LMFDB - Embedded newform 300.5.c.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.c (of order $2$, degree $1$, 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:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 $ x^16 - 6x^15 + 20x^14 - 108x^13 + 492x^12 - 2160x^11 + 7360x^10 - 39552x^9 + 234752x^8 - 632832x^7 + 1884160x^6 - 8847360x^5 + 32243712x^4 - 113246208x^3 + 335544320x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.1
Root			$1.95664 + 3.48878i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.99969 - 0.0498899i) q^{2} -5.19615i q^{3} +(15.9950 + 0.399088i) q^{4} +(-0.259236 + 20.7830i) q^{6} -35.2842i q^{7} +(-63.9552 - 2.39422i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-3.99969 - 0.0498899i) q^{2} -5.19615i q^{3} +(15.9950 + 0.399088i) q^{4} +(-0.259236 + 20.7830i) q^{6} -35.2842i q^{7} +(-63.9552 - 2.39422i) q^{8} -27.0000 q^{9} -3.95158i q^{11} +(2.07372 - 83.1126i) q^{12} -41.0572 q^{13} +(-1.76033 + 141.126i) q^{14} +(255.681 + 12.7668i) q^{16} -186.761 q^{17} +(107.992 + 1.34703i) q^{18} +580.932i q^{19} -183.342 q^{21} +(-0.197144 + 15.8051i) q^{22} -472.336i q^{23} +(-12.4407 + 332.321i) q^{24} +(164.216 + 2.04834i) q^{26} +140.296i q^{27} +(14.0815 - 564.372i) q^{28} -979.409 q^{29} -33.2865i q^{31} +(-1022.01 - 63.8193i) q^{32} -20.5330 q^{33} +(746.987 + 9.31750i) q^{34} +(-431.866 - 10.7754i) q^{36} +623.253 q^{37} +(28.9826 - 2323.55i) q^{38} +213.340i q^{39} +154.478 q^{41} +(733.312 + 9.14693i) q^{42} -2675.32i q^{43} +(1.57703 - 63.2057i) q^{44} +(-23.5648 + 1889.20i) q^{46} +2925.06i q^{47} +(66.3385 - 1328.56i) q^{48} +1156.02 q^{49} +970.440i q^{51} +(-656.711 - 16.3855i) q^{52} -3782.10 q^{53} +(6.99936 - 561.141i) q^{54} +(-84.4782 + 2256.61i) q^{56} +3018.61 q^{57} +(3917.33 + 48.8626i) q^{58} +3487.58i q^{59} -488.539 q^{61} +(-1.66066 + 133.135i) q^{62} +952.674i q^{63} +(4084.54 + 306.245i) q^{64} +(82.1257 + 1.02439i) q^{66} +7491.56i q^{67} +(-2987.25 - 74.5342i) q^{68} -2454.33 q^{69} +4620.06i q^{71} +(1726.79 + 64.6439i) q^{72} +6959.14 q^{73} +(-2492.82 - 31.0940i) q^{74} +(-231.843 + 9292.01i) q^{76} -139.429 q^{77} +(10.6435 - 853.292i) q^{78} +6756.51i q^{79} +729.000 q^{81} +(-617.865 - 7.70690i) q^{82} +4862.15i q^{83} +(-2932.56 - 73.1697i) q^{84} +(-133.471 + 10700.4i) q^{86} +5089.16i q^{87} +(-9.46096 + 252.724i) q^{88} +513.707 q^{89} +1448.67i q^{91} +(188.504 - 7555.03i) q^{92} -172.962 q^{93} +(145.931 - 11699.3i) q^{94} +(-331.615 + 5310.52i) q^{96} -12119.3 q^{97} +(-4623.73 - 57.6739i) q^{98} +106.693i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	$ 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} - 176 q^{13} + 78 q^{14} - 376 q^{16} + 162 q^{18} - 144 q^{21} + 788 q^{22} + 108 q^{24} + 678 q^{26} - 3368 q^{28} + 1728 q^{29} - 2016 q^{32} - 2932 q^{34} - 216 q^{36} + 1568 q^{37} + 6990 q^{38} + 1248 q^{41} - 162 q^{42} + 8088 q^{44} + 5956 q^{46} - 2088 