.754i	−0.0925445	−	1.39824i
$78$		0			0
$79$	−580.333	−	1005.17i	−0.826488	−	1.43152i	−0.900777	−	0.434282i	$-0.857002\pi$
$79$	−580.333	−	1005.17i	−0.826488	−	1.43152i	0.0742888	−	0.997237i	$-0.476331\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−2.93158			−0.00387690			−0.00193845	−	0.999998i	$-0.500617\pi$
$83$	−2.93158			−0.00387690			−0.00193845	+	0.999998i	$0.500617\pi$
$84$		0			0
$85$	276.494			0.352824
$86$		0			0
$87$	−91.6373	+	158.721i	−0.112926	+	0.195593i
$88$		0			0
$89$	639.371	+	1107.42i	0.761496	+	1.31895i	0.942079	+	0.335390i	$0.108868\pi$
$89$	639.371	+	1107.42i	0.761496	+	1.31895i	−0.180583	+	0.983560i	$0.557798\pi$
$90$		0			0
$91$	573.078	−	383.449i	0.660163	−	0.441719i
$92$		0			0
$93$	−479.887	−	831.188i	−0.535075	−	0.926776i
$94$		0			0
$95$	−338.156	+	585.703i	−0.365200	+	0.632545i
$96$		0			0
$97$	79.0596			0.0827555			0.0413777	−	0.999144i	$-0.486825\pi$
$97$	79.0596			0.0827555			0.0413777	+	0.999144i	$0.486825\pi$
$98$		0			0
$99$	−460.112			−0.467101
$100$		0			0
$101$	−686.052	+	1188.28i	−0.675889	+	1.17067i	0.300319	+	0.953839i	$0.402907\pi$
$101$	−686.052	+	1188.28i	−0.675889	+	1.17067i	−0.976208	+	0.216835i	$0.930427\pi$
$102$		0			0
$103$	−129.265	−	223.894i	−0.123659	−	0.214184i	0.797549	−	0.603254i	$-0.206130\pi$
$103$	−129.265	−	223.894i	−0.123659	−	0.214184i	−0.921208	+	0.389070i	$0.872796\pi$
$104$		0			0
$105$	574.733	−	384.557i	0.534174	−	0.357418i
$106$		0			0
$107$	631.184	+	1093.24i	0.570270	+	0.987736i	0.996538	+	0.0831393i	$0.0264946\pi$
$107$	631.184	+	1093.24i	0.570270	+	0.987736i	−0.426268	+	0.904597i	$0.640172\pi$
$108$		0			0
$109$	−138.416	+	239.744i	−0.121632	+	0.210673i	−0.920411	−	0.390951i	$-0.872146\pi$
$109$	−138.416	+	239.744i	−0.121632	+	0.210673i	0.798779	+	0.601624i	$0.205479\pi$
$110$		0			0
$111$	−945.240			−0.808272
$112$		0			0
$113$	52.9156			0.0440520			0.0220260	−	0.999757i	$-0.492988\pi$
$113$	52.9156			0.0440520			0.0220260	+	0.999757i	$0.492988\pi$
$114$		0			0
$115$	−1101.02	+	1907.02i	−0.892789	+	1.54636i
$116$		0			0
$117$	−167.540	−	290.188i	−0.132385	−	0.229298i
$118$		0			0
$119$	27.1715	+	410.531i	0.0209312	+	0.316247i
$120$		0			0
$121$	−641.309	−	1110.78i	−0.481825	−	0.834545i
$122$		0			0
$123$	309.048	−	535.287i	0.226552	−	0.392400i
$124$		0			0
$125$	−1183.53			−0.846866
$126$		0			0
$127$	443.700			0.310016			0.155008	−	0.987913i	$-0.450460\pi$
$127$	443.700			0.310016			0.155008	+	0.987913i	$0.450460\pi$
$128$		0			0
$129$	−509.492	+	882.466i	−0.347739	+	0.602301i
$130$		0			0
$131$	1076.74	+	1864.97i	0.718133	+	1.24384i	0.961739	+	0.273968i	$0.0883363\pi$
$131$	1076.74	+	1864.97i	0.718133	+	1.24384i	−0.243606	+	0.969874i	$0.578330\pi$
$132$		0			0
$133$	−902.867	−	444.527i	−0.588635	−	0.289815i
$134$		0			0
$135$	−168.024	−	291.026i	−0.107120	−	0.185537i
$136$		0			0
$137$	−131.554	+	227.858i	−0.0820394	+	0.142096i	−0.904126	−	0.427266i	$-0.859477\pi$
$137$	−131.554	+	227.858i	−0.0820394	+	0.142096i	0.822086	+	0.569363i	$0.192810\pi$
$138$		0			0
$139$	1165.77			0.711360			0.355680	−	0.934608i	$-0.384249\pi$
$139$	1165.77			0.711360			0.355680	+	0.934608i	$0.384249\pi$
$140$		0			0
$141$	426.192			0.254552
$142$		0			0
$143$	951.693	−	1648.38i	0.556536	−	0.963948i
$144$		0			0
$145$	−380.180	−	658.490i	−0.217739	−	0.377135i
$146$		0			0
$147$	627.460	+	815.558i	0.352055	+	0.457592i
$148$		0			0
$149$	882.597	+	1528.70i	0.485270	+	0.840512i	0.999857	−	0.0169263i	$-0.00538807\pi$
$149$	882.597	+	1528.70i	0.485270	+	0.840512i	−0.514587	+	0.857438i	$0.672055\pi$
$150$		0			0
$151$	−1346.16	+	2331.61i	−0.725488	+	1.25658i	0.233285	+	0.972408i	$0.425052\pi$
$151$	−1346.16	+	2331.61i	−0.725488	+	1.25658i	−0.958773	+	0.284173i	$0.908281\pi$
$152$		0			0
$153$	199.936			0.105646
$154$		0			0
$155$	3981.85			2.06342
$156$		0			0
$157$	970.691	−	1681.29i	0.493437	−	0.854657i	−0.506535	−	0.862220i	$-0.669074\pi$
$157$	970.691	−	1681.29i	0.493437	−	0.854657i	0.999971	+	0.00756226i	$0.00240716\pi$
$158$		0			0
$159$	−465.024	−	805.445i	−0.231942	−	0.401736i
$160$		0			0
$161$	−2939.70	−	1447.36i	−1.43901	−	0.708497i
$162$		0			0
$163$	−1051.42	−	1821.11i	−0.505236	−	0.875094i	−0.999982	−	0.00605658i	$-0.998072\pi$
$163$	−1051.42	−	1821.11i	−0.505236	−	0.875094i	0.494746	−	0.869038i	$-0.335261\pi$
$164$		0			0
$165$	954.443	−	1653.14i	0.450323	−	0.779982i
$166$		0			0
$167$	−2344.22			−1.08623			−0.543116	−	0.839658i	$-0.682756\pi$
$167$	−2344.22			−1.08623			−0.543116	+	0.839658i	$0.682756\pi$
$168$		0			0
$169$	−810.844			−0.369069
$170$		0			0
$171$	−244.524	+	423.528i	−0.109352	+	0.189403i
$172$		0			0
$173$	−1735.32	−	3005.67i	−0.762626	−	1.32091i	−0.941493	−	0.337033i	$-0.890576\pi$
$173$	−1735.32	−	3005.67i	−0.762626	−	1.32091i	0.178867	−	0.983873i	$-0.442757\pi$
$174$		0			0
$175$	36.5813	+	552.703i	0.0158017	+	0.238745i
$176$		0			0
$177$	422.475	+	731.748i	0.179408	+	0.310743i
$178$		0			0
$179$	477.885	−	827.722i	0.199547	−	0.345625i	−0.748835	−	0.662757i	$-0.769386\pi$
$179$	477.885	−	827.722i	0.199547	−	0.345625i	0.948381	+	0.317132i	$0.102720\pi$
$180$		0			0
$181$	4220.26			1.73309			0.866546	−	0.499098i	$-0.166335\pi$
$181$	4220.26			1.73309			0.866546	+	0.499098i	$0.166335\pi$
$182$		0			0
$183$	−1631.55			−0.659057
$184$		0			0
$185$	1960.78	−	3396.17i	0.779239	−	1.34968i
$186$		0			0
$187$	567.858	+	983.558i	0.222063	+	0.384625i
$188$		0			0
$189$	415.596	−	278.077i	0.159948	−	0.107022i
$190$		0			0
$191$	1759.02	+	3046.71i	0.666377	+	1.15420i	0.978910	+	0.204291i	$0.0654890\pi$
$191$	1759.02	+	3046.71i	0.666377	+	1.15420i	−0.312534	+	0.949907i	$0.601178\pi$
$192$		0			0
$193$	2508.84	−	4345.43i	0.935699	−	1.62068i	0.162317	−	0.986739i	$-0.448103\pi$
