LMFDB - Embedded newform 144.5.m.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.m (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:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.7
Root			$2.24452 - 1.72109i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.5.m.a.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.96560 - 0.523430i) q^{2} +(15.4520 - 4.15143i) q^{4} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +(59.1037 - 24.5510i) q^{8} +O(q^{10})$	\(q+(3.96560 - 0.523430i) q^{2} +(15.4520 - 4.15143i) q^{4} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +(59.1037 - 24.5510i) q^{8} +(-74.8239 + 97.5799i) q^{10} +(90.9986 + 90.9986i) q^{11} +(221.402 + 221.402i) q^{13} +(-26.2544 + 3.46539i) q^{14} +(221.531 - 128.296i) q^{16} +132.575 q^{17} +(-402.520 + 402.520i) q^{19} +(-245.646 + 426.128i) q^{20} +(408.496 + 313.233i) q^{22} -27.5037 q^{23} -320.028i q^{25} +(993.879 + 762.103i) q^{26} +(-102.301 + 27.4847i) q^{28} +(-174.909 - 174.909i) q^{29} -1083.96i q^{31} +(811.351 - 624.728i) q^{32} +(525.742 - 69.3940i) q^{34} +(143.913 - 143.913i) q^{35} +(553.474 - 553.474i) q^{37} +(-1385.54 + 1806.93i) q^{38} +(-751.085 + 1818.43i) q^{40} +1803.47i q^{41} +(17.8633 + 17.8633i) q^{43} +(1783.89 + 1028.34i) q^{44} +(-109.069 + 14.3963i) q^{46} -2268.26i q^{47} -2357.17 q^{49} +(-167.512 - 1269.10i) q^{50} +(4340.24 + 2501.97i) q^{52} +(822.415 - 822.415i) q^{53} -3956.14 q^{55} +(-391.298 + 162.541i) q^{56} +(-785.174 - 602.068i) q^{58} +(972.483 + 972.483i) q^{59} +(-2056.32 - 2056.32i) q^{61} +(-567.378 - 4298.57i) q^{62} +(2890.50 - 2902.11i) q^{64} -9625.38 q^{65} +(4611.22 - 4611.22i) q^{67} +(2048.56 - 550.378i) q^{68} +(495.374 - 646.031i) q^{70} +3105.84 q^{71} +723.400i q^{73} +(1905.15 - 2484.56i) q^{74} +(-4548.72 + 7890.79i) q^{76} +(-602.460 - 602.460i) q^{77} -3418.44i q^{79} +(-2026.68 + 7604.33i) q^{80} +(943.989 + 7151.83i) q^{82} +(161.591 - 161.591i) q^{83} +(-2881.84 + 2881.84i) q^{85} +(80.1892 + 61.4887i) q^{86} +(7612.46 + 3144.25i) q^{88} +1464.04i q^{89} +(-1465.80 - 1465.80i) q^{91} +(-424.988 + 114.180i) q^{92} +(-1187.28 - 8995.04i) q^{94} -17499.5i q^{95} -8264.99 q^{97} +(-9347.60 + 1233.81i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	3.96560	−	0.523430i	0.991401	−	0.130858i
$2$	3.96560	−	0.523430i	0.991401	−	0.130858i
$3$		0			0
$3$		0			0
$4$	15.4520	−	4.15143i	0.965753	−	0.259465i
$5$	−21.7374	+	21.7374i	−0.869495	+	0.869495i	−0.992416	−	0.122921i	$-0.960774\pi$
$5$	−21.7374	+	21.7374i	−0.869495	+	0.869495i	0.122921	+	0.992416i	$0.460774\pi$
$6$		0			0
$7$	−6.62054			−0.135113			−0.0675565	−	0.997715i	$-0.521520\pi$
$7$	−6.62054			−0.135113			−0.0675565	+	0.997715i	$0.521520\pi$
$8$	59.1037	−	24.5510i	0.923495	−	0.383610i
$9$		0			0
$10$	−74.8239	+	97.5799i	−0.748239	+	0.975799i
$11$	90.9986	+	90.9986i	0.752054	+	0.752054i	0.974862	−	0.222808i	$-0.0715223\pi$
$11$	90.9986	+	90.9986i	0.752054	+	0.752054i	−0.222808	+	0.974862i	$0.571522\pi$
$12$		0			0
$13$	221.402	+	221.402i	1.31007	+	1.31007i	0.921362	+	0.388707i	$0.127078\pi$
$13$	221.402	+	221.402i	1.31007	+	1.31007i	0.388707	+	0.921362i	$0.372922\pi$
$14$	−26.2544	+	3.46539i	−0.133951	+	0.0176806i
$15$		0			0
$16$	221.531	−	128.296i	0.865356	−	0.501157i
$17$	132.575			0.458738			0.229369	−	0.973339i	$-0.426334\pi$
$17$	132.575			0.458738			0.229369	+	0.973339i	$0.426334\pi$
$18$		0			0
$19$	−402.520	+	402.520i	−1.11501	+	1.11501i	−0.122552	+	0.992462i	$0.539108\pi$
$19$	−402.520	+	402.520i	−1.11501	+	1.11501i	−0.992462	+	0.122552i	$0.960892\pi$
$20$	−245.646	+	426.128i	−0.614114	+	1.06532i
$21$		0			0
$22$	408.496	+	313.233i	0.843999	+	0.647175i
$23$	−27.5037			−0.0519918			−0.0259959	−	0.999662i	$-0.508276\pi$
$23$	−27.5037			−0.0519918			−0.0259959	+	0.999662i	$0.508276\pi$
$24$		0			0
$25$		−	320.028i		−	0.512044i
$26$	993.879	+	762.103i	1.47024	+	1.12737i
$27$		0			0
$28$	−102.301	+	27.4847i	−0.130486	+	0.0350571i
$29$	−174.909	−	174.909i	−0.207978	−	0.207978i	0.595430	−	0.803407i	$-0.296982\pi$
$29$	−174.909	−	174.909i	−0.207978	−	0.207978i	−0.803407	+	0.595430i	$0.796982\pi$
$30$		0			0
$31$		−	1083.96i		−	1.12795i	−0.825791	−	0.563976i	$-0.809271\pi$
$31$		−	1083.96i		−	1.12795i	0.825791	−	0.563976i	$-0.190729\pi$
$32$	811.351	−	624.728i	0.792335	−	0.610086i
$33$		0			0
$34$	525.742	−	69.3940i	0.454794	−	0.0600294i
$35$	143.913	−	143.913i	0.117480	−	0.117480i
$36$		0			0
$37$	553.474	−	553.474i	0.404291	−	0.404291i	−0.475451	−	0.879742i	$-0.657715\pi$
$37$	553.474	−	553.474i	0.404291	−	0.404291i	0.879742	+	0.475451i	$0.157715\pi$
$38$	−1385.54	+	1806.93i	−0.959518	+	1.25133i
$39$		0			0
$40$	−751.085	+	1818.43i	−0.469428	+	1.13652i
$41$			1803.47i			1.07285i	0.843947	+	0.536427i	$0.180226\pi$
$41$			1803.47i			1.07285i	−0.843947	+	0.536427i	$0.819774\pi$
$42$		0			0
$43$	17.8633	+	17.8633i	0.00966108	+	0.00966108i	0.711921	−	0.702260i	$-0.247825\pi$
$43$	17.8633	+	17.8633i	0.00966108	+	0.00966108i	−0.702260	+	0.711921i	$0.747825\pi$
$44$	1783.89	+	1028.34i	0.921430	+	0.531167i
$45$		0			0
$46$	−109.069	+	14.3963i	−0.0515448	+	0.00680352i
$47$		−	2268.26i		−	1.02683i	−0.858141	−	0.513414i	$-0.828380\pi$
$47$		−	2268.26i		−	1.02683i	0.858141	−	0.513414i	$-0.171620\pi$
$48$		0			0
$49$	−2357.17			−0.981744
$50$	−167.512	−	1269.10i	−0.0670048	−	0.507641i
$51$		0			0
$52$	4340.24	+	2501.97i	1.60512	+	0.925285i
$53$	822.415	−	822.415i	0.292779	−	0.292779i	−0.545398	−	0.838177i	$-0.683622\pi$
$53$	822.415	−	822.415i	0.292779	−	0.292779i	0.838177	+	0.545398i	$0.183622\pi$
$54$		0			0
$55$	−3956.14			−1.30782
$56$	−391.298	+	162.541i	−0.124776	+	0.0518307i
$57$		0			0
$58$	−785.174	−	602.068i	−0.233405	−	0.178974i
$59$	972.483	+	972.483i	0.279369	+	0.279369i	0.832857	−	0.553488i	$-0.186704\pi$
$59$	972.483	+	972.483i	0.279369	+	0.279369i	−0.553488	+	0.832857i	$0.686704\pi$
$60$		0			0
$61$	−2056.32	−	2056.32i	−0.552626	−	0.552626i	0.374572	−	0.927198i	$-0.377790\pi$
$61$	−2056.32	−	2056.32i	−0.552626	−	0.552626i	−0.927198	+	0.374572i	$0.877790\pi$
$62$	−567.378	−	4298.57i	−0.147601	−	1.11825i
$63$		0			0
$64$	2890.50	−	2902.11i	0.705687	−	0.708523i
$65$	−9625.38			−2.27820
$66$		0			0
$67$	4611.22	−	4611.22i	1.02723	−	1.02723i	0.0276077	−	0.999619i	$-0.491211\pi$
$67$	4611.22	−	4611.22i	1.02723	−	1.02723i	0.999619	−	0.0276077i	$-0.00878893\pi$
$68$	2048.56	−	550.378i	0.443028	−	0.119026i
$69$		0			0
$70$	495.374	−	646.031i	0.101097	−	0.131843i
$71$	3105.84			0.616115			0.308058	−	0.951368i	$-0.400321\pi$
$71$	3105.84			0.616115			0.308058	+	0.951368i	$0.400321\pi$
$72$		0			0
$73$			723.400i			0.135748i	0.997694	+	0.0678739i	$0.0216216\pi$
$73$			723.400i			0.135748i	−0.997694	+	0.0678739i	$0.978378\pi$
$74$	1905.15	−	2484.56i	0.347910	−	0.453719i
$75$		0			0
$76$	−4548.72	+	7890.79i	−0.787521	+	1.36613i
$77$	−602.460	−	602.460i	−0.101612	−	0.101612i
$78$		0			0
$79$		−	3418.44i		−	0.547739i	−0.961767	−	0.273869i	$-0.911696\pi$
$79$		−	3418.44i		−	0.547739i	0.961767	−	0.273869i	$-0.0883036\pi$
$80$	−2026.68	+	7604.33i	−0.316669	+	1.18818i