q^{48} - 10720 q^{49} - 3128 q^{52} + 288 q^{53} - 486 q^{54} - 10236 q^{56} - 5616 q^{57} + 16164 q^{58} - 3760 q^{61} + 12714 q^{62} + 10544 q^{64} + 8100 q^{66} - 26136 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} - 17004 q^{74} - 28344 q^{76} - 768 q^{77} + 16830 q^{78} + 11664 q^{81} + 21280 q^{82} + 15120 q^{84} + 24414 q^{86} - 52840 q^{88} - 768 q^{89} - 23736 q^{92} + 9936 q^{93} - 45156 q^{94} - 11088 q^{96} - 7248 q^{97} + 58140 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 - 176 * q^13 + 78 * q^14 - 376 * q^16 + 162 * q^18 - 144 * q^21 + 788 * q^22 + 108 * q^24 + 678 * q^26 - 3368 * q^28 + 1728 * q^29 - 2016 * q^32 - 2932 * q^34 - 216 * q^36 + 1568 * q^37 + 6990 * q^38 + 1248 * q^41 - 162 * q^42 + 8088 * q^44 + 5956 * q^46 - 2088 * q^48 - 10720 * q^49 - 3128 * q^52 + 288 * q^53 - 486 * q^54 - 10236 * q^56 - 5616 * q^57 + 16164 * q^58 - 3760 * q^61 + 12714 * q^62 + 10544 * q^64 + 8100 * q^66 - 26136 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 - 17004 * q^74 - 28344 * q^76 - 768 * q^77 + 16830 * q^78 + 11664 * q^81 + 21280 * q^82 + 15120 * q^84 + 24414 * q^86 - 52840 * q^88 - 768 * q^89 - 23736 * q^92 + 9936 * q^93 - 45156 * q^94 - 11088 * q^96 - 7248 * q^97 + 58140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.99969	−	0.0498899i	−0.999922	−	0.0124725i
$2$	−3.99969	−	0.0498899i	−0.999922	−	0.0124725i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	15.9950	+	0.399088i	0.999689	+	0.0249430i
$5$		0			0
$5$		0			0
$6$	−0.259236	+	20.7830i	−0.00720099	+	0.577305i
$7$		−	35.2842i		−	0.720086i	−0.932936	−	0.360043i	$-0.882762\pi$
$7$		−	35.2842i		−	0.720086i	0.932936	−	0.360043i	$-0.117238\pi$
$8$	−63.9552	−	2.39422i	−0.999300	−	0.0374097i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	3.95158i		−	0.0326577i	−0.999867	−	0.0163289i	$-0.994802\pi$
$11$		−	3.95158i		−	0.0326577i	0.999867	−	0.0163289i	$-0.00519787\pi$
$12$	2.07372	−	83.1126i	0.0144009	−	0.577171i
$13$	−41.0572			−0.242942			−0.121471	−	0.992595i	$-0.538761\pi$
$13$	−41.0572			−0.242942			−0.121471	+	0.992595i	$0.538761\pi$
$14$	−1.76033	+	141.126i	−0.00898126	+	0.720030i
$15$		0			0
$16$	255.681	+	12.7668i	0.998756	+	0.0498705i
$17$	−186.761			−0.646233			−0.323116	−	0.946359i	$-0.604731\pi$
$17$	−186.761			−0.646233			−0.323116	+	0.946359i	$0.604731\pi$
$18$	107.992	+	1.34703i	0.333307	+	0.00415749i
$19$			580.932i			1.60923i	0.593798	+	0.804614i	$0.297628\pi$
$19$			580.932i			1.60923i	−0.593798	+	0.804614i	$0.702372\pi$
$20$		0			0
$21$	−183.342			−0.415742
$22$	−0.197144	+	15.8051i	−0.000407323	+	0.0326552i
$23$		−	472.336i		−	0.892885i	−0.894812	−	0.446443i	$-0.852691\pi$
$23$		−	472.336i		−	0.892885i	0.894812	−	0.446443i	$-0.147309\pi$
$24$	−12.4407	+	332.321i	−0.0215985	+	0.576946i
$25$		0			0
$26$	164.216	+	2.04834i	0.242923	+	0.00303009i
$27$			140.296i			0.192450i
$28$	14.0815	−	564.372i	0.0179611	−	0.719862i