$193$	2508.84	−	4345.43i	0.935699	−	1.62068i	0.773382	−	0.633940i	$-0.218563\pi$
$194$		0			0
$195$	1390.16			0.510520
$196$		0			0
$197$	−2838.14			−1.02644			−0.513221	−	0.858257i	$-0.671548\pi$
$197$	−2838.14			−1.02644			−0.513221	+	0.858257i	$0.671548\pi$
$198$		0			0
$199$	−177.451	+	307.354i	−0.0632118	+	0.109486i	−0.895899	−	0.444257i	$-0.853468\pi$
$199$	−177.451	+	307.354i	−0.0632118	+	0.109486i	0.832688	+	0.553743i	$0.186801\pi$
$200$		0			0
$201$	719.039	+	1245.41i	0.252324	+	0.437038i
$202$		0			0
$203$	940.348	−	629.192i	0.325121	−	0.217540i
$204$		0			0
$205$	1282.16	+	2220.77i	0.436829	+	0.756610i
$206$		0			0
$207$	−796.160	+	1378.99i	−0.267328	+	0.463026i
$208$		0			0
$209$	−2777.99			−0.919413
$210$		0			0
$211$	752.672			0.245574			0.122787	−	0.992433i	$-0.460817\pi$
$211$	752.672			0.245574			0.122787	+	0.992433i	$0.460817\pi$
$212$		0			0
$213$	−1658.45	+	2872.52i	−0.533498	+	0.924046i
$214$		0			0
$215$	−2113.75	−	3661.12i	−0.670496	−	1.16133i
$216$		0			0
$217$	391.303	+	5912.15i	0.122412	+	1.84951i
$218$		0			0
$219$	−359.025	−	621.850i	−0.110779	−	0.191876i
$220$		0			0
$221$	−413.547	+	716.284i	−0.125874	+	0.218020i
$222$		0			0
$223$	−3077.75			−0.924221			−0.462111	−	0.886822i	$-0.652908\pi$
$223$	−3077.75			−0.924221			−0.462111	+	0.886822i	$0.652908\pi$
$224$		0			0
$225$	269.176			0.0797558
$226$		0			0
$227$	3108.72	−	5384.46i	0.908955	−	1.57436i	0.0934368	−	0.995625i	$-0.470215\pi$
$227$	3108.72	−	5384.46i	0.908955	−	1.57436i	0.815518	−	0.578731i	$-0.196452\pi$
$228$		0			0
$229$	−251.627	−	435.831i	−0.0726113	−	0.125766i	0.827434	−	0.561563i	$-0.189800\pi$
$229$	−251.627	−	435.831i	−0.0726113	−	0.125766i	−0.900045	+	0.435797i	$0.856467\pi$
$230$		0			0
$231$	2548.34	+	1254.67i	0.725837	+	0.357366i
$232$		0			0
$233$	134.170	+	232.389i	0.0377243	+	0.0653404i	0.884271	−	0.466974i	$-0.154656\pi$
$233$	134.170	+	232.389i	0.0377243	+	0.0653404i	−0.846547	+	0.532314i	$0.821322\pi$
$234$		0			0
$235$	−884.080	+	1531.27i	−0.245409	+	0.425060i
$236$		0			0
$237$	3482.00			0.954346
$238$		0			0
$239$	−5189.77			−1.40459			−0.702297	−	0.711884i	$-0.747842\pi$
$239$	−5189.77			−1.40459			−0.702297	+	0.711884i	$0.747842\pi$
$240$		0			0
$241$	−3085.47	+	5344.19i	−0.824699	+	1.42842i	0.0774495	+	0.996996i	$0.475322\pi$
$241$	−3085.47	+	5344.19i	−0.824699	+	1.42842i	−0.902149	+	0.431425i	$0.858011\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−4231.82	+	562.641i	−1.10351	+	0.146718i
$246$		0			0
$247$	−1011.54	−	1752.05i	−0.260579	−	0.451336i
$248$		0			0
$249$	4.39737	−	7.61646i	0.00111916	−	0.00193845i
$250$		0			0
$251$	1891.91			0.475763			0.237882	−	0.971294i	$-0.423547\pi$
$251$	1891.91			0.475763			0.237882	+	0.971294i	$0.423547\pi$
$252$		0			0
$253$	−9045.01			−2.24765
$254$		0			0
$255$	−414.741	+	718.353i	−0.101851	+	0.176412i
$256$		0			0
$257$	3269.97	+	5663.75i	0.793676	+	1.37469i	0.923676	+	0.383174i	$0.125169\pi$
$257$	3269.97	+	5663.75i	0.793676	+	1.37469i	−0.130000	+	0.991514i	$0.541498\pi$
$258$		0			0
$259$	5235.23	+	2577.56i	1.25599	+	0.618386i
$260$		0			0
$261$	−274.912	−	476.162i	−0.0651978	−	0.112926i
$262$		0			0
$263$	−2687.95	+	4655.67i	−0.630214	+	1.09156i	0.357294	+	0.933992i	$0.383699\pi$
$263$	−2687.95	+	4655.67i	−0.630214	+	1.09156i	−0.987508	+	0.157570i	$0.949634\pi$
$264$		0			0
$265$	3858.53			0.894443
$266$		0			0
$267$	−3836.22			−0.879300
$268$		0			0
$269$	1619.44	−	2804.95i	0.367060	−	0.635766i	−0.622045	−	0.782982i	$-0.713698\pi$
$269$	1619.44	−	2804.95i	0.367060	−	0.635766i	0.989104	+	0.147216i	$0.0470311\pi$
$270$		0			0
$271$	−678.729	−	1175.59i	−0.152140	−	0.263514i	0.779874	−	0.625936i	$-0.215283\pi$
$271$	−678.729	−	1175.59i	−0.152140	−	0.263514i	−0.932014	+	0.362423i	$0.881950\pi$
$272$		0			0
$273$	136.613	+	2064.07i	0.0302865	+	0.457595i
$274$		0			0
$275$	764.513	+	1324.18i	0.167643	+	0.290366i
$276$		0			0
$277$	1280.82	−	2218.44i	0.277823	−	0.481203i	−0.693021	−	0.720918i	$-0.743721\pi$
$277$	1280.82	−	2218.44i	0.277823	−	0.481203i	0.970843	+	0.239715i	$0.0770539\pi$
$278$		0			0
$279$	2879.32			0.617851
$280$		0			0
$281$	1786.17			0.379196			0.189598	−	0.981862i	$-0.439282\pi$
$281$	1786.17			0.379196			0.189598	+	0.981862i	$0.439282\pi$
$282$		0			0
$283$	3694.14	−	6398.44i	0.775950	−	1.34398i	−0.158309	−	0.987390i	$-0.550604\pi$
$283$	3694.14	−	6398.44i	0.775950	−	1.34398i	0.934259	−	0.356595i	$-0.116063\pi$
$284$		0			0
$285$	−1014.47	−	1757.11i	−0.210848	−	0.365200i
$286$		0			0
$287$	−3171.34	+	2121.96i	−0.652258	+	0.436429i
$288$		0			0
$289$	2209.74	+	3827.39i	0.449775	+	0.779033i
$290$		0			0
$291$	−118.589	+	205.403i	−0.0238895	+	0.0413777i
$292$		0			0
$293$	492.981			0.0982945			0.0491472	−	0.998792i	$-0.484350\pi$
$293$	492.981			0.0982945			0.0491472	+	0.998792i	$0.484350\pi$
$294$		0			0
$295$	−3505.48			−0.691853
$296$		0			0
$297$	690.168	−	1195.41i	0.134840	−	0.233550i
$298$		0			0
$299$	−3293.55	−	5704.59i	−0.637026	−	1.10336i
$300$		0			0
$301$	5228.22	−	3498.23i	1.00116	−	0.669882i
$302$		0			0
$303$	−2058.16	−	3564.83i	−0.390225	−	0.675889i
$304$		0			0
$305$	3384.43	−	5862.01i	0.635384	−	1.10052i
$306$		0			0
$307$	−988.810			−0.183825			−0.0919126	−	0.995767i	$-0.529298\pi$
$307$	−988.810			−0.183825			−0.0919126	+	0.995767i	$0.529298\pi$
$308$		0			0
$309$	775.592			0.142789
$310$		0			0
$311$	4798.28	−	8310.87i	0.874874	−	1.51533i	0.0179763	−	0.999838i	$-0.494278\pi$
$311$	4798.28	−	8310.87i	0.874874	−	1.51533i	0.856897	−	0.515487i	$-0.172389\pi$
$312$		0			0
$313$	−482.856	−	836.332i	−0.0871970	−	0.151030i	0.819128	−	0.573610i	$-0.194458\pi$
$313$	−482.856	−	836.332i	−0.0871970	−	0.151030i	−0.906325	+	0.422581i	$0.861124\pi$
$314$		0			0
$315$	137.008	+	2070.04i	0.0245064	+	0.370265i
$316$		0			0