$81$		0			0
$82$	943.989	+	7151.83i	0.140391	+	1.06363i
$83$	161.591	−	161.591i	0.0234563	−	0.0234563i	−0.695281	−	0.718738i	$-0.744720\pi$
$83$	161.591	−	161.591i	0.0234563	−	0.0234563i	0.718738	+	0.695281i	$0.244720\pi$
$84$		0			0
$85$	−2881.84	+	2881.84i	−0.398871	+	0.398871i
$86$	80.1892	+	61.4887i	0.0108422	+	0.00831378i
$87$		0			0
$88$	7612.46	+	3144.25i	0.983014	+	0.406023i
$89$			1464.04i			0.184830i	0.995721	+	0.0924150i	$0.0294586\pi$
$89$			1464.04i			0.184830i	−0.995721	+	0.0924150i	$0.970541\pi$
$90$		0			0
$91$	−1465.80	−	1465.80i	−0.177007	−	0.177007i
$92$	−424.988	+	114.180i	−0.0502113	+	0.0134900i
$93$		0			0
$94$	−1187.28	−	8995.04i	−0.134368	−	1.01800i
$95$		−	17499.5i		−	1.93900i
$96$		0			0
$97$	−8264.99			−0.878413			−0.439207	−	0.898386i	$-0.644740\pi$
$97$	−8264.99			−0.878413			−0.439207	+	0.898386i	$0.644740\pi$
$98$	−9347.60	+	1233.81i	−0.973303	+	0.128469i
$99$		0			0
$100$	−1328.57	−	4945.08i	−0.132857	−	0.494508i
$101$	−5035.04	+	5035.04i	−0.493583	+	0.493583i	−0.909433	−	0.415850i	$-0.863484\pi$
$101$	−5035.04	+	5035.04i	−0.493583	+	0.493583i	0.415850	+	0.909433i	$0.363484\pi$
$102$		0			0
$103$	1427.24			0.134531			0.0672653	−	0.997735i	$-0.478573\pi$
$103$	1427.24			0.134531			0.0672653	+	0.997735i	$0.478573\pi$
$104$	18521.3	+	7650.02i	1.71240	+	0.707287i
$105$		0			0
$106$	2830.90	−	3691.85i	0.251949	−	0.328573i
$107$	−9978.53	−	9978.53i	−0.871564	−	0.871564i	0.121079	−	0.992643i	$-0.461365\pi$
$107$	−9978.53	−	9978.53i	−0.871564	−	0.871564i	−0.992643	+	0.121079i	$0.961365\pi$
$108$		0			0
$109$	9.47842	+	9.47842i	0.000797780	+	0.000797780i	0.707506	−	0.706708i	$-0.249820\pi$
$109$	9.47842	+	9.47842i	0.000797780	+	0.000797780i	−0.706708	+	0.707506i	$0.749820\pi$
$110$	−15688.5	+	2070.76i	−1.29657	+	0.171137i
$111$		0			0
$112$	−1466.66	+	849.391i	−0.116921	+	0.0677129i
$113$	13634.7			1.06780			0.533900	−	0.845548i	$-0.320726\pi$
$113$	13634.7			1.06780			0.533900	+	0.845548i	$0.320726\pi$
$114$		0			0
$115$	597.858	−	597.858i	0.0452067	−	0.0452067i
$116$	−3428.83	−	1976.58i	−0.254818	−	0.146892i
$117$		0			0
$118$	4365.51	+	3347.46i	0.313524	+	0.240409i
$119$	−877.721			−0.0619816
$120$		0			0
$121$			1920.47i			0.131171i
$122$	−9230.89	−	7078.21i	−0.620189	−	0.475559i
$123$		0			0
$124$	−4500.00	−	16749.4i	−0.292664	−	1.08932i
$125$	−6629.30	−	6629.30i	−0.424275	−	0.424275i
$126$		0			0
$127$		−	8047.14i		−	0.498923i	−0.968385	−	0.249462i	$-0.919746\pi$
$127$		−	8047.14i		−	0.498923i	0.968385	−	0.249462i	$-0.0802537\pi$
$128$	9943.51	−	13021.6i	0.606904	−	0.794775i
$129$		0			0
$130$	−38170.5	+	5038.21i	−2.25861	+	0.298119i
$131$	15904.8	−	15904.8i	0.926799	−	0.926799i	−0.0706991	−	0.997498i	$-0.522523\pi$
$131$	15904.8	−	15904.8i	0.926799	−	0.926799i	0.997498	+	0.0706991i	$0.0225230\pi$
$132$		0			0
$133$	2664.90	−	2664.90i	0.150653	−	0.150653i
$134$	15872.6	−	20699.9i	0.883973	−	1.15281i
$135$		0			0
$136$	7835.70	−	3254.86i	0.423643	−	0.175976i
$137$			31169.3i			1.66068i	0.557257	+	0.830340i	$0.311854\pi$
$137$			31169.3i			1.66068i	−0.557257	+	0.830340i	$0.688146\pi$
$138$		0			0
$139$	21432.1	+	21432.1i	1.10926	+	1.10926i	0.993247	+	0.116017i	$0.0370126\pi$
$139$	21432.1	+	21432.1i	1.10926	+	1.10926i	0.116017	+	0.993247i	$0.462987\pi$
$140$	1626.31	−	2821.20i	0.0829748	−	0.143939i
$141$		0			0
$142$	12316.5	−	1625.69i	0.610818	−	0.0806233i
$143$			40294.4i			1.97048i
$144$		0			0
$145$	7604.14			0.361671
$146$	378.649	+	2868.72i	0.0177636	+	0.134581i
$147$		0			0
$148$	6254.59	−	10850.0i	0.285546	−	0.495344i
$149$	−11772.7	+	11772.7i	−0.530276	+	0.530276i	−0.920654	−	0.390378i	$-0.872344\pi$
$149$	−11772.7	+	11772.7i	−0.530276	+	0.530276i	0.390378	+	0.920654i	$0.372344\pi$
$150$		0			0
$151$	−19454.9			−0.853246			−0.426623	−	0.904429i	$-0.640297\pi$
$151$	−19454.9			−0.853246			−0.426623	+	0.904429i	$0.640297\pi$
$152$	−13908.2	+	33672.7i	−0.601980	+	1.45744i
$153$		0			0
$154$	−2704.46	−	2073.77i	−0.114035	−	0.0874419i
$155$	23562.5	+	23562.5i	0.980749	+	0.980749i
$156$		0			0
$157$	18097.5	+	18097.5i	0.734208	+	0.734208i	0.971450	−	0.237242i	$-0.0762436\pi$
$157$	18097.5	+	18097.5i	0.734208	+	0.734208i	−0.237242	+	0.971450i	$0.576244\pi$
$158$	−1789.31	−	13556.2i	−0.0716757	−	0.543029i
$159$		0			0
$160$	−4056.69	+	31216.6i	−0.158464	+	1.21940i
$161$	182.089			0.00702478
$162$		0			0
$163$	17673.1	−	17673.1i	0.665178	−	0.665178i	−0.291418	−	0.956596i	$-0.594127\pi$
$163$	17673.1	−	17673.1i	0.665178	−	0.665178i	0.956596	+	0.291418i	$0.0941270\pi$
$164$	7486.97	+	27867.2i	0.278367	+	1.03611i
$165$		0			0
$166$	556.223	−	725.386i	0.0201852	−	0.0263241i
$167$	11374.1			0.407834			0.203917	−	0.978988i	$-0.434633\pi$
$167$	11374.1			0.407834			0.203917	+	0.978988i	$0.434633\pi$
$168$		0			0
$169$			69476.3i			2.43256i
$170$	−9919.80	+	12936.7i	−0.343246	+	0.447636i
$171$		0			0
$172$	350.184	+	201.867i	0.0118369	+	0.00682351i
$173$	11289.3	+	11289.3i	0.377204	+	0.377204i	0.870092	−	0.492888i	$-0.164059\pi$
$173$	11289.3	+	11289.3i	0.377204	+	0.377204i	−0.492888	+	0.870092i	$0.664059\pi$
$174$		0			0
$175$			2118.76i			0.0691838i
$176$	31833.8	+	8484.24i	1.02769	+	0.273897i
$177$		0			0
$178$	766.322	+	5805.80i	0.0241864	+	0.183241i
$179$	25338.8	−	25338.8i	0.790825	−	0.790825i	−0.190803	−	0.981628i	$-0.561109\pi$
$179$	25338.8	−	25338.8i	0.790825	−	0.790825i	0.981628	+	0.190803i	$0.0611091\pi$
$180$		0			0
$181$	22579.8	−	22579.8i	0.689228	−	0.689228i	−0.272833	−	0.962061i	$-0.587961\pi$
$181$	22579.8	−	22579.8i	0.689228	−	0.689228i	0.962061	+	0.272833i	$0.0879608\pi$
$182$	−6580.02	−	5045.53i	−0.198648	−	0.152323i
$183$		0			0
$184$	−1625.57	+	675.243i	−0.0480142	+	0.0199446i
$185$			24062.2i			0.703058i
$186$		0			0
$187$	12064.2	+	12064.2i	0.344996	+	0.344996i
$188$	−9416.55	−	35049.3i	−0.266426	−	0.991663i
$189$		0			0
$190$	−9159.75	−	69396.0i	−0.253733	−	1.92233i
$191$		−	62994.4i		−	1.72677i	−0.504543	−	0.863386i	$-0.668339\pi$
$191$		−	62994.4i		−	1.72677i	0.504543	−	0.863386i	$-0.331661\pi$
$192$		0			0
$193$	−25039.7			−0.672225			−0.336112	−	0.941822i	$-0.609112\pi$
$193$	−25039.7			−0.672225			−0.336112	+	0.941822i	$0.609112\pi$
$194$	−32775.7	+	4326.14i	−0.870860	+	0.114947i
$195$		0			0
$196$	−36423.1	+	9785.63i	−0.948122	+	0.254728i
$197$	6468.96	−	6468.96i	0.166687	−	0.166687i	−0.618834	−	0.785521i	$-0.712395\pi$
$197$	6468.96	−	6468.96i	0.166687	−	0.166687i	0.785521	+	0.618834i	$0.212395\pi$
$198$		0			0
$199$	55793.6			1.40889			0.704446	−	0.709757i	$-0.251195\pi$
$199$	55793.6			1.40889			0.704446	+	0.709757i	$0.251195\pi$
$200$	−7857.00	−	18914.8i	−0.196425	−	0.472870i
$201$		0			0
$202$	−17331.5	+	22602.5i	−0.424750	+	0.553928i
$203$	1157.99	+	1157.99i	0.0281005	+	0.0281005i
$204$		0			0
$205$	−39202.6	−	39202.6i	−0.932841	−	0.932841i
$206$	5659.85	−	747.058i	0.133374	−	0.0176044i
$207$		0			0
$208$	77452.3	+	20642.4i	1.79023	+	0.477126i
$209$	−73257.5			−1.67710
$210$		0			0
$211$	−11403.6	+	11403.6i	−0.256139	+	0.256139i	−0.823482	−	0.567343i	$-0.807971\pi$
$211$	−11403.6	+	11403.6i	−0.256139	+	0.256139i	0.567343	+	0.823482i	$0.307971\pi$