$29$	−979.409			−1.16458			−0.582288	−	0.812982i	$-0.697843\pi$
$29$	−979.409			−1.16458			−0.582288	+	0.812982i	$0.697843\pi$
$30$		0			0
$31$		−	33.2865i		−	0.0346373i	−0.999850	−	0.0173187i	$-0.994487\pi$
$31$		−	33.2865i		−	0.0346373i	0.999850	−	0.0173187i	$-0.00551298\pi$
$32$	−1022.01	−	63.8193i	−0.998056	−	0.0623236i
$33$	−20.5330			−0.0188549
$34$	746.987	+	9.31750i	0.646183	+	0.00806012i
$35$		0			0
$36$	−431.866	−	10.7754i	−0.333230	−	0.00831434i
$37$	623.253			0.455262			0.227631	−	0.973748i	$-0.426902\pi$
$37$	623.253			0.455262			0.227631	+	0.973748i	$0.426902\pi$
$38$	28.9826	−	2323.55i	0.0200711	−	1.60910i
$39$			213.340i			0.140263i
$40$		0			0
$41$	154.478			0.0918966			0.0459483	−	0.998944i	$-0.485369\pi$
$41$	154.478			0.0918966			0.0459483	+	0.998944i	$0.485369\pi$
$42$	733.312	+	9.14693i	0.415710	+	0.00518533i
$43$		−	2675.32i		−	1.44690i	−0.690377	−	0.723450i	$-0.742555\pi$
$43$		−	2675.32i		−	1.44690i	0.690377	−	0.723450i	$-0.257445\pi$
$44$	1.57703	−	63.2057i	0.000814582	−	0.0326476i
$45$		0			0
$46$	−23.5648	+	1889.20i	−0.0111365	+	0.892816i
$47$			2925.06i			1.32416i	0.749434	+	0.662079i	$0.230326\pi$
$47$			2925.06i			1.32416i	−0.749434	+	0.662079i	$0.769674\pi$
$48$	66.3385	−	1328.56i	0.0287927	−	0.576632i
$49$	1156.02			0.481476
$50$		0			0
$51$			970.440i			0.373103i
$52$	−656.711	−	16.3855i	−0.242867	−	0.00605971i
$53$	−3782.10			−1.34642			−0.673212	−	0.739450i	$-0.735086\pi$
$53$	−3782.10			−1.34642			−0.673212	+	0.739450i	$0.735086\pi$
$54$	6.99936	−	561.141i	0.00240033	−	0.192435i
$55$		0			0
$56$	−84.4782	+	2256.61i	−0.0269382	+	0.719582i
$57$	3018.61			0.929089
$58$	3917.33	+	48.8626i	1.16449	+	0.0145252i
$59$			3487.58i			1.00189i	0.865479	+	0.500945i	$0.167014\pi$
$59$			3487.58i			1.00189i	−0.865479	+	0.500945i	$0.832986\pi$
$60$		0			0
$61$	−488.539			−0.131292			−0.0656462	−	0.997843i	$-0.520911\pi$
$61$	−488.539			−0.131292			−0.0656462	+	0.997843i	$0.520911\pi$
$62$	−1.66066	+	133.135i	−0.000432013	+	0.0346346i
$63$			952.674i			0.240029i
$64$	4084.54	+	306.245i	0.997201	+	0.0747670i
$65$		0			0
$66$	82.1257	+	1.02439i	0.0188535	+	0.000235168i
$67$			7491.56i			1.66887i	0.551107	+	0.834435i	$0.314206\pi$
$67$			7491.56i			1.66887i	−0.551107	+	0.834435i	$0.685794\pi$
$68$	−2987.25	−	74.5342i	−0.646032	−	0.0161190i
$69$	−2454.33			−0.515507
$70$		0			0
$71$			4620.06i			0.916496i	0.888824	+	0.458248i	$0.151523\pi$
$71$			4620.06i			0.916496i	−0.888824	+	0.458248i	$0.848477\pi$
$72$	1726.79	+	64.6439i	0.333100	+	0.0124699i
$73$	6959.14			1.30590			0.652950	−	0.757401i	$-0.273531\pi$
$73$	6959.14			1.30590			0.652950	+	0.757401i	$0.273531\pi$
$74$	−2492.82	−	31.0940i	−0.455226	−	0.00567824i
$75$		0			0
$76$	−231.843	+	9292.01i	−0.0401390	+	1.60873i
$77$	−139.429			−0.0235164
$78$	10.6435	−	853.292i	0.00174942	−	0.140252i
$79$			6756.51i			1.08260i	0.840829	+	0.541300i	$0.182068\pi$