$317$	4492.99	+	7782.08i	0.796061	+	1.37882i	0.922163	+	0.386801i	$0.126420\pi$
$317$	4492.99	+	7782.08i	0.796061	+	1.37882i	−0.126103	+	0.992017i	$0.540247\pi$
$318$		0			0
$319$	1561.61	−	2704.79i	0.274086	−	0.474730i
$320$		0			0
$321$	−3787.10			−0.658491
$322$		0			0
$323$	1207.14			0.207947
$324$		0			0
$325$	−556.762	+	964.340i	−0.0950265	+	0.164591i
$326$		0			0
$327$	−415.249	−	719.233i	−0.0702243	−	0.121632i
$328$		0			0
$329$	−2360.47	−	1162.18i	−0.395553	−	0.194751i
$330$		0			0
$331$	1903.65	+	3297.22i	0.316115	+	0.547527i	0.979674	−	0.200597i	$-0.0642882\pi$
$331$	1903.65	+	3297.22i	0.316115	+	0.547527i	−0.663559	+	0.748124i	$0.730955\pi$
$332$		0			0
$333$	1417.86	−	2455.81i	0.233328	−	0.404136i
$334$		0			0
$335$	−5966.21			−0.973041
$336$		0			0
$337$	−1649.82			−0.266681			−0.133340	−	0.991070i	$-0.542570\pi$
$337$	−1649.82			−0.266681			−0.133340	+	0.991070i	$0.542570\pi$
$338$		0			0
$339$	−79.3734	+	137.479i	−0.0127167	+	0.0220260i
$340$		0			0
$341$	8177.84	+	14164.4i	1.29869	+	2.24940i
$342$		0			0
$343$	−1251.26	−	6228.00i	−0.196973	−	0.980409i
$344$		0			0
$345$	−3303.06	−	5721.07i	−0.515452	−	0.892789i
$346$		0			0
$347$	−2855.00	+	4945.00i	−0.441684	+	0.765019i	−0.997815	−	0.0660760i	$-0.978952\pi$
$347$	−2855.00	+	4945.00i	−0.441684	+	0.765019i	0.556131	+	0.831095i	$0.312285\pi$
$348$		0			0
$349$	−447.244			−0.0685973			−0.0342986	−	0.999412i	$-0.510920\pi$
$349$	−447.244			−0.0685973			−0.0342986	+	0.999412i	$0.510920\pi$
$350$		0			0
$351$	1005.24			0.152865
$352$		0			0
$353$	5322.85	−	9219.45i	0.802569	−	1.39009i	−0.115352	−	0.993325i	$-0.536799\pi$
$353$	5322.85	−	9219.45i	0.802569	−	1.39009i	0.917920	−	0.396765i	$-0.129867\pi$
$354$		0			0
$355$	−6880.48	−	11917.3i	−1.02867	−	1.78171i
$356$		0			0
$357$	−1107.35	−	545.203i	−0.164166	−	0.0808270i
$358$		0			0
$359$	4548.73	+	7878.64i	0.668727	+	1.15827i	0.978260	+	0.207381i	$0.0664939\pi$
$359$	4548.73	+	7878.64i	0.668727	+	1.15827i	−0.309533	+	0.950889i	$0.600173\pi$
$360$		0			0
$361$	1953.15	−	3382.96i	0.284758	−	0.493215i
$362$		0			0
$363$	3847.85			0.556363
$364$		0			0
$365$	2979.01			0.427201
$366$		0			0
$367$	−2643.91	+	4579.39i	−0.376052	+	0.651341i	−0.990484	−	0.137629i	$-0.956052\pi$
$367$	−2643.91	+	4579.39i	−0.376052	+	0.651341i	0.614432	+	0.788970i	$0.289385\pi$
$368$		0			0
$369$	927.144	+	1605.86i	0.130800	+	0.226552i
$370$		0			0
$371$	379.184	+	5729.04i	0.0530627	+	0.801717i
$372$		0			0
$373$	−2947.51	−	5105.23i	−0.409159	−	0.708683i	0.585637	−	0.810573i	$-0.300844\pi$
$373$	−2947.51	−	5105.23i	−0.409159	−	0.708683i	−0.994796	+	0.101890i	$0.967511\pi$
$374$		0			0
$375$	1775.30	−	3074.90i	0.244469	−	0.423433i
$376$		0			0
$377$	2274.51			0.310724
$378$		0			0
$379$	3842.41			0.520769			0.260384	−	0.965505i	$-0.416151\pi$
$379$	3842.41			0.520769			0.260384	+	0.965505i	$0.416151\pi$
$380$		0			0
$381$	−665.551	+	1152.77i	−0.0894940	+	0.155008i
$382$		0			0
$383$	−2506.87	−	4342.02i	−0.334452	−	0.579287i	0.648928	−	0.760850i	$-0.275218\pi$
$383$	−2506.87	−	4342.02i	−0.334452	−	0.579287i	−0.983379	+	0.181563i	$0.941884\pi$
$384$		0			0
$385$	−9794.14	+	6553.30i	−1.29651	+	0.867499i
$386$		0			0
$387$	−1528.48	−	2647.40i	−0.200767	−	0.347739i
$388$		0			0
$389$	−5591.24	+	9684.31i	−0.728758	+	1.26225i	0.228650	+	0.973509i	$0.426569\pi$
$389$	−5591.24	+	9684.31i	−0.728758	+	1.26225i	−0.957408	+	0.288738i	$0.906765\pi$
$390$		0			0
$391$	3930.40			0.508360
$392$		0			0
$393$	−6460.45			−0.829228
$394$		0			0
$395$	−7222.95	+	12510.5i	−0.920066	+	1.59360i
$396$		0			0
$397$	1703.40	+	2950.37i	0.215343	+	0.372985i	0.953379	−	0.301777i	$-0.0975798\pi$
$397$	1703.40	+	2950.37i	0.215343	+	0.372985i	−0.738036	+	0.674762i	$0.764246\pi$
$398$		0			0
$399$	2509.21	−	1678.93i	0.314832	−	0.210655i
$400$		0			0
$401$	−41.5201	−	71.9149i	−0.00517061	−	0.00895575i	0.863429	−	0.504471i	$-0.168313\pi$
$401$	−41.5201	−	71.9149i	−0.00517061	−	0.00895575i	−0.868599	+	0.495515i	$0.834979\pi$
$402$		0			0
$403$	−5955.57	+	10315.4i	−0.736149	+	1.27505i
$404$		0			0
$405$	1008.14			0.123692
$406$		0			0
$407$	16108.0			1.96178
$408$		0			0
$409$	−1228.10	+	2127.13i	−0.148473	+	0.257164i	−0.930663	−	0.365876i	$-0.880769\pi$
$409$	−1228.10	+	2127.13i	−0.148473	+	0.257164i	0.782190	+	0.623040i	$0.214103\pi$
$410$		0			0
$411$	−394.661	−	683.573i	−0.0473655	−	0.0820394i
$412$		0			0
$413$	−344.489	−	5204.84i	−0.0410440	−	0.620129i
$414$		0			0
$415$	18.2435	+	31.5987i	0.00215793	+	0.00373764i
$416$		0			0
$417$	−1748.65	+	3028.75i	−0.205352	+	0.355680i
$418$		0			0
$419$	−3437.96			−0.400848			−0.200424	−	0.979709i	$-0.564232\pi$
$419$	−3437.96			−0.400848			−0.200424	+	0.979709i	$0.564232\pi$
$420$		0			0
$421$	−5347.62			−0.619067			−0.309533	−	0.950889i	$-0.600173\pi$
$421$	−5347.62			−0.619067			−0.309533	+	0.950889i	$0.600173\pi$
$422$		0			0
$423$	−639.288	+	1107.28i	−0.0734828	+	0.127276i
$424$		0			0
$425$	−332.210	−	575.404i	−0.0379166	−	0.0656734i
$426$		0			0
$427$	9036.35	+	4449.05i	1.02412	+	0.504226i
$428$		0			0
$429$	2855.08	+	4945.14i	0.321316	+	0.556536i
$430$		0			0
$431$	−425.821	+	737.544i	−0.0475895	+	0.0824275i	−0.888839	−	0.458220i	$-0.848487\pi$
$431$	−425.821	+	737.544i	−0.0475895	+	0.0824275i	0.841249	+	0.540647i	$0.181821\pi$
$432$		0			0
$433$	−3433.42			−0.381061			−0.190531	−	0.981681i	$-0.561021\pi$
$433$	−3433.42			−0.381061			−0.190531	+	0.981681i	$0.561021\pi$
$434$		0			0
$435$	2281.08			0.251424
$436$		0			0
$437$	−4806.92	+	8325.83i	−0.526192	+	0.911392i
$438$		0			0
$439$	4869.20	+	8433.70i	0.529371	+	0.916898i	0.999413	+	0.0342540i	$0.0109055\pi$
$439$	4869.20	+	8433.70i	0.529371	+	0.916898i	−0.470042	+	0.882644i	$0.655761\pi$
$440$		0			0