$212$	9293.79	−	16122.2i	0.206786	−	0.358717i
$213$		0			0
$214$	−44794.0	−	34347.9i	−0.978120	−	0.750019i
$215$	−776.604			−0.0168005
$216$		0			0
$217$			7176.41i			0.152401i
$218$	42.5490	+	32.6264i	0.000895315	+	0.000686524i
$219$		0			0
$220$	−61130.5	+	16423.7i	−1.26303	+	0.339332i
$221$	29352.4	+	29352.4i	0.600979	+	0.600979i
$222$		0			0
$223$		−	15194.4i		−	0.305545i	−0.988261	−	0.152772i	$-0.951180\pi$
$223$		−	15194.4i		−	0.305545i	0.988261	−	0.152772i	$-0.0488201\pi$
$224$	−5371.58	+	4136.04i	−0.107055	+	0.0824306i
$225$		0			0
$226$	54070.0	−	7136.83i	1.05862	−	0.139730i
$227$	−47509.0	+	47509.0i	−0.921986	+	0.921986i	−0.997170	−	0.0751841i	$-0.976046\pi$
$227$	−47509.0	+	47509.0i	−0.921986	+	0.921986i	0.0751841	+	0.997170i	$0.476046\pi$
$228$		0			0
$229$	15628.9	−	15628.9i	0.298028	−	0.298028i	−0.542213	−	0.840241i	$-0.682413\pi$
$229$	15628.9	−	15628.9i	0.298028	−	0.298028i	0.840241	+	0.542213i	$0.182413\pi$
$230$	2057.93	−	2683.81i	0.0389023	−	0.0507336i
$231$		0			0
$232$	−14632.0	−	6043.59i	−0.271849	−	0.112284i
$233$		−	63151.2i		−	1.16324i	−0.813460	−	0.581621i	$-0.802419\pi$
$233$		−	63151.2i		−	1.16324i	0.813460	−	0.581621i	$-0.197581\pi$
$234$		0			0
$235$	49306.1	+	49306.1i	0.892823	+	0.892823i
$236$	19064.1	+	10989.7i	0.342288	+	0.197315i
$237$		0			0
$238$	−3480.69	+	459.426i	−0.0614486	+	0.00811075i
$239$		−	33331.4i		−	0.583522i	−0.956491	−	0.291761i	$-0.905759\pi$
$239$		−	33331.4i		−	0.583522i	0.956491	−	0.291761i	$-0.0942412\pi$
$240$		0			0
$241$	5625.72			0.0968599			0.0484299	−	0.998827i	$-0.484578\pi$
$241$	5625.72			0.0968599			0.0484299	+	0.998827i	$0.484578\pi$
$242$	1005.23	+	7615.84i	0.0171647	+	0.130043i
$243$		0			0
$244$	−40311.0	−	23237.7i	−0.677087	−	0.390313i
$245$	51238.7	−	51238.7i	0.853622	−	0.853622i
$246$		0			0
$247$	−178237.			−2.92149
$248$	−26612.4	−	64066.2i	−0.432693	−	1.04166i
$249$		0			0
$250$	−29759.2	−	22819.2i	−0.476147	−	0.365107i
$251$	62195.0	+	62195.0i	0.987206	+	0.987206i	0.999919	−	0.0127130i	$-0.00404679\pi$
$251$	62195.0	+	62195.0i	0.987206	+	0.987206i	−0.0127130	+	0.999919i	$0.504047\pi$
$252$		0			0
$253$	−2502.80	−	2502.80i	−0.0391007	−	0.0391007i
$254$	−4212.11	−	31911.8i	−0.0652879	−	0.494633i
$255$		0			0
$256$	32616.1	−	56843.2i	0.497683	−	0.867359i
$257$	−22791.9			−0.345075			−0.172538	−	0.985003i	$-0.555197\pi$
$257$	−22791.9			−0.345075			−0.172538	+	0.985003i	$0.555197\pi$
$258$		0			0
$259$	−3664.30	+	3664.30i	−0.0546250	+	0.0546250i
$260$	−148732.	+	39959.1i	−2.20017	+	0.591111i
$261$		0			0
$262$	54747.1	−	71397.2i	0.797551	−	1.04011i
$263$	−126611.			−1.83047			−0.915233	−	0.402926i	$-0.867993\pi$
$263$	−126611.			−1.83047			−0.915233	+	0.402926i	$0.867993\pi$
$264$		0			0
$265$			35754.3i			0.509139i
$266$	9173.05	−	11962.8i	0.129643	−	0.169072i
$267$		0			0
$268$	52109.6	−	90395.9i	0.725518	−	1.25858i
$269$	−65428.7	−	65428.7i	−0.904198	−	0.904198i	0.0915982	−	0.995796i	$-0.470802\pi$
$269$	−65428.7	−	65428.7i	−0.904198	−	0.904198i	−0.995796	+	0.0915982i	$0.970802\pi$
$270$		0			0
$271$		−	93429.2i		−	1.27217i	−0.771621	−	0.636083i	$-0.780554\pi$
$271$		−	93429.2i		−	1.27217i	0.771621	−	0.636083i	$-0.219446\pi$
$272$	29369.6	−	17008.9i	0.396972	−	0.229900i
$273$		0			0
$274$	16314.9	+	123605.i	0.217312	+	1.64640i
$275$	29122.0	−	29122.0i	0.385085	−	0.385085i
$276$		0			0
$277$	105271.	−	105271.i	1.37198	−	1.37198i	0.514477	−	0.857504i	$-0.327986\pi$
$277$	105271.	−	105271.i	1.37198	−	1.37198i	0.857504	−	0.514477i	$-0.172014\pi$
$278$	96209.4	+	73773.0i	1.24488	+	0.954570i
$279$		0			0
$280$	4972.59	−	12039.0i	0.0634259	−	0.153559i
$281$			42955.1i			0.544004i	0.962297	+	0.272002i	$0.0876857\pi$
$281$			42955.1i			0.544004i	−0.962297	+	0.272002i	$0.912314\pi$
$282$		0			0
$283$	−36538.7	−	36538.7i	−0.456226	−	0.456226i	0.441189	−	0.897414i	$-0.354557\pi$
$283$	−36538.7	−	36538.7i	−0.456226	−	0.456226i	−0.897414	+	0.441189i	$0.854557\pi$
$284$	47991.5	−	12893.7i	0.595015	−	0.159860i
$285$		0			0
$286$	21091.3	+	159792.i	0.257853	+	1.95354i
$287$		−	11939.9i		−	0.144957i
$288$		0			0
$289$	−65944.8			−0.789559
$290$	30155.0	−	3980.24i	0.358561	−	0.0473274i
$291$		0			0
$292$	3003.15	+	11178.0i	0.0352217	+	0.131099i
$293$	45359.7	−	45359.7i	0.528367	−	0.528367i	−0.391719	−	0.920085i	$-0.628119\pi$
$293$	45359.7	−	45359.7i	0.528367	−	0.528367i	0.920085	+	0.391719i	$0.128119\pi$
$294$		0			0
$295$	−42278.5			−0.485820
$296$	19124.0	−	46300.7i	0.218271	−	0.528450i
$297$		0			0
$298$	−40523.5	+	52847.9i	−0.456326	+	0.595107i
$299$	−6089.36	−	6089.36i	−0.0681129	−	0.0681129i
$300$		0			0
$301$	−118.265	−	118.265i	−0.00130534	−	0.00130534i
$302$	−77150.3	+	10183.3i	−0.845909	+	0.111654i
$303$		0			0
$304$	−37528.9	+	140813.i	−0.406087	+	1.52368i
$305$	89398.0			0.961011
$306$		0			0
$307$	−10035.4	+	10035.4i	−0.106478	+	0.106478i	−0.758339	−	0.651861i	$-0.773989\pi$
$307$	−10035.4	+	10035.4i	−0.106478	+	0.106478i	0.651861	+	0.758339i	$0.273989\pi$
$308$	−11810.3	−	6808.16i	−0.124497	−	0.0717676i
$309$		0			0
$310$	105773.	+	81106.2i	1.10065	+	0.843977i
$311$	−102401.			−1.05873			−0.529365	−	0.848394i	$-0.677570\pi$
$311$	−102401.			−1.05873			−0.529365	+	0.848394i	$0.677570\pi$
$312$		0			0
$313$			60933.1i			0.621963i	0.950416	+	0.310981i	$0.100658\pi$
$313$			60933.1i			0.621963i	−0.950416	+	0.310981i	$0.899342\pi$
$314$	81240.3	+	62294.7i	0.823971	+	0.631818i
$315$		0			0
$316$	−14191.4	−	52821.8i	−0.142119	−	0.528980i
$317$	10217.2	+	10217.2i	0.101675	+	0.101675i	0.756115	−	0.654439i	$-0.227095\pi$
$317$	10217.2	+	10217.2i	0.101675	+	0.101675i	−0.654439	+	0.756115i	$0.727095\pi$
$318$		0			0
$319$		−	31833.0i		−	0.312821i
$320$	252.488	+	125916.i	0.00246571	+	1.22965i
$321$		0			0
$322$	722.094	−	95.3110i	0.00696437	−	0.000919245i
$323$	−53364.3	+	53364.3i	−0.511500	+	0.511500i
$324$		0			0
$325$	70854.6	−	70854.6i	0.670813	−	0.670813i
$326$	60834.0	−	79335.2i	0.572415	−	0.746502i
$327$		0			0
$328$	44276.9	+	106592.i	0.411557	+	0.990775i
$329$			15017.1i			0.138738i
$330$		0			0
$331$	123603.	+	123603.i	1.12817	+	1.12817i	0.990475	+	0.137692i	$0.0439684\pi$
$331$	123603.	+	123603.i	1.12817	+	1.12817i	0.137692	+	0.990475i	$0.456032\pi$
$332$	1826.07	−	3167.74i	0.0165669	−	0.0287391i
$333$		0			0
$334$	45105.1	−	5953.53i	0.404327	−	0.0533681i
$335$			200472.i			1.78634i
$336$		0			0
$337$	−102441.			−0.902018			−0.451009	−	0.892519i	$-0.648936\pi$
$337$	−102441.			−0.902018			−0.451009	+	0.892519i	$0.648936\pi$
$338$	36366.0	+	275515.i	0.318318	+	2.41164i
$339$		0			0
$340$	−32566.6	+	56494.1i	−0.281718	+	0.488704i
$341$	98639.0	−	98639.0i	0.848281	−	0.848281i
$342$		0			0
$343$	31501.6			0.267760
$344$	1494.35	+	617.227i	0.0126280	+	0.00521588i
$345$		0			0
$346$	50678.2	+	38859.9i	0.423320	+	0.324601i
$347$	−63342.4	−	63342.4i	−0.526061	−	0.526061i	0.393335	−	0.919395i	$-0.371321\pi$
$347$	−63342.4	−	63342.4i	−0.526061	−	0.526061i	−0.919395	+	0.393335i	$0.871321\pi$
$348$		0			0
$349$	−114645.	−	114645.i	−0.941247	−	0.941247i	0.0571205	−	0.998367i	$-0.481808\pi$