$79$			6756.51i			1.08260i	−0.840829	+	0.541300i	$0.817932\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−617.865	−	7.70690i	−0.0918895	−	0.00114618i
$83$			4862.15i			0.705785i	0.935664	+	0.352893i	$0.114802\pi$
$83$			4862.15i			0.705785i	−0.935664	+	0.352893i	$0.885198\pi$
$84$	−2932.56	−	73.1697i	−0.415613	−	0.0103699i
$85$		0			0
$86$	−133.471	+	10700.4i	−0.0180464	+	1.44679i
$87$			5089.16i			0.672369i
$88$	−9.46096	+	252.724i	−0.00122171	+	0.0326349i
$89$	513.707			0.0648538			0.0324269	−	0.999474i	$-0.489676\pi$
$89$	513.707			0.0648538			0.0324269	+	0.999474i	$0.489676\pi$
$90$		0			0
$91$			1448.67i			0.174939i
$92$	188.504	−	7555.03i	0.0222712	−	0.892607i
$93$	−172.962			−0.0199979
$94$	145.931	−	11699.3i	0.0165155	−	1.32405i
$95$		0			0
$96$	−331.615	+	5310.52i	−0.0359825	+	0.576228i
$97$	−12119.3			−1.28805			−0.644026	−	0.765004i	$-0.722737\pi$
$97$	−12119.3			−1.28805			−0.644026	+	0.765004i	$0.722737\pi$
$98$	−4623.73	−	57.6739i	−0.481438	−	0.00600519i
$99$			106.693i			0.0108859i
$100$		0			0
$101$	−7191.20			−0.704951			−0.352475	−	0.935821i	$-0.614660\pi$
$101$	−7191.20			−0.704951			−0.352475	+	0.935821i	$0.614660\pi$
$102$	48.4152	−	3881.46i	0.00465351	−	0.373074i
$103$			10189.6i			0.960470i	0.877140	+	0.480235i	$0.159449\pi$
$103$			10189.6i			0.960470i	−0.877140	+	0.480235i	$0.840551\pi$
$104$	2625.82	+	98.3000i	0.242772	+	0.00908839i
$105$		0			0
$106$	15127.2	+	188.689i	1.34632	+	0.0167932i
$107$			21648.8i			1.89089i	0.325777	+	0.945446i	$0.394374\pi$
$107$			21648.8i			1.89089i	−0.325777	+	0.945446i	$0.605626\pi$
$108$	−55.9905	+	2244.04i	−0.00480028	+	0.192390i
$109$	10655.6			0.896859			0.448430	−	0.893818i	$-0.351983\pi$
$109$	10655.6			0.896859			0.448430	+	0.893818i	$0.351983\pi$
$110$		0			0
$111$		−	3238.52i		−	0.262845i
$112$	450.468	−	9021.52i	0.0359111	−	0.719190i
$113$	−9876.07			−0.773441			−0.386721	−	0.922197i	$-0.626392\pi$
$113$	−9876.07			−0.773441			−0.386721	+	0.922197i	$0.626392\pi$
$114$	−12073.5	−	150.598i	−0.929017	−	0.0115880i
$115$		0			0
$116$	−15665.7	−	390.871i	−1.16421	−	0.0290480i
$117$	1108.55			0.0809807
$118$	173.995	−	13949.2i	0.0124961	−	1.00181i
$119$			6589.73i			0.465343i
$120$		0			0
$121$	14625.4			0.998933
$122$	1954.00	+	24.3732i	0.131282	+	0.00163754i
$123$		−	802.692i		−	0.0530565i
$124$	13.2842	−	532.418i	0.000863959	−	0.0346265i
$125$		0			0
$126$	47.5288	−	3810.40i	0.00299375	−	0.240010i
$127$			19972.7i			1.23831i	0.785269	+	0.619155i	$0.212525\pi$
$127$			19972.7i			1.23831i	−0.785269	+	0.619155i	$0.787475\pi$
$128$	−16321.6	−	1428.66i	−0.996191	−	0.0871987i
$129$	−13901.4			−0.835368
$130$		0			0
$131$		−	30733.6i		−	1.79090i	−0.445164	−	0.895449i	$-0.646855\pi$
$131$		−	30733.6i		−	1.79090i	0.445164	−	0.895449i	$-0.353145\pi$
$132$	−328.426	−	8.19449i	−0.0188491	−	0.000470299i
$133$	20497.7			1.15878
$134$	373.753	−	29963.9i	0.0208149	−	1.66874i
$135$		0			0
$136$	11944.4	+	447.147i	0.645780	+	0.0241754i
$137$	7177.05			0.382388			0.191194	−	0.981552i	$-0.438764\pi$