$441$	−3060.07	+	406.852i	−0.330426	+	0.0439317i
$442$		0			0
$443$	−4967.48	−	8603.93i	−0.532759	−	0.922765i	−0.999268	−	0.0382491i	$-0.987822\pi$
$443$	−4967.48	−	8603.93i	−0.532759	−	0.922765i	0.466509	−	0.884516i	$-0.345511\pi$
$444$		0			0
$445$	7957.75	−	13783.2i	0.847716	−	1.46829i
$446$		0			0
$447$	−5295.58			−0.560341
$448$		0			0
$449$	−7557.33			−0.794327			−0.397163	−	0.917748i	$-0.630005\pi$
$449$	−7557.33			−0.794327			−0.397163	+	0.917748i	$0.630005\pi$
$450$		0			0
$451$	−5266.54	+	9121.92i	−0.549871	+	0.952405i
$452$		0			0
$453$	−4038.47	−	6994.83i	−0.418861	−	0.725488i
$454$		0			0
$455$	−7699.43	−	3790.81i	−0.793307	−	0.390585i
$456$		0			0
$457$	−7005.92	−	12134.6i	−0.717118	−	1.24209i	−0.962137	−	0.272567i	$-0.912127\pi$
$457$	−7005.92	−	12134.6i	−0.717118	−	1.24209i	0.245018	−	0.969518i	$-0.421206\pi$
$458$		0			0
$459$	−299.904	+	519.449i	−0.0304974	+	0.0528231i
$460$		0			0
$461$	−1669.61			−0.168680			−0.0843399	−	0.996437i	$-0.526878\pi$
$461$	−1669.61			−0.168680			−0.0843399	+	0.996437i	$0.526878\pi$
$462$		0			0
$463$	14785.4			1.48409			0.742046	−	0.670349i	$-0.233856\pi$
$463$	14785.4			1.48409			0.742046	+	0.670349i	$0.233856\pi$
$464$		0			0
$465$	−5972.78	+	10345.2i	−0.595658	+	1.03171i
$466$		0			0
$467$	−2301.58	−	3986.46i	−0.228061	−	0.395014i	0.729172	−	0.684330i	$-0.239905\pi$
$467$	−2301.58	−	3986.46i	−0.228061	−	0.395014i	−0.957233	+	0.289317i	$0.906572\pi$
$468$		0			0
$469$	−586.309	−	8858.47i	−0.0577255	−	0.872167i
$470$		0			0
$471$	2912.07	+	5043.86i	0.284886	+	0.493437i
$472$		0			0
$473$	8682.35	−	15038.3i	0.844006	−	1.46186i
$474$		0			0
$475$	1625.18			0.156987
$476$		0			0
$477$	2790.14			0.267824
$478$		0			0
$479$	−1738.68	+	3011.47i	−0.165850	+	0.287261i	−0.936957	−	0.349445i	$-0.886370\pi$
$479$	−1738.68	+	3011.47i	−0.165850	+	0.287261i	0.771107	+	0.636706i	$0.219703\pi$
$480$		0			0
$481$	5865.39	+	10159.2i	0.556006	+	0.963030i
$482$		0			0
$483$	8169.90	−	5466.52i	0.769655	−	0.514980i
$484$		0			0
$485$	−491.996	−	852.163i	−0.0460627	−	0.0797829i
$486$		0			0
$487$	−2172.08	+	3762.16i	−0.202108	+	0.350061i	−0.949207	−	0.314651i	$-0.898112\pi$
$487$	−2172.08	+	3762.16i	−0.202108	+	0.350061i	0.747100	+	0.664712i	$0.231446\pi$
$488$		0			0
$489$	6308.51			0.583396
$490$		0			0
$491$	4982.89			0.457993			0.228997	−	0.973427i	$-0.426456\pi$
$491$	4982.89			0.457993			0.228997	+	0.973427i	$0.426456\pi$
$492$		0			0
$493$	−678.578	+	1175.33i	−0.0619911	+	0.107372i
$494$		0			0
$495$	2863.33	+	4959.43i	0.259994	+	0.450323i
$496$		0			0
$497$	17018.4	−	11387.1i	1.53598	−	1.02773i
$498$		0			0
$499$	−7663.08	−	13272.8i	−0.687468	−	1.19073i	−0.972654	−	0.232257i	$-0.925389\pi$
$499$	−7663.08	−	13272.8i	−0.687468	−	1.19073i	0.285187	−	0.958472i	$-0.407944\pi$
$500$		0			0
$501$	3516.32	−	6090.45i	0.313568	−	0.543116i
$502$		0			0
$503$	−1516.04			−0.134387			−0.0671936	−	0.997740i	$-0.521405\pi$
$503$	−1516.04			−0.134387			−0.0671936	+	0.997740i	$0.521405\pi$
$504$		0			0
$505$	17077.5			1.50483
$506$		0			0
$507$	1216.27	−	2106.64i	0.106541	−	0.184534i
$508$		0			0
$509$	−1326.82	−	2298.12i	−0.115541	−	0.200122i	0.802455	−	0.596713i	$-0.203527\pi$
$509$	−1326.82	−	2298.12i	−0.115541	−	0.200122i	−0.917996	+	0.396590i	$0.870193\pi$
$510$		0			0
$511$	292.752	+	4423.15i	0.0253436	+	0.382913i
$512$		0			0
$513$	−733.572	−	1270.58i	−0.0631345	−	0.109352i
$514$		0			0
$515$	−1608.86	+	2786.64i	−0.137660	+	0.238435i
$516$		0			0
$517$	−7262.82			−0.617830
$518$		0			0
$519$	10411.9			0.880604
$520$		0			0
$521$	6566.06	−	11372.8i	0.552139	−	0.956333i	−0.445981	−	0.895042i	$-0.647145\pi$
$521$	6566.06	−	11372.8i	0.552139	−	0.956333i	0.998120	−	0.0612905i	$-0.0195216\pi$
$522$		0			0
$523$	1543.17	+	2672.85i	0.129021	+	0.223471i	0.923298	−	0.384085i	$-0.125483\pi$
$523$	1543.17	+	2672.85i	0.129021	+	0.223471i	−0.794276	+	0.607557i	$0.792150\pi$
$524$		0			0
$525$	−1490.84	−	734.013i	−0.123934	−	0.0610190i
$526$		0			0
$527$	−3553.58	−	6154.98i	−0.293731	−	0.508757i
$528$		0			0
$529$	−9567.63	+	16571.6i	−0.786359	+	1.36201i
$530$		0			0
$531$	−2534.85			−0.207162
$532$		0			0
$533$	−7670.80			−0.623376
$534$		0			0
$535$	7855.86	−	13606.7i	0.634838	−	1.09957i
$536$		0			0
$537$	1433.66	+	2483.16i	0.115208	+	0.199547i
$538$		0			0
$539$	−10692.7	−	13898.1i	−0.854482	−	1.11064i
$540$		0			0
$541$	−463.047	−	802.022i	−0.0367985	−	0.0637368i	0.847040	−	0.531530i	$-0.178383\pi$
$541$	−463.047	−	802.022i	−0.0367985	−	0.0637368i	−0.883838	+	0.467793i	$0.845049\pi$
$542$		0			0
$543$	−6330.39	+	10964.6i	−0.500300	+	0.866546i
$544$		0			0
$545$	3445.52			0.270807
$546$		0			0
$547$	592.871			0.0463425			0.0231712	−	0.999732i	$-0.492624\pi$
$547$	592.871			0.0463425			0.0231712	+	0.999732i	$0.492624\pi$
$548$		0			0
$549$	2447.32	−	4238.88i	0.190253	−	0.329528i
$550$		0			0
$551$	−1659.82	−	2874.89i	−0.128331	−	0.222276i
$552$		0			0
$553$	−19285.1	−	9495.02i	−1.48298	−	0.730144i
$554$		0			0
$555$	5882.33	+	10188.5i	0.449894	+	0.779239i
$556$		0			0
$557$	6122.67	−	10604.8i	0.465756	−	0.806713i	−0.533480	−	0.845813i	$-0.679116\pi$
$557$	6122.67	−	10604.8i	0.465756	−	0.806713i	0.999235	+	0.0391003i	$0.0124492\pi$
$558$		0			0
$559$	12646.0			0.956829
$560$		0			0
$561$	−3407.15			−0.256417
$562$		0			0
$563$	−7297.31	+	12639.3i	−0.546261	+	0.946152i	0.452266	+	0.891883i	$0.350616\pi$
$563$	−7297.31	+	12639.3i	−0.546261	+	0.946152i	−0.998526	+	0.0542682i	$0.982717\pi$
$564$		0			0
$565$	−329.300	−	570.364i	−0.0245199	−	0.0424697i
$566$		0			0
$567$	99.0720	+	1496.87i	0.00733798	+	0.110869i
$568$		0			0
$569$	−11455.6	−	19841.7i	−0.844015	−	1.46188i	−0.886474	−	0.462779i	$-0.846853\pi$
$569$	−11455.6	−	19841.7i	−0.844015	−	1.46188i	0.0424590	−	0.999098i	$-0.486481\pi$