$349$	−114645.	−	114645.i	−0.941247	−	0.941247i	−0.998367	+	0.0571205i	$0.981808\pi$
$350$	1109.02	+	8402.15i	0.00905323	+	0.0685889i
$351$		0			0
$352$	130681.	+	16982.4i	1.05470	+	0.137061i
$353$	94430.7			0.757816			0.378908	−	0.925434i	$-0.376300\pi$
$353$	94430.7			0.757816			0.378908	+	0.925434i	$0.376300\pi$
$354$		0			0
$355$	−67512.8	+	67512.8i	−0.535709	+	0.535709i
$356$	6077.86	+	22622.4i	0.0479568	+	0.178500i
$357$		0			0
$358$	87220.7	−	113747.i	0.680540	−	0.887511i
$359$	59001.0			0.457794			0.228897	−	0.973451i	$-0.426488\pi$
$359$	59001.0			0.457794			0.228897	+	0.973451i	$0.426488\pi$
$360$		0			0
$361$		−	193724.i		−	1.48651i
$362$	77723.6	−	101361.i	0.593111	−	0.773492i
$363$		0			0
$364$	−28734.7	−	16564.4i	−0.216872	−	0.125018i
$365$	−15724.8	−	15724.8i	−0.118032	−	0.118032i
$366$		0			0
$367$			120112.i			0.891775i	0.895089	+	0.445888i	$0.147112\pi$
$367$			120112.i			0.891775i	−0.895089	+	0.445888i	$0.852888\pi$
$368$	−6092.92	+	3528.62i	−0.0449915	+	0.0260561i
$369$		0			0
$370$	12594.9	+	95421.0i	0.0920004	+	0.697012i
$371$	−5444.83	+	5444.83i	−0.0395582	+	0.0395582i
$372$		0			0
$373$	−113849.	+	113849.i	−0.818300	+	0.818300i	−0.985862	−	0.167562i	$-0.946411\pi$
$373$	−113849.	+	113849.i	−0.818300	+	0.818300i	0.167562	+	0.985862i	$0.446411\pi$
$374$	54156.5	+	41527.0i	0.387175	+	0.296884i
$375$		0			0
$376$	−55688.2	−	134063.i	−0.393901	−	0.948272i
$377$		−	77450.4i		−	0.544930i
$378$		0			0
$379$	−75841.4	−	75841.4i	−0.527993	−	0.527993i	0.391981	−	0.919973i	$-0.371790\pi$
$379$	−75841.4	−	75841.4i	−0.527993	−	0.527993i	−0.919973	+	0.391981i	$0.871790\pi$
$380$	−72647.9	−	270403.i	−0.503102	−	1.87259i
$381$		0			0
$382$	−32973.2	−	249811.i	−0.225961	−	1.71192i
$383$			80282.4i			0.547297i	0.961830	+	0.273648i	$0.0882304\pi$
$383$			80282.4i			0.547297i	−0.961830	+	0.273648i	$0.911770\pi$
$384$		0			0
$385$	26191.8			0.176703
$386$	−99297.6	+	13106.5i	−0.666445	+	0.0879657i
$387$		0			0
$388$	−127711.	+	34311.6i	−0.848330	+	0.227917i
$389$	−89476.2	+	89476.2i	−0.591301	+	0.591301i	−0.937983	−	0.346682i	$-0.887308\pi$
$389$	−89476.2	+	89476.2i	−0.591301	+	0.591301i	0.346682	+	0.937983i	$0.387308\pi$
$390$		0			0
$391$	−3646.31			−0.0238507
$392$	−139317.	+	57870.9i	−0.906636	+	0.376607i
$393$		0			0
$394$	22267.3	−	29039.4i	0.143441	−	0.187066i
$395$	74307.8	+	74307.8i	0.476256	+	0.476256i
$396$		0			0
$397$	128824.	+	128824.i	0.817363	+	0.817363i	0.985725	−	0.168362i	$-0.0538479\pi$
$397$	128824.	+	128824.i	0.817363	+	0.817363i	−0.168362	+	0.985725i	$0.553848\pi$
$398$	221255.	−	29204.0i	1.39678	−	0.184364i
$399$		0			0
$400$	−41058.3	−	70896.1i	−0.256615	−	0.443101i
$401$	−71110.1			−0.442224			−0.221112	−	0.975248i	$-0.570969\pi$
$401$	−71110.1			−0.442224			−0.221112	+	0.975248i	$0.570969\pi$
$402$		0			0
$403$	239991.	−	239991.i	1.47769	−	1.47769i
$404$	−56899.1	+	98704.4i	−0.348612	+	0.604747i
$405$		0			0
$406$	5198.27	+	3986.02i	0.0315360	+	0.0241817i
$407$	100731.			0.608097
$408$		0			0
$409$			87416.4i			0.522572i	0.965261	+	0.261286i	$0.0841466\pi$
$409$			87416.4i			0.522572i	−0.965261	+	0.261286i	$0.915853\pi$
$410$	−175982.	−	134942.i	−1.04689	−	0.802750i
$411$		0			0
$412$	22053.7	−	5925.08i	0.129923	−	0.0349059i
$413$	−6438.36	−	6438.36i	−0.0377464	−	0.0377464i
$414$		0			0
$415$			7025.11i			0.0407903i
$416$	317950.	+	41318.5i	1.83727	+	0.238758i
$417$		0			0
$418$	−290510.	+	38345.2i	−1.66268	+	0.219461i
$419$	−156666.	+	156666.i	−0.892373	+	0.892373i	−0.994746	−	0.102373i	$-0.967356\pi$
$419$	−156666.	+	156666.i	−0.892373	+	0.892373i	0.102373	+	0.994746i	$0.467356\pi$
$420$		0			0
$421$	20636.7	−	20636.7i	0.116433	−	0.116433i	−0.646490	−	0.762923i	$-0.723764\pi$
$421$	20636.7	−	20636.7i	0.116433	−	0.116433i	0.762923	+	0.646490i	$0.223764\pi$
$422$	−39253.1	+	51191.0i	−0.220419	+	0.287454i
$423$		0			0
$424$	28416.7	−	68798.9i	0.158067	−	0.382692i
$425$		−	42427.8i		−	0.234894i
$426$		0			0
$427$	13614.0	+	13614.0i	0.0746670	+	0.0746670i
$428$	−195614.	−	112763.i	−1.06785	−	0.615575i
$429$		0			0
$430$	−3079.71	+	406.498i	−0.0166561	+	0.00219848i
$431$		−	294349.i		−	1.58456i	−0.610160	−	0.792279i	$-0.708895\pi$
$431$		−	294349.i		−	1.58456i	0.610160	−	0.792279i	$-0.291105\pi$
$432$		0			0
$433$	240460.			1.28253			0.641264	−	0.767321i	$-0.278411\pi$
$433$	240460.			1.28253			0.641264	+	0.767321i	$0.278411\pi$
$434$	3756.35	+	28458.8i	0.0199428	+	0.151091i
$435$		0			0
$436$	185.810	+	107.112i	0.000977454	+	0.000563462i
$437$	11070.8	−	11070.8i	0.0579716	−	0.0579716i
$438$		0			0
$439$	−294699.			−1.52915			−0.764574	−	0.644536i	$-0.777051\pi$
$439$	−294699.			−1.52915			−0.764574	+	0.644536i	$0.777051\pi$
$440$	−233823.	+	97127.2i	−1.20776	+	0.501690i
$441$		0			0
$442$	131764.	+	101036.i	0.674454	+	0.517168i
$443$	−118964.	−	118964.i	−0.606187	−	0.606187i	0.335760	−	0.941948i	$-0.391007\pi$
$443$	−118964.	−	118964.i	−0.606187	−	0.606187i	−0.941948	+	0.335760i	$0.891007\pi$
$444$		0			0
$445$	−31824.4	−	31824.4i	−0.160709	−	0.160709i
$446$	−7953.22	−	60255.1i	−0.0399828	−	0.302917i
$447$		0			0
$448$	−19136.6	+	19213.5i	−0.0953476	+	0.0957308i
$449$	82129.5			0.407386			0.203693	−	0.979035i	$-0.434706\pi$
$449$	82129.5			0.407386			0.203693	+	0.979035i	$0.434706\pi$
$450$		0			0
$451$	−164113.	+	164113.i	−0.806844	+	0.806844i
$452$	210684.	−	56603.7i	1.03123	−	0.277056i
$453$		0			0
$454$	−163534.	+	213270.i	−0.793409	+	1.03471i
$455$	63725.2			0.307814
$456$		0			0
$457$			172358.i			0.825277i	0.910895	+	0.412638i	$0.135393\pi$
$457$			172358.i			0.825277i	−0.910895	+	0.412638i	$0.864607\pi$
$458$	53797.4	−	70158.6i	0.256466	−	0.334465i
$459$		0			0
$460$	6756.16	−	11720.1i	0.0319289	−	0.0553880i
$461$	−96898.8	−	96898.8i	−0.455950	−	0.455950i	0.441374	−	0.897323i	$-0.354491\pi$
$461$	−96898.8	−	96898.8i	−0.455950	−	0.455950i	−0.897323	+	0.441374i	$0.854491\pi$
$462$		0			0
$463$			142244.i			0.663549i	0.943359	+	0.331775i	$0.107647\pi$
$463$			142244.i			0.663549i	−0.943359	+	0.331775i	$0.892353\pi$
$464$	−61188.1	−	16307.7i	−0.284204	−	0.0757453i
$465$		0			0
$466$	−33055.2	−	250433.i	−0.152219	−	1.15324i
$467$	139194.	−	139194.i	0.638246	−	0.638246i	−0.311877	−	0.950123i	$-0.600958\pi$
$467$	139194.	−	139194.i	0.638246	−	0.638246i	0.950123	+	0.311877i	$0.100958\pi$
$468$		0			0
$469$	−30528.8	+	30528.8i	−0.138792	+	0.138792i
$470$	221337.	+	169720.i	1.00198	+	0.768313i
$471$		0			0
$472$	81352.8	+	33601.9i	0.365164	+	0.150827i
$473$			3251.08i			0.0145313i
$474$		0			0
$475$	128818.	+	128818.i	0.570936	+	0.570936i
$476$	−13562.6	+	3643.80i	−0.0598589	+	0.0160820i
$477$		0			0
$478$	−17446.6	−	132179.i	−0.0763582	−	0.578504i
$479$			216764.i			0.944749i	0.881398	+	0.472374i	$0.156603\pi$
$479$			216764.i			0.944749i	−0.881398	+	0.472374i	$0.843397\pi$
$480$		0			0
$481$	245080.			1.05930
$482$	22309.4	−	2944.67i	0.0960270	−	0.0126748i
$483$		0			0
$484$	7972.72	+	29675.2i	0.0340342	+	0.126679i
$485$	179659.	−	179659.i	0.763776	−	0.763776i
$486$		0			0
$487$	146986.			0.619752			0.309876	−	0.950777i	$-0.399713\pi$