$570$		0			0
$571$	−2952.32	+	5113.57i	−0.216376	+	0.374774i	−0.953697	−	0.300768i	$-0.902757\pi$
$571$	−2952.32	+	5113.57i	−0.216376	+	0.374774i	0.737321	+	0.675542i	$0.236090\pi$
$572$		0			0
$573$	−10554.1			−0.769465
$574$		0			0
$575$	5291.53			0.383778
$576$		0			0
$577$	−4756.61	+	8238.68i	−0.343189	+	0.594421i	−0.985023	−	0.172423i	$-0.944840\pi$
$577$	−4756.61	+	8238.68i	−0.343189	+	0.594421i	0.641834	+	0.766844i	$0.278174\pi$
$578$		0			0
$579$	7526.51	+	13036.3i	0.540226	+	0.935699i
$580$		0			0
$581$	−45.1242	+	30.1928i	−0.00322214	+	0.00215595i
$582$		0			0
$583$	7924.56	+	13725.7i	0.562953	+	0.975064i
$584$		0			0
$585$	−2085.24	+	3611.74i	−0.147374	+	0.255260i
$586$		0			0
$587$	−22790.6			−1.60250			−0.801252	−	0.598327i	$-0.795833\pi$
$587$	−22790.6			−1.60250			−0.801252	+	0.598327i	$0.795833\pi$
$588$		0			0
$589$	17384.3			1.21614
$590$		0			0
$591$	4257.21	−	7373.70i	0.296308	−	0.513221i
$592$		0			0
$593$	9131.39	+	15816.0i	0.632346	+	1.09526i	0.987071	+	0.160285i	$0.0512414\pi$
$593$	9131.39	+	15816.0i	0.632346	+	1.09526i	−0.354724	+	0.934971i	$0.615425\pi$
$594$		0			0
$595$	4255.92	−	2847.66i	0.293237	−	0.196206i
$596$		0			0
$597$	−532.352	−	922.061i	−0.0364953	−	0.0632118i
$598$		0			0
$599$	−3479.05	+	6025.88i	−0.237312	+	0.411037i	−0.959942	−	0.280198i	$-0.909600\pi$
$599$	−3479.05	+	6025.88i	−0.237312	+	0.411037i	0.722630	+	0.691235i	$0.242933\pi$
$600$		0			0
$601$	2305.39			0.156471			0.0782353	−	0.996935i	$-0.475071\pi$
$601$	2305.39			0.156471			0.0782353	+	0.996935i	$0.475071\pi$
$602$		0			0
$603$	−4314.23			−0.291358
$604$		0			0
$605$	−7981.87	+	13825.0i	−0.536379	+	0.929036i
$606$		0			0
$607$	8089.62	+	14011.6i	0.540935	+	0.936927i	0.998851	+	0.0479312i	$0.0152628\pi$
$607$	8089.62	+	14011.6i	0.540935	+	0.936927i	−0.457916	+	0.888996i	$0.651404\pi$
$608$		0			0
$609$	224.165	+	3386.88i	0.0149157	+	0.225359i
$610$		0			0
$611$	−2644.60	−	4580.58i	−0.175105	−	0.303291i
$612$		0			0
$613$	−10270.4	+	17788.8i	−0.676699	+	1.17208i	0.299271	+	0.954168i	$0.403257\pi$
$613$	−10270.4	+	17788.8i	−0.676699	+	1.17208i	−0.975969	+	0.217908i	$0.930077\pi$
$614$		0			0
$615$	−7692.96			−0.504407
$616$		0			0
$617$	6918.19			0.451403			0.225702	−	0.974196i	$-0.427533\pi$
$617$	6918.19			0.451403			0.225702	+	0.974196i	$0.427533\pi$
$618$		0			0
$619$	4040.81	−	6998.89i	0.262381	−	0.454457i	−0.704493	−	0.709711i	$-0.748826\pi$
$619$	4040.81	−	6998.89i	0.262381	−	0.454457i	0.966874	+	0.255254i	$0.0821589\pi$
$620$		0			0
$621$	−2388.48	−	4136.97i	−0.154342	−	0.267328i
$622$		0			0
$623$	21247.0	+	10461.0i	1.36636	+	0.672728i
$624$		0			0
$625$	9234.52	+	15994.7i	0.591009	+	1.02366i
$626$		0			0
$627$	4166.98	−	7217.42i	0.265412	−	0.459706i
$628$		0			0
$629$	−6999.54			−0.443704
$630$		0			0
$631$	−27293.3			−1.72191			−0.860957	−	0.508677i	$-0.830135\pi$
$631$	−27293.3			−1.72191			−0.860957	+	0.508677i	$0.830135\pi$
$632$		0			0
$633$	−1129.01	+	1955.50i	−0.0708910	+	0.122787i
$634$		0			0
$635$	−2761.20	−	4782.53i	−0.172559	−	0.298880i
$636$		0			0
$637$	4871.86	−	11804.4i	0.303030	−	0.734237i
$638$		0			0
$639$	−4975.35	−	8617.56i	−0.308015	−	0.533498i
$640$		0			0
$641$	−9627.82	+	16675.9i	−0.593254	+	1.02755i	0.400536	+	0.916281i	$0.368824\pi$
$641$	−9627.82	+	16675.9i	−0.593254	+	1.02755i	−0.993791	+	0.111266i	$0.964509\pi$
$642$		0			0
$643$	−19996.4			−1.22641			−0.613204	−	0.789925i	$-0.710120\pi$
$643$	−19996.4			−1.22641			−0.613204	+	0.789925i	$0.710120\pi$
$644$		0			0
$645$	12682.5			0.774222
$646$		0			0
$647$	−3532.10	+	6117.77i	−0.214623	+	0.371738i	−0.953156	−	0.302479i	$-0.902186\pi$
$647$	−3532.10	+	6117.77i	−0.214623	+	0.371738i	0.738533	+	0.674218i	$0.235519\pi$
$648$		0			0
$649$	−7199.47	−	12469.8i	−0.435445	−	0.754213i
$650$		0			0
$651$	−15947.2	−	7851.59i	−0.960090	−	0.472700i
$652$		0			0
$653$	6910.53	+	11969.4i	0.414134	+	0.717302i	0.995337	−	0.0964570i	$-0.0307510\pi$
$653$	6910.53	+	11969.4i	0.414134	+	0.717302i	−0.581203	+	0.813759i	$0.697418\pi$
$654$		0			0
$655$	13401.4	−	23211.9i	0.799443	−	1.38468i
$656$		0			0
$657$	2154.15			0.127917
$658$		0			0
$659$	−7802.80			−0.461235			−0.230617	−	0.973044i	$-0.574075\pi$
$659$	−7802.80			−0.461235			−0.230617	+	0.973044i	$0.574075\pi$
$660$		0			0
$661$	−7908.65	+	13698.2i	−0.465372	+	0.806048i	−0.999218	−	0.0395338i	$-0.987413\pi$
$661$	−7908.65	+	13698.2i	−0.465372	+	0.806048i	0.533846	+	0.845581i	$0.320746\pi$
$662$		0			0
$663$	−1240.64	−	2148.85i	−0.0726734	−	0.125874i
$664$		0			0
$665$	827.204	+	12498.1i	0.0482370	+	0.728806i
$666$		0			0
$667$	−5404.29	−	9360.51i	−0.313726	−	0.543389i
$668$		0			0
$669$	4616.62	−	7996.23i	0.266800	−	0.462111i
$670$		0			0
$671$	27803.5			1.59962
$672$		0			0
$673$	2943.30			0.168582			0.0842911	−	0.996441i	$-0.473137\pi$
$673$	2943.30			0.168582			0.0842911	+	0.996441i	$0.473137\pi$
$674$		0			0
$675$	−403.764	+	699.340i	−0.0230235	+	0.0398779i
$676$		0			0
$677$	1585.74	+	2746.58i	0.0900220	+	0.155923i	0.907520	−	0.420009i	$-0.137973\pi$
$677$	1585.74	+	2746.58i	0.0900220	+	0.155923i	−0.817498	+	0.575931i	$0.804640\pi$
$678$		0			0
$679$	1216.92	−	814.247i	0.0687792	−	0.0460205i
$680$		0			0
$681$	9326.15	+	16153.4i	0.524785	+	0.908955i
$682$		0			0
$683$	12226.6	−	21177.1i	0.684975	−	1.18641i	−0.288470	−	0.957489i	$-0.593146\pi$
$683$	12226.6	−	21177.1i	0.684975	−	1.18641i	0.973445	−	0.228923i	$-0.0735202\pi$
$684$		0			0
$685$	3274.70			0.182656
$686$		0			0
$687$	1509.76			0.0838443
$688$		0			0
$689$	−5771.12	+	9995.87i	−0.319103	+	0.552703i
$690$		0			0
$691$	−4297.95	−	7444.26i	−0.236616	−	0.409831i	0.723125	−	0.690717i	$-0.242705\pi$
$691$	−4297.95	−	7444.26i	−0.236616	−	0.409831i	−0.959741	+	0.280886i	$0.909372\pi$
$692$		0			0
$693$	−7082.25	+	4738.77i	−0.388214	+	0.259756i
$694$		0			0
$695$	−7254.69	−	12565.5i	−0.395951	−	0.685808i
$696$		0			0
$697$	2288.51	−	3963.82i	0.124367	−	0.215409i
$698$		0			0
$699$	−805.019			−0.0435602
$700$		0			0
$701$	−21476.1			−1.15712			−0.578561	−	0.815639i	$-0.696385\pi$
$701$	−21476.1			−1.15712			−0.578561	+	0.815639i	$0.696385\pi$
$702$		0			0
$703$	8560.51	−	14827.2i	0.459269	−	0.795477i
$704$		0			0
$705$	−2652.24	−	4593.81i	−0.141687	−	0.245409i
$706$		0			0
$707$	1678.24	+	25356.3i	0.0892738	+	1.34883i
$708$		0			0
$709$	6769.46	+	11725.0i	0.358579	+	0.621077i	0.987724	−	0.156211i	$-0.0499281\pi$
$709$	6769.46	+	11725.0i	0.358579	+	0.621077i	−0.629145	+	0.777288i	$0.716595\pi$
$710$		0			0
$711$	−5223.00	+	9046.49i	−0.275496	+	0.477173i
$712$		0			0
$713$	56602.5			2.97304
$714$		0			0
$715$	−23690.0			−1.23910
$716$		0			0
$717$	7784.65	−	13483.4i	0.405471	−	0.702297i
$718$		0			0
$719$	−6941.84	−	12023.6i	−0.360065	−	0.623652i	0.627906	−	0.778289i	$-0.283912\pi$
$719$	−6941.84	−	12023.6i	−0.360065	−	0.623652i	−0.987971	+	0.154638i	$0.950579\pi$
$720$		0			0
$721$	−4295.63	−	2114.95i	−0.221883	−	0.109244i
$722$		0			0
$723$	−9256.41	−	16032.6i	−0.476140	−	0.824699i
$724$		0			0
$725$	−913.577	+	1582.36i	−0.0467992	+	0.0810585i
$726$		0			0
$727$	−18292.9			−0.933215			−0.466607	−	0.884465i	$-0.654524\pi$
$727$	−18292.9			−0.933215			−0.466607	+	0.884465i	$0.654524\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−3772.81	+	6534.69i	−0.190892	+	0.330635i
$732$		0			0
$733$	−7122.92	−	12337.3i	−0.358924	−	0.621674i	0.628857	−	0.777521i	$-0.283523\pi$
$733$	−7122.92	−	12337.3i	−0.358924	−	0.621674i	−0.987781	+	0.155846i	$0.950190\pi$
$734$		0			0
$735$	4885.94	−	11838.5i	0.245198	−	0.594110i
$736$		0			0
$737$	−12253.3	−	21223.3i	−0.612422	−	1.06075i
$738$		0			0
$739$	681.947	−	1181.17i	0.0339456	−	0.0587956i	−0.848553	−	0.529110i	$-0.822526\pi$
$739$	681.947	−	1181.17i	0.0339456	−	0.0587956i	0.882499	+	0.470314i	$0.155859\pi$
$740$		0			0
$741$	6069.27			0.300891
$742$		0			0
$743$	21789.4			1.07588			0.537938	−	0.842984i	$-0.319203\pi$
$743$	21789.4			1.07588			0.537938	+	0.842984i	$0.319203\pi$
$744$		0			0
$745$	10985.0	−	19026.6i	0.540214	−	0.935678i
$746$		0			0
$747$	13.1921	+	22.8494i	0.000646150	+	0.00111916i
$748$		0			0
$749$	20974.9	+	10327.0i	1.02324	+	0.503793i
$750$		0			0
$751$	1059.78	+	1835.59i	0.0514937	+	0.0891898i	0.890623	−	0.454742i	$-0.150268\pi$
$751$	1059.78	+	1835.59i	0.0514937	+	0.0891898i	−0.839130	+	0.543932i	$0.816935\pi$
$752$		0			0
$753$	−2837.87	+	4915.34i	−0.137341	+	0.237882i
$754$		0			0
$755$	33509.1			1.61526
$756$		0			0
$757$	28202.4			1.35408			0.677038	−	0.735948i	$-0.263263\pi$
$757$	28202.4			1.35408			0.677038	+	0.735948i	$0.263263\pi$
$758$		0			0
$759$	13567.5	−	23499.6i	0.648840	−	1.12382i
$760$		0			0
$761$	−5573.52	−	9653.62i	−0.265493	−	0.459847i	0.702200	−	0.711980i	$-0.252201\pi$
$761$	−5573.52	−	9653.62i	−0.265493	−	0.459847i	−0.967693	+	0.252133i	$0.918868\pi$
$762$		0			0
$763$	338.597	+	5115.82i	0.0160656	+	0.242733i
$764$		0			0
$765$	−1244.22	−	2155.06i	−0.0588039	−	0.101851i
$766$		0			0
$767$	5243.07	−	9081.26i	0.246827	−	0.427517i
$768$		0			0
$769$	−4109.29			−0.192698			−0.0963491	−	0.995348i	$-0.530717\pi$
$769$	−4109.29			−0.192698			−0.0963491	+	0.995348i	$0.530717\pi$
$770$		0			0
$771$	−19619.8			−0.916459
$772$		0			0
$773$	−6945.68	+	12030.3i	−0.323181	+	0.559766i	−0.981143	−	0.193286i	$-0.938086\pi$
$773$	−6945.68	+	12030.3i	−0.323181	+	0.559766i	0.657962	+	0.753052i	$0.271419\pi$
$774$		0			0
$775$	−4784.22	−	8286.51i	−0.221747	−	0.384078i
$776$		0			0
$777$	−14549.6	+	9735.18i	−0.671766	+	0.449482i
$778$		0			0
$779$	5597.75	+	9695.59i	0.257459	+	0.445931i
$780$		0			0
$781$	28262.0	−	48951.2i	1.29487	−	2.24278i
$782$		0			0
$783$	1649.47			0.0752839
$784$		0			0
$785$	−24162.9			−1.09861
$786$		0			0
$787$	4671.18	−	8090.71i	0.211575	−	0.366458i	−0.740633	−	0.671910i	$-0.765474\pi$
$787$	4671.18	−	8090.71i	0.211575	−	0.366458i	0.952208	+	0.305452i	$0.0988074\pi$
$788$		0			0
$789$	−8063.86	−	13967.0i	−0.363854	−	0.630214i
$790$		0			0
$791$	814.500	−	544.986i	0.0366123	−	0.0244974i
$792$		0			0
$793$	10124.0	+	17535.4i	0.453361	+	0.785245i
$794$		0			0
$795$	−5787.79	+	10024.7i	−0.258204	+	0.447222i
$796$		0			0
$797$	−24324.3			−1.08107			−0.540534	−	0.841322i	$-0.681778\pi$
$797$	−24324.3			−1.08107			−0.540534	+	0.841322i	$0.681778\pi$
$798$		0			0
$799$	3155.97			0.139737
$800$		0			0
$801$	5754.34	−	9966.80i	0.253832	−	0.439650i
$802$		0			0
$803$	6118.22	+	10597.1i	0.268876	+	0.465706i
$804$		0			0
$805$	2693.34	+	40693.3i	0.117923	+	1.78168i
$806$		0			0
$807$	4858.32	+	8414.86i	0.211922	+	0.367060i
$808$		0			0
$809$	−17227.5	+	29838.8i	−0.748684	+	1.29676i	0.199770	+	0.979843i	$0.435980\pi$
$809$	−17227.5	+	29838.8i	−0.748684	+	1.29676i	−0.948454	+	0.316915i	$0.897353\pi$
$810$		0			0
$811$	−8350.13			−0.361545			−0.180772	−	0.983525i	$-0.557860\pi$
$811$	−8350.13			−0.361545			−0.180772	+	0.983525i	$0.557860\pi$
$812$		0			0
$813$	4072.37			0.175676
$814$		0			0
$815$	−13086.2	+	22665.9i	−0.562441	+	0.974176i
$816$		0			0
$817$	−9228.37	−	15984.0i	−0.395177	−	0.684467i
$818$		0			0
$819$	−5567.54	−	2741.18i	−0.237540	−	0.116953i
$820$		0			0
$821$	9417.38	+	16311.4i	0.400327	+	0.693387i	0.993765	−	0.111492i	$-0.0355631\pi$
$821$	9417.38	+	16311.4i	0.400327	+	0.693387i	−0.593438	+	0.804880i	$0.702230\pi$
$822$		0			0
$823$	−4828.38	+	8363.00i	−0.204504	+	0.354211i	−0.949975	−	0.312327i	$-0.898891\pi$
$823$	−4828.38	+	8363.00i	−0.204504	+	0.354211i	0.745471	+	0.666538i	$0.232225\pi$
$824$		0			0
$825$	−4587.08			−0.193578
$826$		0			0