$487$	146986.			0.619752			0.309876	+	0.950777i	$0.399713\pi$
$488$	−172021.	−	71051.4i	−0.722340	−	0.298355i
$489$		0			0
$490$	176372.	−	230012.i	0.734579	−	0.957985i
$491$	207292.	+	207292.i	0.859843	+	0.859843i	0.991319	−	0.131476i	$-0.0419716\pi$
$491$	207292.	+	207292.i	0.859843	+	0.859843i	−0.131476	+	0.991319i	$0.541972\pi$
$492$		0			0
$493$	−23188.7	−	23188.7i	−0.0954074	−	0.0954074i
$494$	−706818.	+	93294.7i	−2.89637	+	0.382299i
$495$		0			0
$496$	−139068.	−	240131.i	−0.565281	−	0.976080i
$497$	−20562.3			−0.0832452
$498$		0			0
$499$	5591.76	−	5591.76i	0.0224568	−	0.0224568i	−0.695789	−	0.718246i	$-0.744945\pi$
$499$	5591.76	−	5591.76i	0.0224568	−	0.0224568i	0.718246	+	0.695789i	$0.244945\pi$
$500$	−129957.	−	74915.2i	−0.519829	−	0.299661i
$501$		0			0
$502$	279195.	+	214086.i	1.10790	+	0.849534i
$503$	−154345.			−0.610037			−0.305018	−	0.952346i	$-0.598663\pi$
$503$	−154345.			−0.610037			−0.305018	+	0.952346i	$0.598663\pi$
$504$		0			0
$505$		−	218897.i		−	0.858337i
$506$	−11235.1	−	8615.06i	−0.0438811	−	0.0336478i
$507$		0			0
$508$	−33407.2	−	124345.i	−0.129453	−	0.481837i
$509$	7996.84	+	7996.84i	0.0308662	+	0.0308662i	0.722371	−	0.691505i	$-0.243052\pi$
$509$	7996.84	+	7996.84i	0.0308662	+	0.0308662i	−0.691505	+	0.722371i	$0.743052\pi$
$510$		0			0
$511$		−	4789.30i		−	0.0183413i
$512$	99589.3	−	242490.i	0.379903	−	0.925026i
$513$		0			0
$514$	−90383.6	+	11930.0i	−0.342108	+	0.0451557i
$515$	−31024.4	+	31024.4i	−0.116974	+	0.116974i
$516$		0			0
$517$	206409.	−	206409.i	0.772231	−	0.772231i
$518$	−12613.2	+	16449.2i	−0.0470072	+	0.0613033i
$519$		0			0
$520$	−568896.	+	236313.i	−2.10390	+	0.873938i
$521$			215831.i			0.795130i	0.917574	+	0.397565i	$0.130145\pi$
$521$			215831.i			0.795130i	−0.917574	+	0.397565i	$0.869855\pi$
$522$		0			0
$523$	−73690.2	−	73690.2i	−0.269405	−	0.269405i	0.559455	−	0.828861i	$-0.311010\pi$
$523$	−73690.2	−	73690.2i	−0.269405	−	0.269405i	−0.828861	+	0.559455i	$0.811010\pi$
$524$	179734.	−	311789.i	0.654587	−	1.13553i
$525$		0			0
$526$	−502091.	+	66272.3i	−1.81473	+	0.239530i
$527$		−	143707.i		−	0.517435i
$528$		0			0
$529$	−279085.			−0.997297
$530$	18714.9	+	141787.i	0.0666247	+	0.504761i
$531$		0			0
$532$	30115.0	−	52241.3i	0.106404	−	0.184583i
$533$	−399290.	+	399290.i	−1.40551	+	1.40551i
$534$		0			0
$535$	433814.			1.51564
$536$	159330.	−	385750.i	0.554585	−	1.34269i
$537$		0			0
$538$	−293712.	−	225217.i	−1.01474	−	0.778102i
$539$	−214499.	−	214499.i	−0.738325	−	0.738325i
$540$		0			0
$541$	260589.	+	260589.i	0.890352	+	0.890352i	0.994556	−	0.104204i	$-0.0332294\pi$
$541$	260589.	+	260589.i	0.890352	+	0.890352i	−0.104204	+	0.994556i	$0.533229\pi$
$542$	−48903.6	−	370503.i	−0.166473	−	1.26123i
$543$		0			0
$544$	107565.	−	82823.6i	0.363475	−	0.279870i
$545$	−412.072			−0.00138733
$546$		0			0
$547$	−87290.1	+	87290.1i	−0.291736	+	0.291736i	−0.837766	−	0.546030i	$-0.816139\pi$
$547$	−87290.1	+	87290.1i	−0.291736	+	0.291736i	0.546030	+	0.837766i	$0.316139\pi$
$548$	129397.	+	481629.i	0.430888	+	1.60381i
$549$		0			0
$550$	100243.	−	130730.i	0.331382	−	0.432165i
$551$	140809.			0.463796
$552$		0			0
$553$			22631.9i			0.0740066i
$554$	362360.	−	472564.i	1.18065	−	1.53972i
$555$		0			0
$556$	420143.	+	242196.i	1.35909	+	0.783460i
$557$	342322.	+	342322.i	1.10338	+	1.10338i	0.994000	+	0.109377i	$0.0348855\pi$
$557$	342322.	+	342322.i	1.10338	+	1.10338i	0.109377	+	0.994000i	$0.465114\pi$
$558$		0			0
$559$			7909.94i			0.0253134i
$560$	13417.7	−	50344.8i	0.0427862	−	0.160538i
$561$		0			0
$562$	22484.0	+	170343.i	0.0711870	+	0.539326i
$563$	77521.3	−	77521.3i	0.244571	−	0.244571i	−0.574167	−	0.818738i	$-0.694674\pi$
$563$	77521.3	−	77521.3i	0.244571	−	0.244571i	0.818738	+	0.574167i	$0.194674\pi$
$564$		0			0
$565$	−296383.	+	296383.i	−0.928447	+	0.928447i
$566$	−164023.	−	125772.i	−0.512003	−	0.392602i
$567$		0			0
$568$	183567.	−	76251.5i	0.568980	−	0.236348i
$569$			304409.i			0.940229i	0.882605	+	0.470115i	$0.155787\pi$
$569$			304409.i			0.940229i	−0.882605	+	0.470115i	$0.844213\pi$
$570$		0			0
$571$	−254051.	−	254051.i	−0.779201	−	0.779201i	0.200494	−	0.979695i	$-0.435745\pi$
$571$	−254051.	−	254051.i	−0.779201	−	0.779201i	−0.979695	+	0.200494i	$0.935745\pi$
$572$	167280.	+	622631.i	0.511271	+	1.90300i
$573$		0			0
$574$	−6249.71	−	47349.0i	−0.0189686	−	0.143710i
$575$			8801.94i			0.0266221i
$576$		0			0
$577$	−486229.			−1.46046			−0.730229	−	0.683202i	$-0.760587\pi$
$577$	−486229.			−1.46046			−0.730229	+	0.683202i	$0.760587\pi$
$578$	−261511.	+	34517.5i	−0.782770	+	0.103320i
$579$		0			0
$580$	117499.	−	31568.1i	0.349285	−	0.0938409i
$581$	−1069.82	+	1069.82i	−0.00316926	+	0.00316926i
$582$		0			0
$583$	149677.			0.440371
$584$	17760.2	+	42755.6i	0.0520741	+	0.125362i
$585$		0			0
$586$	156136.	−	203621.i	0.454682	−	0.592964i
$587$	26612.4	+	26612.4i	0.0772339	+	0.0772339i	0.744668	−	0.667435i	$-0.232608\pi$
$587$	26612.4	+	26612.4i	0.0772339	+	0.0772339i	−0.667435	+	0.744668i	$0.732608\pi$
$588$		0			0
$589$	436317.	+	436317.i	1.25768	+	1.25768i
$590$	−167660.	+	22129.8i	−0.481642	+	0.0635732i
$591$		0			0
$592$	51603.1	−	193620.i	0.147242	−	0.552469i
$593$	−301795.			−0.858228			−0.429114	−	0.903250i	$-0.641174\pi$
$593$	−301795.			−0.858228			−0.429114	+	0.903250i	$0.641174\pi$
$594$		0			0
$595$	19079.4	−	19079.4i	0.0538927	−	0.0538927i
$596$	−133038.	+	230785.i	−0.374528	+	0.649703i
$597$		0			0
$598$	−27335.3	−	20960.6i	−0.0764402	−	0.0586141i
$599$	208748.			0.581795			0.290897	−	0.956754i	$-0.406046\pi$
$599$	208748.			0.581795			0.290897	+	0.956754i	$0.406046\pi$
$600$		0			0
$601$		−	355946.i		−	0.985451i	−0.870185	−	0.492725i	$-0.836001\pi$
$601$		−	355946.i		−	0.985451i	0.870185	−	0.492725i	$-0.163999\pi$
$602$	−530.896	−	407.089i	−0.00146493	−	0.00112330i
$603$		0			0
$604$	−300617.	+	80765.6i	−0.824025	+	0.221387i
$605$	−41746.1	−	41746.1i	−0.114053	−	0.114053i
$606$		0			0
$607$		−	680696.i		−	1.84746i	−0.383040	−	0.923732i	$-0.625123\pi$
$607$		−	680696.i		−	1.84746i	0.383040	−	0.923732i	$-0.374877\pi$
$608$	−75119.4	+	578051.i	−0.203210	+	1.56372i
$609$		0			0
$610$	354517.	−	46793.6i	0.952747	−	0.125756i
$611$	502197.	−	502197.i	1.34522	−	1.34522i
$612$		0			0
$613$	−504818.	+	504818.i	−1.34343	+	1.34343i	−0.450800	+	0.892625i	$0.648861\pi$
$613$	−504818.	+	504818.i	−1.34343	+	1.34343i	−0.892625	+	0.450800i	$0.851139\pi$
$614$	−34543.7	+	45049.4i	−0.0916289	+	0.119496i
$615$		0			0
$616$	−50398.6	−	20816.6i	−0.132818	−	0.0548591i
$617$		−	601668.i		−	1.58047i	−0.612803	−	0.790236i	$-0.709958\pi$
$617$		−	601668.i		−	1.58047i	0.612803	−	0.790236i	$-0.290042\pi$
$618$		0			0
$619$	−34687.6	−	34687.6i	−0.0905300	−	0.0905300i	0.660391	−	0.750922i	$-0.270390\pi$
$619$	−34687.6	−	34687.6i	−0.0905300	−	0.0905300i	−0.750922	+	0.660391i	$0.770390\pi$
$620$	461907.	+	266271.i	1.20163	+	0.692691i
$621$		0			0
$622$	−406084.	+	53600.0i	−1.04963	+	0.138543i
$623$		−	9692.72i		−	0.0249729i
$624$		0			0
$625$	488225.			1.24985
$626$	31894.2	+	241636.i	0.0813885	+	0.616615i
$627$		0			0