$827$	−20759.6			−0.872892			−0.436446	−	0.899731i	$-0.643763\pi$
$827$	−20759.6			−0.872892			−0.436446	+	0.899731i	$0.643763\pi$
$828$		0			0
$829$	7808.05	−	13523.9i	0.327123	−	0.566593i	−0.654817	−	0.755787i	$-0.727254\pi$
$829$	7808.05	−	13523.9i	0.327123	−	0.566593i	0.981940	+	0.189194i	$0.0605876\pi$
$830$		0			0
$831$	3842.45	+	6655.32i	0.160401	+	0.277823i
$832$		0			0
$833$	4646.36	+	6039.24i	0.193262	+	0.251197i
$834$		0			0
$835$	14588.3	+	25267.7i	0.604610	+	1.04722i
$836$		0			0
$837$	−4318.98	+	7480.69i	−0.178358	+	0.308925i
$838$		0			0
$839$	−417.027			−0.0171601			−0.00858007	−	0.999963i	$-0.502731\pi$
$839$	−417.027			−0.0171601			−0.00858007	+	0.999963i	$0.502731\pi$
$840$		0			0
$841$	−20656.8			−0.846973
$842$		0			0
$843$	−2679.26	+	4640.61i	−0.109464	+	0.189598i
$844$		0			0
$845$	5045.98	+	8739.89i	0.205428	+	0.355812i
$846$		0			0
$847$	−21311.4	−	10492.7i	−0.864544	−	0.425658i
$848$		0			0
$849$	11082.4	+	19195.3i	0.447995	+	0.775950i
$850$		0			0
$851$	27872.7	−	48276.9i	1.12275	−	1.94467i
$852$		0			0
$853$	−24917.4			−1.00018			−0.500092	−	0.865972i	$-0.666700\pi$
$853$	−24917.4			−1.00018			−0.500092	+	0.865972i	$0.666700\pi$
$854$		0			0
$855$	6086.80			0.243467
$856$		0			0
$857$	22261.9	−	38558.7i	0.887342	−	1.53692i	0.0443361	−	0.999017i	$-0.485883\pi$
$857$	22261.9	−	38558.7i	0.887342	−	1.53692i	0.843006	−	0.537904i	$-0.180784\pi$
$858$		0			0
$859$	12073.2	+	20911.4i	0.479548	+	0.830602i	0.999725	−	0.0234566i	$-0.00746716\pi$
$859$	12073.2	+	20911.4i	0.479548	+	0.830602i	−0.520176	+	0.854059i	$0.674134\pi$
$860$		0			0
$861$	−756.000	−	11422.3i	−0.0299238	−	0.452115i
$862$		0			0
$863$	13221.3	+	22900.0i	0.521505	+	0.903273i	0.999687	+	0.0250123i	$0.00796250\pi$
$863$	13221.3	+	22900.0i	0.521505	+	0.903273i	−0.478182	+	0.878261i	$0.658704\pi$
$864$		0			0
$865$	−21598.2	+	37409.2i	−0.848973	+	1.47046i
$866$		0			0
$867$	−13258.5			−0.519355
$868$		0			0
$869$	−59337.4			−2.31632
$870$		0			0
$871$	8923.54	−	15456.0i	0.347144	−	0.601271i
$872$		0			0
$873$	−355.768	−	616.208i	−0.0137926	−	0.0238895i
$874$		0			0
$875$	−18217.4	+	12189.4i	−0.703842	+	0.470944i
$876$		0			0
$877$	11258.1	+	19499.5i	0.433475	+	0.750801i	0.997170	−	0.0751826i	$-0.0239540\pi$
$877$	11258.1	+	19499.5i	0.433475	+	0.750801i	−0.563695	+	0.825983i	$0.690621\pi$
$878$		0			0
$879$	−739.472	+	1280.80i	−0.0283752	+	0.0491472i
$880$		0			0
$881$	10120.6			0.387027			0.193514	−	0.981098i	$-0.438012\pi$
$881$	10120.6			0.387027			0.193514	+	0.981098i	$0.438012\pi$
$882$		0			0
$883$	−20748.5			−0.790761			−0.395380	−	0.918517i	$-0.629387\pi$
$883$	−20748.5			−0.790761			−0.395380	+	0.918517i	$0.629387\pi$
$884$		0			0
$885$	5258.21	−	9107.49i	0.199721	−	0.345927i
$886$		0			0
$887$	−12749.7	−	22083.1i	−0.482630	−	0.835939i	0.517172	−	0.855882i	$-0.326985\pi$
$887$	−12749.7	−	22083.1i	−0.482630	−	0.835939i	−0.999801	+	0.0199428i	$0.993652\pi$
$888$		0			0
$889$	6829.63	−	4569.74i	0.257659	−	0.172401i
$890$		0			0
$891$	2070.50	+	3586.22i	0.0778502	+	0.134840i
$892$		0			0
$893$	−3859.78	+	6685.34i	−0.144639	+	0.250522i
$894$		0			0
$895$	−11895.7			−0.444280
$896$		0			0
$897$	19761.3			0.735574
$898$		0			0
$899$	−9772.34	+	16926.2i	−0.362543	+	0.627942i
$900$		0			0
$901$	−3443.52	−	5964.35i	−0.127326	−	0.220534i
$902$		0			0
$903$	1246.33	+	18830.6i	0.0459305	+	0.693959i
$904$		0			0
$905$	−26263.1	−	45489.1i	−0.964659	−	1.67084i
$906$		0			0
$907$	−18903.5	+	32741.8i	−0.692040	+	1.19865i	0.279128	+	0.960254i	$0.409954\pi$
$907$	−18903.5	+	32741.8i	−0.692040	+	1.19865i	−0.971168	+	0.238395i	$0.923379\pi$
$908$		0			0
$909$	12348.9			0.450593
$910$		0			0
$911$	−3230.08			−0.117472			−0.0587362	−	0.998274i	$-0.518707\pi$
$911$	−3230.08			−0.117472			−0.0587362	+	0.998274i	$0.518707\pi$
$912$		0			0
$913$	−74.9364	+	129.794i	−0.00271635	+	0.00470486i
$914$		0			0
$915$	10153.3	+	17586.0i	0.366839	+	0.635384i
$916$		0			0
$917$	35781.3	+	17616.9i	1.28855	+	0.634419i
$918$		0			0
$919$	17671.6	+	30608.0i	0.634310	+	1.09866i	0.986661	+	0.162789i	$0.0520490\pi$
$919$	17671.6	+	30608.0i	0.634310	+	1.09866i	−0.352351	+	0.935868i	$0.614618\pi$
$920$		0			0
$921$	1483.21	−	2569.00i	0.0530658	−	0.0919126i
$922$		0			0
$923$	41164.0			1.46796
$924$		0			0
$925$	−9423.55			−0.334967
$926$		0			0
$927$	−1163.39	+	2015.05i	−0.0412197	+	0.0713946i
$928$		0			0
$929$	−16515.1	−	28605.0i	−0.583254	−	1.01023i	−0.995091	−	0.0989684i	$-0.968446\pi$
$929$	−16515.1	−	28605.0i	−0.583254	−	1.01023i	0.411836	−	0.911258i	$-0.364888\pi$
$930$		0			0
$931$	−18475.6	+	2456.42i	−0.650390	+	0.0864725i
$932$		0			0
$933$	14394.9	+	24932.6i	0.505109	+	0.874874i
$934$		0			0
$935$	7067.68	−	12241.6i	0.247206	−	0.428174i
$936$		0			0
$937$	54695.9			1.90698			0.953488	−	0.301430i	$-0.0974640\pi$
$937$	54695.9			1.90698			0.953488	+	0.301430i	$0.0974640\pi$
$938$		0			0
$939$	2897.14			0.100686
$940$		0			0
$941$	9127.64	−	15809.5i	0.316209	−	0.547690i	−0.663485	−	0.748190i	$-0.730923\pi$
$941$	9127.64	−	15809.5i	0.316209	−	0.547690i	0.979694	+	0.200500i	$0.0642566\pi$
$942$		0			0
$943$	18226.0	+	31568.4i	0.629397	+	1.09015i
$944$		0			0
$945$	−5583.62	−	2749.10i	−0.192207	−	0.0946329i
$946$		0			0
$947$	−3107.88	−	5383.00i	−0.106645	−	0.184714i	0.807764	−	0.589506i	$-0.200677\pi$
$947$	−3107.88	−	5383.00i	−0.106645	−	0.184714i	−0.914409	+	0.404792i	$0.867344\pi$
$948$		0			0
$949$	−4455.64	+	7717.39i	−0.152409	+	0.263980i
$950$		0			0
$951$	−26957.9			−0.919212
$952$		0			0
$953$	8594.53			0.292135			0.146067	−	0.989275i	$-0.453338\pi$
$953$	8594.53			0.292135			0.146067	+	0.989275i	$0.453338\pi$
$954$		0			0
$955$	21893.1	−	37920.0i	0.741826	−	1.28488i
$956$		0			0
$957$	4684.83	+	8114.36i	0.158243	+	0.274086i
$958$		0			0