$628$	354774.	+	204513.i	0.899564	+	0.518562i
$629$	73377.0	−	73377.0i	0.185464	−	0.185464i
$630$		0			0
$631$	557209.			1.39946			0.699728	−	0.714409i	$-0.253304\pi$
$631$	557209.			1.39946			0.699728	+	0.714409i	$0.253304\pi$
$632$	−83926.1	−	202042.i	−0.210118	−	0.505834i
$633$		0			0
$634$	45865.6	+	35169.5i	0.114106	+	0.0874960i
$635$	174924.	+	174924.i	0.433812	+	0.433812i
$636$		0			0
$637$	−521881.	−	521881.i	−1.28615	−	1.28615i
$638$	−16662.3	−	126237.i	−0.0409350	−	0.310131i
$639$		0			0
$640$	66909.6	+	499201.i	0.163353	+	1.21875i
$641$	−354670.			−0.863193			−0.431597	−	0.902067i	$-0.642050\pi$
$641$	−354670.			−0.863193			−0.431597	+	0.902067i	$0.642050\pi$
$642$		0			0
$643$	−89105.3	+	89105.3i	−0.215517	+	0.215517i	−0.806606	−	0.591089i	$-0.798698\pi$
$643$	−89105.3	+	89105.3i	−0.215517	+	0.215517i	0.591089	+	0.806606i	$0.298698\pi$
$644$	2813.65	−	755.931i	0.00678420	−	0.00182268i
$645$		0			0
$646$	−183689.	+	239554.i	−0.440168	+	0.574035i
$647$	669197.			1.59862			0.799311	−	0.600918i	$-0.205198\pi$
$647$	669197.			1.59862			0.799311	+	0.600918i	$0.205198\pi$
$648$		0			0
$649$			176989.i			0.420201i
$650$	243894.	−	318069.i	0.577264	−	0.752825i
$651$		0			0
$652$	199717.	−	346455.i	0.469807	−	0.814988i
$653$	−6136.50	−	6136.50i	−0.0143911	−	0.0143911i	0.699875	−	0.714266i	$-0.253239\pi$
$653$	−6136.50	−	6136.50i	−0.0143911	−	0.0143911i	−0.714266	+	0.699875i	$0.753239\pi$
$654$		0			0
$655$			691457.i			1.61169i
$656$	231378.	+	399524.i	0.537668	+	0.928400i
$657$		0			0
$658$	7860.42	+	59552.0i	0.0181549	+	0.137545i
$659$	−484888.	+	484888.i	−1.11653	+	1.11653i	−0.124283	+	0.992247i	$0.539663\pi$
$659$	−484888.	+	484888.i	−1.11653	+	1.11653i	−0.992247	+	0.124283i	$0.960337\pi$
$660$		0			0
$661$	−71185.1	+	71185.1i	−0.162924	+	0.162924i	−0.783861	−	0.620937i	$-0.786752\pi$
$661$	−71185.1	+	71185.1i	−0.162924	+	0.162924i	0.620937	+	0.783861i	$0.286752\pi$
$662$	554859.	+	425463.i	1.26610	+	0.970837i
$663$		0			0
$664$	5583.39	−	13517.8i	0.0126637	−	0.0306599i
$665$			115856.i			0.261984i
$666$		0			0
$667$	4810.65	+	4810.65i	0.0108131	+	0.0108131i
$668$	175753.	−	47218.7i	0.393867	−	0.105818i
$669$		0			0
$670$	104933.	+	794992.i	0.233756	+	1.77098i
$671$		−	374244.i		−	0.831209i
$672$		0			0
$673$	116807.			0.257893			0.128947	−	0.991652i	$-0.458840\pi$
$673$	116807.			0.257893			0.128947	+	0.991652i	$0.458840\pi$
$674$	−406242.	+	53620.9i	−0.894262	+	0.118036i
$675$		0			0
$676$	288426.	+	1.07355e6i	0.631163	+	2.34925i
$677$	−562443.	+	562443.i	−1.22716	+	1.22716i	−0.262127	+	0.965033i	$0.584424\pi$
$677$	−562443.	+	562443.i	−1.22716	+	1.22716i	−0.965033	+	0.262127i	$0.915576\pi$
$678$		0			0
$679$	54718.7			0.118685
$680$	−99575.4	+	241080.i	−0.215345	+	0.521366i
$681$		0			0
$682$	339533.	−	442794.i	0.729983	−	0.951991i
$683$	−392290.	−	392290.i	−0.840941	−	0.840941i	0.148040	−	0.988981i	$-0.452703\pi$
$683$	−392290.	−	392290.i	−0.840941	−	0.840941i	−0.988981	+	0.148040i	$0.952703\pi$
$684$		0			0
$685$	−677539.	−	677539.i	−1.44395	−	1.44395i
$686$	124923.	−	16488.9i	0.265457	−	0.0350384i
$687$		0			0
$688$	6249.09	+	1665.49i	0.0132020	+	0.00351856i
$689$	364168.			0.767120
$690$		0			0
$691$	424716.	−	424716.i	0.889493	−	0.889493i	−0.104981	−	0.994474i	$-0.533478\pi$
$691$	424716.	−	424716.i	0.889493	−	0.889493i	0.994474	+	0.104981i	$0.0334781\pi$
$692$	221310.	+	127576.i	0.462157	+	0.266415i
$693$		0			0
$694$	−284346.	−	218036.i	−0.590376	−	0.452698i
$695$	−931755.			−1.92900
$696$		0			0
$697$			239095.i			0.492159i
$698$	−514645.	−	394627.i	−1.05632	−	0.809984i
$699$		0			0
$700$	8795.87	+	32739.1i	0.0179508	+	0.0668145i
$701$	92393.5	+	92393.5i	0.188021	+	0.188021i	0.794840	−	0.606819i	$-0.207555\pi$
$701$	92393.5	+	92393.5i	0.188021	+	0.188021i	−0.606819	+	0.794840i	$0.707555\pi$
$702$		0			0
$703$			445569.i			0.901580i
$704$	527119.	−	1056.98i	1.06356	−	0.00213267i
$705$		0			0
$706$	374475.	−	49427.9i	0.751300	−	0.0991659i
$707$	33334.7	−	33334.7i	0.0666896	−	0.0666896i
$708$		0			0
$709$	29997.3	−	29997.3i	0.0596746	−	0.0596746i	−0.676640	−	0.736314i	$-0.736565\pi$
$709$	29997.3	−	29997.3i	0.0596746	−	0.0596746i	0.736314	+	0.676640i	$0.236565\pi$
$710$	−232391.	+	303067.i	−0.461001	+	0.601205i
$711$		0			0
$712$	35943.6	+	86530.1i	0.0709025	+	0.170690i
$713$			29812.9i			0.0586443i
$714$		0			0
$715$	−875896.	−	875896.i	−1.71333	−	1.71333i
$716$	286344.	−	496729.i	0.558551	−	0.968933i
$717$		0			0
$718$	233974.	−	30882.9i	0.453858	−	0.0599058i
$719$		−	284133.i		−	0.549622i	−0.961498	−	0.274811i	$-0.911385\pi$
$719$		−	284133.i		−	0.549622i	0.961498	−	0.274811i	$-0.0886152\pi$
$720$		0			0
$721$	−9449.07			−0.0181769
$722$	−101401.	−	768232.i	−0.194521	−	1.47373i
$723$		0			0
$724$	255165.	−	442642.i	0.486793	−	0.844454i
$725$	−55975.8	+	55975.8i	−0.106494	+	0.106494i
$726$		0			0
$727$	39096.3			0.0739719			0.0369860	−	0.999316i	$-0.488224\pi$
$727$	39096.3			0.0739719			0.0369860	+	0.999316i	$0.488224\pi$
$728$	−122621.	−	50647.3i	−0.231367	−	0.0955638i
$729$		0			0
$730$	−70589.3	−	54127.6i	−0.132463	−	0.101572i
$731$	2368.24	+	2368.24i	0.00443191	+	0.00443191i
$732$		0			0
$733$	82927.3	+	82927.3i	0.154344	+	0.154344i	0.780055	−	0.625711i	$-0.215191\pi$
$733$	82927.3	+	82927.3i	0.154344	+	0.154344i	−0.625711	+	0.780055i	$0.715191\pi$
$734$	62870.4	+	476318.i	0.116695	+	0.884107i
$735$		0			0
$736$	−22315.1	+	17182.3i	−0.0411950	+	0.0317195i
$737$	839229.			1.54506
$738$		0			0
$739$	−97643.8	+	97643.8i	−0.178795	+	0.178795i	−0.790830	−	0.612035i	$-0.790351\pi$
$739$	−97643.8	+	97643.8i	−0.178795	+	0.178795i	0.612035	+	0.790830i	$0.290351\pi$
$740$	99892.4	+	371809.i	0.182419	+	0.678980i
$741$		0			0
$742$	−18742.1	+	24442.0i	−0.0340416	+	0.0443945i
$743$	552181.			1.00024			0.500120	−	0.865956i	$-0.333289\pi$
$743$	552181.			1.00024			0.500120	+	0.865956i	$0.333289\pi$
$744$		0			0
$745$		−	511813.i		−	0.922145i
$746$	−391889.	+	511073.i	−0.704182	+	0.918344i
$747$		0			0
$748$	236500.	+	136332.i	0.422695	+	0.243667i
$749$	66063.3	+	66063.3i	0.117760	+	0.117760i
$750$		0			0
$751$		−	318447.i		−	0.564621i	−0.959323	−	0.282310i	$-0.908899\pi$
$751$		−	318447.i		−	0.564621i	0.959323	−	0.282310i	$-0.0911008\pi$
$752$	−291010.	−	502491.i	−0.514603	−	0.888573i
$753$		0			0
$754$	−40539.9	−	307138.i	−0.0713082	−	0.540244i
$755$	422898.	−	422898.i	0.741894	−	0.741894i
$756$		0			0
$757$	−478701.	+	478701.i	−0.835357	+	0.835357i	−0.988244	−	0.152886i	$-0.951143\pi$
$757$	−478701.	+	478701.i	−0.835357	+	0.835357i	0.152886	+	0.988244i	$0.451143\pi$
$758$	−340455.	−	261059.i	−0.592544	−	0.454361i
$759$		0			0
$760$	−429630.	−	1.03428e6i	−0.743819	−	1.79066i
$761$		−	398315.i		−	0.687793i	−0.939008	−	0.343896i	$-0.888253\pi$
$761$		−	398315.i		−	0.687793i	0.939008	−	0.343896i	$-0.111747\pi$
$762$		0			0
$763$	−62.7523	−	62.7523i	−0.000107790	−	0.000107790i
$764$	−261517.	−	973392.i	−0.448036	−	1.66764i
$765$		0			0
$766$	42022.2	+	318368.i	0.0716179	+	0.542591i
$767$			430619.i			0.731985i
$768$		0			0
$769$	658868.			1.11416			0.557078	−	0.830460i	$-0.311922\pi$
$769$	658868.			1.11416			0.557078	+	0.830460i	$0.311922\pi$
$770$	103866.	−	13709.6i	0.175183	−	0.0231229i
$771$		0			0
$772$	−386915.	+	103951.i	−0.649203	+	0.174419i
$773$	−833367.	+	833367.i	−1.39469	+	1.39469i	−0.580250	+	0.814439i	$0.697045\pi$
$773$	−833367.	+	833367.i	−1.39469	+	1.39469i	−0.814439	+	0.580250i	$0.802955\pi$
$774$		0			0
$775$	−346898.			−0.577561
$776$	−488491.	+	202914.i	−0.811210	+	0.336968i
$777$		0			0
$778$	−307993.	+	401662.i	−0.508840	+	0.663592i
$779$	−725932.	−	725932.i	−1.19625	−	1.19625i
$780$		0			0
$781$	282627.	+	282627.i	0.463352	+	0.463352i
$782$	−14459.8	+	1908.59i	−0.0236456	+	0.00312104i
$783$		0			0
$784$	−522186.	+	302416.i	−0.849559	+	0.492008i
$785$	−786784.			−1.27678
$786$		0			0
$787$	−265518.	+	265518.i	−0.428691	+	0.428691i	−0.888182	−	0.459491i	$-0.848032\pi$
$787$	−265518.	+	265518.i	−0.428691	+	0.428691i	0.459491	+	0.888182i	$0.348032\pi$
$788$	73103.2	−	126814.i	0.117729	−	0.204228i
$789$		0			0
$790$	333571.	+	255781.i	0.534482	+	0.409839i
$791$	−90269.3			−0.144274
$792$		0			0
$793$		−	910545.i		−	1.44795i
$794$	578294.	+	443434.i	0.917292	+	0.703376i
$795$		0			0
$796$	862124.	−	231623.i	1.36064	−	0.365558i
$797$	−51155.1	−	51155.1i	−0.0805327	−	0.0805327i	0.665693	−	0.746226i	$-0.268136\pi$
$797$	−51155.1	−	51155.1i	−0.0805327	−	0.0805327i	−0.746226	+	0.665693i	$0.768136\pi$
$798$		0			0
$799$		−	300716.i		−	0.471046i
$800$	−199930.	−	259655.i	−0.312391	−	0.405710i
$801$		0			0
$802$	−281994.	+	37221.1i	−0.438421	+	0.0578683i
$803$	−65828.4	+	65828.4i	−0.102090	+	0.102090i
$804$		0			0
$805$	−3958.14	+	3958.14i	−0.00610801	+	0.00610801i
$806$	826090.	−	1.07733e6i	1.27162	−	1.65836i
$807$		0			0
$808$	−173974.	+	421205.i	−0.266479	+	0.645165i
$809$		−	608654.i		−	0.929979i	−0.885316	−	0.464990i	$-0.846058\pi$
$809$		−	608654.i		−	0.929979i	0.885316	−	0.464990i	$-0.153942\pi$
$810$		0			0
$811$	−693367.	−	693367.i	−1.05420	−	1.05420i	−0.998445	−	0.0557512i	$-0.982245\pi$
$811$	−693367.	−	693367.i	−1.05420	−	1.05420i	−0.0557512	−	0.998445i	$-0.517755\pi$
$812$	22700.7	+	13086.0i	0.0344292	+	0.0198471i
$813$		0			0
$814$	399458.	−	52725.5i	0.602868	−	0.0795741i
$815$			768335.i			1.15674i
$816$		0			0
$817$	−14380.7			−0.0215445
$818$	45756.4	+	346659.i	0.0683825	+	0.518079i
$819$		0			0
$820$	−768508.	−	443014.i	−1.14293	−	0.658854i
$821$	843960.	−	843960.i	1.25209	−	1.25209i	0.297308	−	0.954781i	$-0.403911\pi$
$821$	843960.	−	843960.i	1.25209	−	1.25209i	0.954781	−	0.297308i	$-0.0960890\pi$
$822$		0			0
$823$	−562057.			−0.829815			−0.414907	−	0.909864i	$-0.636186\pi$
$823$	−562057.			−0.829815			−0.414907	+	0.909864i	$0.636186\pi$
$824$	84354.9	−	35040.1i	0.124238	−	0.0516072i
$825$		0			0
$826$	−28902.0	−	22162.0i	−0.0423612	−	0.0324824i
$827$	−49278.3	−	49278.3i	−0.0720518	−	0.0720518i	0.670163	−	0.742214i	$-0.266224\pi$
$827$	−49278.3	−	49278.3i	−0.0720518	−	0.0720518i	−0.742214	+	0.670163i	$0.766224\pi$
$828$		0			0
$829$	519755.	+	519755.i	0.756291	+	0.756291i	0.975645	−	0.219354i	$-0.0703949\pi$
$829$	519755.	+	519755.i	0.756291	+	0.756291i	−0.219354	+	0.975645i	$0.570395\pi$
$830$	3677.16	+	27858.8i	0.00533772	+	0.0404396i
$831$		0			0
$832$	1.28249e6	−	2571.67i	1.85271	−	0.00371508i
$833$	−312503.			−0.450364
$834$		0			0
$835$	−247243.	+	247243.i	−0.354610	+	0.354610i
$836$	−1.13198e6	+	304124.i	−1.61967	+	0.435149i
$837$		0			0
$838$	−539271.	+	703278.i	−0.767926	+	1.00147i
$839$	311968.			0.443186			0.221593	−	0.975139i	$-0.428874\pi$
$839$	311968.			0.443186			0.221593	+	0.975139i	$0.428874\pi$
$840$		0			0
$841$		−	646094.i		−	0.913491i
$842$	71035.0	−	92638.7i	0.100196	−	0.130668i
$843$		0			0
$844$	−128867.	+	223550.i	−0.180908	+	0.313826i
$845$	−1.51023e6	−	1.51023e6i	−2.11510	−	2.11510i
$846$		0			0
$847$		−	12714.6i		−	0.0177229i
$848$	76677.8	−	287703.i	0.106630	−	0.400086i
$849$		0			0
$850$	−22208.0	−	168252.i	−0.0307377	−	0.232874i
$851$	−15222.6	+	15222.6i	−0.0210198	+	0.0210198i
$852$		0			0
$853$	306461.	−	306461.i	0.421190	−	0.421190i	−0.464424	−	0.885613i	$-0.653738\pi$
$853$	306461.	−	306461.i	0.421190	−	0.421190i	0.885613	+	0.464424i	$0.153738\pi$
$854$	61113.5	+	46861.6i	0.0837956	+	0.0642542i
$855$		0			0
$856$	−834751.	−	344785.i	−1.13923	−	0.470545i
$857$		−	16157.2i		−	0.0219991i	−0.999940	−	0.0109995i	$-0.996499\pi$
$857$		−	16157.2i		−	0.0219991i	0.999940	−	0.0109995i	$-0.00350133\pi$
$858$		0			0
$859$	74800.4	+	74800.4i	0.101372	+	0.101372i	0.755974	−	0.654602i	$-0.227164\pi$
$859$	74800.4	+	74800.4i	0.101372	+	0.101372i	−0.654602	+	0.755974i	$0.727164\pi$
$860$	−12000.1	+	3224.02i	−0.0162252	+	0.00435914i
$861$		0			0
$862$	−154071.	−	1.16727e6i	−0.207351	−	1.57093i
$863$			902987.i			1.21244i	0.795297	+	0.606220i	$0.207315\pi$
$863$			902987.i			1.21244i	−0.795297	+	0.606220i	$0.792685\pi$
$864$		0			0
$865$	−490801.			−0.655954
$866$	953568.	−	125864.i	1.27150	−	0.167828i
$867$		0			0
$868$	29792.4	+	110890.i	0.0395427	+	0.147182i
$869$	311073.	−	311073.i	0.411929	−	0.411929i
$870$		0			0
$871$	2.04186e6			2.69147
$872$	792.915	+	327.505i	0.00104278	+	0.000430710i
$873$		0			0
$874$	38107.6	−	49697.1i	0.0498871	−	0.0650592i
$875$	43889.6	+	43889.6i	0.0573251	+	0.0573251i
$876$		0			0
$877$	526163.	+	526163.i	0.684102	+	0.684102i	0.960922	−	0.276820i	$-0.0892805\pi$
$877$	526163.	+	526163.i	0.684102	+	0.684102i	−0.276820	+	0.960922i	$0.589281\pi$
$878$	−1.16866e6	+	154254.i	−1.51600	+	0.200100i
$879$		0			0
$880$	−876409.	+	507558.i	−1.13173	+	0.655421i
$881$	1.39036e6			1.79133			0.895664	−	0.444732i	$-0.146701\pi$
$881$	1.39036e6			1.79133			0.895664	+	0.444732i	$0.146701\pi$
$882$		0			0
$883$	−717884.	+	717884.i	−0.920731	+	0.920731i	−0.997081	−	0.0763499i	$-0.975673\pi$
$883$	−717884.	+	717884.i	−0.920731	+	0.920731i	0.0763499	+	0.997081i	$0.475673\pi$
$884$	575409.	+	331700.i	0.736329	+	0.424464i
$885$		0			0
$886$	−534032.	−	409494.i	−0.680299	−	0.521651i
$887$	398604.			0.506633			0.253317	−	0.967383i	$-0.418479\pi$
$887$	398604.			0.506633			0.253317	+	0.967383i	$0.418479\pi$
$888$		0			0
$889$			53276.4i			0.0674111i
$890$	−142861.	−	109545.i	−0.180357	−	0.138297i
$891$		0			0
$892$	−63078.7	−	234785.i	−0.0792780	−	0.295081i
$893$	913022.	+	913022.i	1.14493	+	1.14493i
$894$		0			0
$895$			1.10160e6i			1.37524i
$896$	−65831.4	+	86210.0i	−0.0820006	+	0.107385i
$897$		0			0
$898$	325693.	−	42989.0i	0.403883	−	0.0533096i
$899$	−189595.	+	189595.i	−0.234589	+	0.234589i
$900$		0			0
$901$	109032.	−	109032.i	0.134309	−	0.134309i
$902$	−564905.	+	736708.i	−0.694324	+	0.905487i
$903$		0			0
$904$	805863.	−	334746.i	0.986108	−	0.409618i
$905$			981651.i			1.19856i
$906$		0			0
$907$	954485.	+	954485.i	1.16026	+	1.16026i	0.984419	+	0.175840i	$0.0562640\pi$
$907$	954485.	+	954485.i	1.16026	+	1.16026i	0.175840	+	0.984419i	$0.443736\pi$
$908$	−536881.	+	931341.i	−0.651187	+	1.12963i
$909$		0			0
$910$	252709.	−	33355.7i	0.305167	−	0.0402798i
$911$		−	876782.i		−	1.05646i	−0.849100	−	0.528232i	$-0.822855\pi$
$911$		−	876782.i		−	1.05646i	0.849100	−	0.528232i	$-0.177145\pi$