$959$	321.810	+	4862.18i	0.0108361	+	0.163721i
$960$		0			0
$961$	−36280.3	−	62839.4i	−1.21783	−	2.10934i
$962$		0			0
$963$	5680.66	−	9839.18i	0.190090	−	0.329245i
$964$		0			0
$965$	−62451.1			−2.08329
$966$		0			0
$967$	−17168.1			−0.570929			−0.285464	−	0.958389i	$-0.592148\pi$
$967$	−17168.1			−0.570929			−0.285464	+	0.958389i	$0.592148\pi$
$968$		0			0
$969$	−1810.71	+	3136.24i	−0.0600293	+	0.103974i
$970$		0			0
$971$	−5963.11	−	10328.4i	−0.197081	−	0.341354i	0.750500	−	0.660871i	$-0.229813\pi$
$971$	−5963.11	−	10328.4i	−0.197081	−	0.341354i	−0.947581	+	0.319517i	$0.896479\pi$
$972$		0			0
$973$	17944.0	−	12006.4i	0.591221	−	0.395589i
$974$		0			0
$975$	−1670.29	−	2893.02i	−0.0548636	−	0.0950265i
$976$		0			0
$977$	−7019.12	+	12157.5i	−0.229848	+	0.398108i	−0.957763	−	0.287559i	$-0.907156\pi$
$977$	−7019.12	+	12157.5i	−0.229848	+	0.398108i	0.727915	+	0.685667i	$0.240490\pi$
$978$		0			0
$979$	65373.8			2.13417
$980$		0			0
$981$	2491.50			0.0810880
$982$		0			0
$983$	−10175.7	+	17624.8i	−0.330167	+	0.571866i	−0.982544	−	0.186028i	$-0.940438\pi$
$983$	−10175.7	+	17624.8i	−0.330167	+	0.571866i	0.652378	+	0.757894i	$0.273772\pi$
$984$		0			0
$985$	17662.0	+	30591.6i	0.571329	+	0.989571i
$986$		0			0
$987$	6560.14	−	4389.42i	0.211562	−	0.141557i
$988$		0			0
$989$	−30047.2	−	52043.3i	−0.966072	−	1.67329i
$990$		0			0
$991$	16252.9	−	28150.8i	0.520978	−	0.902360i	−0.478724	−	0.877965i	$-0.658901\pi$
$991$	16252.9	−	28150.8i	0.520978	−	0.902360i	0.999702	−	0.0243951i	$-0.00776598\pi$
$992$		0			0
$993$	−11421.9			−0.365018
$994$		0			0
$995$	4417.18			0.140738
$996$		0			0
$997$	12423.5	−	21518.2i	0.394641	−	0.683539i	−0.598414	−	0.801187i	$-0.704202\pi$
$997$	12423.5	−	21518.2i	0.394641	−	0.683539i	0.993055	+	0.117648i	$0.0375356\pi$
$998$		0			0
$999$	4253.58	+	7367.42i	0.134712	+	0.233328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.i.a.25.1	✓	4
3.2	odd	2		252.4.k.f.109.2		4
4.3	odd	2		336.4.q.i.193.1		4
7.2	even	3	inner	84.4.i.a.37.1	yes	4
7.3	odd	6		588.4.a.f.1.1		2
7.4	even	3		588.4.a.i.1.2		2
7.5	odd	6		588.4.i.j.373.2		4
7.6	odd	2		588.4.i.j.361.2		4
21.2	odd	6		252.4.k.f.37.2		4
21.5	even	6		1764.4.k.q.1549.1		4
21.11	odd	6		1764.4.a.o.1.1		2
21.17	even	6		1764.4.a.y.1.2		2
21.20	even	2		1764.4.k.q.361.1		4
28.3	even	6		2352.4.a.bx.1.1		2
28.11	odd	6		2352.4.a.bt.1.2		2
28.23	odd	6		336.4.q.i.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.i.a.25.1	✓	4	1.1	even	1	trivial
84.4.i.a.37.1	yes	4	7.2	even	3	inner
252.4.k.f.37.2		4	21.2	odd	6
252.4.k.f.109.2		4	3.2	odd	2
336.4.q.i.193.1		4	4.3	odd	2
336.4.q.i.289.1		4	28.23	odd	6
588.4.a.f.1.1		2	7.3	odd	6
588.4.a.i.1.2		2	7.4	even	3
588.4.i.j.361.2		4	7.6	odd	2
588.4.i.j.373.2		4	7.5	odd	6
1764.4.a.o.1.1		2	21.11	odd	6
1764.4.a.y.1.2		2	21.17	even	6
1764.4.k.q.361.1		4	21.20	even	2
1764.4.k.q.1549.1		4	21.5	even	6
2352.4.a.bt.1.2		2	28.11	odd	6
2352.4.a.bx.1.1		2	28.3	even	6

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(-6.22311 - 10.7787i) q^{5} +(15.3924 - 10.2992i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +(-6.22311 - 10.7787i) q^{5} +(15.3924 - 10.2992i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(25.5618 - 44.2743i) q^{11} +37.2311 q^{13} +37.3387 q^{15} +(-11.1076 + 19.2389i) q^{17} +(-27.1693 - 47.0587i) q^{19} +(3.66933 + 55.4395i) q^{21} +(-88.4622 - 153.221i) q^{23} +(-14.9542 + 25.9015i) q^{25} +27.0000 q^{27} +61.0916 q^{29} +(-159.962 + 277.063i) q^{31} +(76.6853 + 132.823i) q^{33} +(-206.801 - 101.818i) q^{35} +(157.540 + 272.867i) q^{37} +(-55.8467 + 96.7293i) q^{39} -206.032 q^{41} +339.661 q^{43} +(-56.0080 + 97.0087i) q^{45} +(-71.0320 - 123.031i) q^{47} +(130.855 - 317.058i) q^{49} +(-33.3227 - 57.7166i) q^{51} +(-155.008 + 268.482i) q^{53} -636.295 q^{55} +163.016 q^{57} +(140.825 - 243.916i) q^{59} +(271.924 + 470.987i) q^{61} +(-149.540 - 73.6260i) q^{63} +(-231.693 - 401.305i) q^{65} +(239.680 - 415.137i) q^{67} +530.773 q^{69} +1105.63 q^{71} +(-119.675 + 207.283i) q^{73} +(-44.8627 - 77.7044i) q^{75} +(-62.5298 - 944.754i) q^{77} +(-580.333 - 1005.17i) q^{79} +(-40.5000 + 70.1481i) q^{81} -2.93158 q^{83} +276.494 q^{85} +(-91.6373 + 158.721i) q^{87} +(639.371 + 1107.42i) q^{89} +(573.078 - 383.449i) q^{91} +(-479.887 - 831.188i) q^{93} +(-338.156 + 585.703i) q^{95} +79.0596 q^{97} -460.112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9	\( 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9} + 5 q^{11} + 10 q^{13} + 66 q^{15} - 100 q^{17} - 67 q^{19} - 27 q^{21} - 76 q^{23} + 93 q^{25} + 108 q^{27} + 550 q^{29} - 362 q^{31} + 15 q^{33} - 466 q^{35} + 5 q^{37} - 15 q^{39} - 324 q^{41} + 1442 q^{43} - 99 q^{45} + 216 q^{47} + 190 q^{49} - 300 q^{51} - 495 q^{53} - 1406 q^{55} + 402 q^{57} - 173 q^{59} + 532 q^{61} + 27 q^{63} - 510 q^{65} - 111 q^{67} + 456 q^{69} + 3200 q^{71} - 1215 q^{73} + 279 q^{75} - 653 q^{77} - 1460 q^{79} - 162 q^{81} - 2818 q^{83} + 328 q^{85} - 825 q^{87} + 1974 q^{89} + 1945 q^{91} - 1086 q^{93} - 658 q^{95} + 1122 q^{97} - 90 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9 + 5 * q^11 + 10 * q^13 + 66 * q^15 - 100 * q^17 - 67 * q^19 - 27 * q^21 - 76 * q^23 + 93 * q^25 + 108 * q^27 + 550 * q^29 - 362 * q^31 + 15 * q^33 - 466 * q^35 + 5 * q^37 - 15 * q^39 - 324 * q^41 + 1442 * q^43 - 99 * q^45 + 216 * q^47 + 190 * q^49 - 300 * q^51 - 495 * q^53 - 1406 * q^55 + 402 * q^57 - 173 * q^59 + 532 * q^61 + 27 * q^63 - 510 * q^65 - 111 * q^67 + 456 * q^69 + 3200 * q^71 - 1215 * q^73 + 279 * q^75 - 653 * q^77 - 1460 * q^79 - 162 * q^81 - 2818 * q^83 + 328 * q^85 - 825 * q^87 + 1974 * q^89 + 1945 * q^91 - 1086 * q^93 - 658 * q^95 + 1122 * q^97 - 90 * q^99

Introduction

L-functions

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