$912$		0			0
$913$	29409.0			0.0352808
$914$	90217.5	+	683505.i	0.107994	+	0.818180i
$915$		0			0
$916$	176616.	−	306381.i	0.210494	−	0.365149i
$917$	−105298.	+	105298.i	−0.125223	+	0.125223i
$918$		0			0
$919$	−146433.			−0.173384			−0.0866920	−	0.996235i	$-0.527630\pi$
$919$	−146433.			−0.173384			−0.0866920	+	0.996235i	$0.527630\pi$
$920$	20657.6	−	50013.6i	0.0244064	−	0.0590898i
$921$		0			0
$922$	−434982.	−	333543.i	−0.511693	−	0.392364i
$923$	687637.	+	687637.i	0.807153	+	0.807153i
$924$		0			0
$925$	−177127.	−	177127.i	−0.207015	−	0.207015i
$926$	74455.0	+	564085.i	0.0868304	+	0.657844i
$927$		0			0
$928$	−251184.	−	32642.0i	−0.291672	−	0.0379037i
$929$	357969.			0.414776			0.207388	−	0.978259i	$-0.433504\pi$
$929$	357969.			0.414776			0.207388	+	0.978259i	$0.433504\pi$
$930$		0			0
$931$	948808.	−	948808.i	1.09466	−	1.09466i
$932$	−262168.	−	975815.i	−0.301820	−	1.12340i
$933$		0			0
$934$	479131.	−	624848.i	0.549238	−	0.716277i
$935$	−524487.			−0.599945
$936$		0			0
$937$			1.49027e6i			1.69740i	0.528871	+	0.848702i	$0.322616\pi$
$937$			1.49027e6i			1.69740i	−0.528871	+	0.848702i	$0.677384\pi$
$938$	−105085.	+	137045.i	−0.119436	+	0.155760i
$939$		0			0
$940$	966572.	+	557189.i	1.09390	+	0.630590i
$941$	977475.	+	977475.i	1.10389	+	1.10389i	0.993937	+	0.109954i	$0.0350705\pi$
$941$	977475.	+	977475.i	1.10389	+	1.10389i	0.109954	+	0.993937i	$0.464929\pi$
$942$		0			0
$943$		−	49602.0i		−	0.0557796i
$944$	340201.	+	90669.4i	0.381761	+	0.101746i
$945$		0			0
$946$	1701.71	+	12892.5i	0.00190153	+	0.0144064i
$947$	−573883.	+	573883.i	−0.639917	+	0.639917i	−0.950535	−	0.310618i	$-0.899464\pi$
$947$	−573883.	+	573883.i	−0.639917	+	0.639917i	0.310618	+	0.950535i	$0.399464\pi$
$948$		0			0
$949$	−160162.	+	160162.i	−0.177839	+	0.177839i
$950$	578266.	+	443412.i	0.640738	+	0.491316i
$951$		0			0
$952$	−51876.6	+	21548.9i	−0.0572397	+	0.0237767i
$953$			356334.i			0.392348i	0.980569	+	0.196174i	$0.0628517\pi$
$953$			356334.i			0.392348i	−0.980569	+	0.196174i	$0.937148\pi$
$954$		0			0
$955$	1.36933e6	+	1.36933e6i	1.50142	+	1.50142i
$956$	−138373.	−	515038.i	−0.151403	−	0.563538i
$957$		0			0
$958$	113461.	+	859601.i	0.123628	+	0.936625i
$959$		−	206358.i		−	0.224380i
$960$		0			0
$961$	−251453.			−0.272276
$962$	971890.	−	128282.i	1.05019	−	0.138617i
$963$		0			0
$964$	86928.8	−	23354.8i	0.0935427	−	0.0251317i
$965$	544298.	−	544298.i	0.584496	−	0.584496i
$966$		0			0
$967$	−1.37297e6			−1.46828			−0.734138	−	0.679001i	$-0.762413\pi$
$967$	−1.37297e6			−1.46828			−0.734138	+	0.679001i	$0.762413\pi$
$968$	47149.6	+	113507.i	0.0503184	+	0.121136i
$969$		0			0
$970$	618418.	−	806497.i	0.657263	−	0.857154i
$971$	424934.	+	424934.i	0.450696	+	0.450696i	0.895585	−	0.444890i	$-0.146757\pi$
$971$	424934.	+	424934.i	0.450696	+	0.450696i	−0.444890	+	0.895585i	$0.646757\pi$
$972$		0			0
$973$	−141892.	−	141892.i	−0.149876	−	0.149876i
$974$	582888.	−	76936.8i	0.614422	−	0.0810992i
$975$		0			0
$976$	−719357.	−	191721.i	−0.755171	−	0.201266i
$977$	−985948.			−1.03292			−0.516458	−	0.856313i	$-0.672750\pi$
$977$	−985948.			−1.03292			−0.516458	+	0.856313i	$0.672750\pi$
$978$		0			0
$979$	−133225.	+	133225.i	−0.139002	+	0.139002i
$980$	579028.	−	1.00446e6i	0.602903	−	1.04587i
$981$		0			0
$982$	930541.	+	713535.i	0.964967	+	0.739933i
$983$	−92886.2			−0.0961268			−0.0480634	−	0.998844i	$-0.515305\pi$
$983$	−92886.2			−0.0961268			−0.0480634	+	0.998844i	$0.515305\pi$
$984$		0			0
$985$			281236.i			0.289867i
$986$	−104095.	−	79819.4i	−0.107072	−	0.0821022i
$987$		0			0
$988$	−2.75413e6	+	739940.i	−2.82144	+	0.758023i
$989$	−491.308	−	491.308i	−0.000502297	−	0.000502297i
$990$		0			0
$991$			1.28759e6i			1.31109i	0.755157	+	0.655543i	$0.227560\pi$
$991$			1.28759e6i			1.31109i	−0.755157	+	0.655543i	$0.772440\pi$
$992$	−677182.	−	879474.i	−0.688148	−	0.893716i
$993$		0			0
$994$	−81542.1	+	10762.9i	−0.0825294	+	0.0108933i
$995$	−1.21281e6	+	1.21281e6i	−1.22503	+	1.22503i
$996$		0			0
$997$	−388032.	+	388032.i	−0.390370	+	0.390370i	−0.874819	−	0.484449i	$-0.839020\pi$
$997$	−388032.	+	388032.i	−0.390370	+	0.390370i	0.484449	+	0.874819i	$0.339020\pi$
$998$	19247.8	−	25101.6i	0.0193250	−	0.0252023i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.m.a.19.7		14
3.2	odd	2		16.5.f.a.3.1	✓	14
4.3	odd	2		576.5.m.a.559.2		14
12.11	even	2		64.5.f.a.47.2		14
16.5	even	4		576.5.m.a.271.2		14
16.11	odd	4	inner	144.5.m.a.91.7		14
24.5	odd	2		128.5.f.b.95.2		14
24.11	even	2		128.5.f.a.95.6		14
48.5	odd	4		64.5.f.a.15.2		14
48.11	even	4		16.5.f.a.11.1	yes	14
48.29	odd	4		128.5.f.a.31.6		14
48.35	even	4		128.5.f.b.31.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.1	✓	14	3.2	odd	2
16.5.f.a.11.1	yes	14	48.11	even	4
64.5.f.a.15.2		14	48.5	odd	4
64.5.f.a.47.2		14	12.11	even	2
128.5.f.a.31.6		14	48.29	odd	4
128.5.f.a.95.6		14	24.11	even	2
128.5.f.b.31.2		14	48.35	even	4
128.5.f.b.95.2		14	24.5	odd	2
144.5.m.a.19.7		14	1.1	even	1	trivial
144.5.m.a.91.7		14	16.11	odd	4	inner
576.5.m.a.271.2		14	16.5	even	4
576.5.m.a.559.2		14	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.96560 - 0.523430i) q^{2} +(15.4520 - 4.15143i) q^{4} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +(59.1037 - 24.5510i) q^{8} +O(q^{10})\)	\(q+(3.96560 - 0.523430i) q^{2} +(15.4520 - 4.15143i) q^{4} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +(59.1037 - 24.5510i) q^{8} +(-74.8239 + 97.5799i) q^{10} +(90.9986 + 90.9986i) q^{11} +(221.402 + 221.402i) q^{13} +(-26.2544 + 3.46539i) q^{14} +(221.531 - 128.296i) q^{16} +132.575 q^{17} +(-402.520 + 402.520i) q^{19} +(-245.646 + 426.128i) q^{20} +(408.496 + 313.233i) q^{22} -27.5037 q^{23} -320.028i q^{25} +(993.879 + 762.103i) q^{26} +(-102.301 + 27.4847i) q^{28} +(-174.909 - 174.909i) q^{29} -1083.96i q^{31} +(811.351 - 624.728i) q^{32} +(525.742 - 69.3940i) q^{34} +(143.913 - 143.913i) q^{35} +(553.474 - 553.474i) q^{37} +(-1385.54 + 1806.93i) q^{38} +(-751.085 + 1818.43i) q^{40} +1803.47i q^{41} +(17.8633 + 17.8633i) q^{43} +(1783.89 + 1028.34i) q^{44} +(-109.069 + 14.3963i) q^{46} -2268.26i q^{47} -2357.17 q^{49} +(-167.512 - 1269.10i) q^{50} +(4340.24 + 2501.97i) q^{52} +(822.415 - 822.415i) q^{53} -3956.14 q^{55} +(-391.298 + 162.541i) q^{56} +(-785.174 - 602.068i) q^{58} +(972.483 + 972.483i) q^{59} +(-2056.32 - 2056.32i) q^{61} +(-567.378 - 4298.57i) q^{62} +(2890.50 - 2902.11i) q^{64} -9625.38 q^{65} +(4611.22 - 4611.22i) q^{67} +(2048.56 - 550.378i) q^{68} +(495.374 - 646.031i) q^{70} +3105.84 q^{71} +723.400i q^{73} +(1905.15 - 2484.56i) q^{74} +(-4548.72 + 7890.79i) q^{76} +(-602.460 - 602.460i) q^{77} -3418.44i q^{79} +(-2026.68 + 7604.33i) q^{80} +(943.989 + 7151.83i) q^{82} +(161.591 - 161.591i) q^{83} +(-2881.84 + 2881.84i) q^{85} +(80.1892 + 61.4887i) q^{86} +(7612.46 + 3144.25i) q^{88} +1464.04i q^{89} +(-1465.80 - 1465.80i) q^{91} +(-424.988 + 114.180i) q^{92} +(-1187.28 - 8995.04i) q^{94} -17499.5i q^{95} -8264.99 q^{97} +(-9347.60 + 1233.81i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

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