$137$	7177.05			0.382388			0.191194	+	0.981552i	$0.438764\pi$
$138$	9816.56	+	122.446i	0.515467	+	0.00642965i
$139$			4628.80i			0.239574i	0.992800	+	0.119787i	$0.0382211\pi$
$139$			4628.80i			0.239574i	−0.992800	+	0.119787i	$0.961779\pi$
$140$		0			0
$141$	15199.1			0.764503
$142$	230.494	−	18478.8i	0.0114310	−	0.916425i
$143$			162.241i			0.00793394i
$144$	−6903.40	−	344.705i	−0.332919	−	0.0166235i
$145$		0			0
$146$	−27834.4	−	347.191i	−1.30580	−	0.0162878i
$147$		−	6006.87i		−	0.277980i
$148$	9968.95	+	248.733i	0.455120	+	0.0113556i
$149$	35128.8			1.58231			0.791154	−	0.611617i	$-0.209481\pi$
$149$	35128.8			1.58231			0.791154	+	0.611617i	$0.209481\pi$
$150$		0			0
$151$		−	41309.8i		−	1.81176i	−0.423539	−	0.905878i	$-0.639212\pi$
$151$		−	41309.8i		−	1.81176i	0.423539	−	0.905878i	$-0.360788\pi$
$152$	1390.88	−	37153.6i	0.0602007	−	1.60810i
$153$	5042.55			0.215411
$154$	557.671	+	6.95608i	0.0235146	+	0.000293307i
$155$		0			0
$156$	−85.1413	+	3412.37i	−0.00349857	+	0.140219i
$157$	−3581.96			−0.145319			−0.0726594	−	0.997357i	$-0.523149\pi$
$157$	−3581.96			−0.145319			−0.0726594	+	0.997357i	$0.523149\pi$
$158$	337.082	−	27023.9i	0.0135027	−	1.08252i
$159$			19652.4i			0.777358i
$160$		0			0
$161$	−16666.0			−0.642954
$162$	−2915.77	−	36.3697i	−0.111102	−	0.00138583i
$163$			14969.6i			0.563422i	0.959499	+	0.281711i	$0.0909020\pi$
$163$			14969.6i			0.563422i	−0.959499	+	0.281711i	$0.909098\pi$
$164$	2470.88	+	61.6504i	0.0918680	+	0.00229218i
$165$		0			0
$166$	242.572	−	19447.1i	0.00880289	−	0.705730i
$167$		−	12510.0i		−	0.448564i	−0.974524	−	0.224282i	$-0.927996\pi$
$167$		−	12510.0i		−	0.448564i	0.974524	−	0.224282i	$-0.0720037\pi$
$168$	11725.7	+	438.961i	0.415451	+	0.0155528i
$169$	−26875.3			−0.940979
$170$		0			0
$171$		−	15685.2i		−	0.536410i
$172$	1067.69	−	42791.8i	0.0360901	−	1.44645i
$173$	−51365.9			−1.71626			−0.858129	−	0.513434i	$-0.828373\pi$
$173$	−51365.9			−1.71626			−0.858129	+	0.513434i	$0.828373\pi$
$174$	253.898	−	20355.0i	0.00838610	−	0.672316i
$175$		0			0
$176$	50.4493	−	1010.35i	0.00162866	−	0.0326171i
$177$	18122.0			0.578442
$178$	−2054.67	−	25.6288i	−0.0648487	−	0.000808887i
$179$			29989.3i			0.935967i	0.883737	+	0.467984i	$0.155019\pi$
$179$			29989.3i			0.935967i	−0.883737	+	0.467984i	$0.844981\pi$
$180$		0			0
$181$	−47416.2			−1.44734			−0.723668	−	0.690149i	$-0.757545\pi$
$181$	−47416.2			−1.44734			−0.723668	+	0.690149i	$0.757545\pi$
$182$	72.2741	−	5794.24i	0.00218193	−	0.174926i
$183$			2538.52i			0.0758017i
$184$	−1130.88	+	30208.4i	−0.0334025	+	0.892260i
$185$		0			0
$186$	691.792	+	8.62903i	0.0199963	+	0.000249423i
$187$			738.003i			0.0211045i
$188$	−1167.36	+	46786.5i	−0.0330285	+	1.32375i
$189$	4950.24			0.138581
$190$		0			0
$191$		−	41028.6i		−	1.12466i	−0.826914	−	0.562329i	$-0.809905\pi$
$191$		−	41028.6i		−	1.12466i	0.826914	−	0.562329i	$-0.190095\pi$
$192$	1591.30	−	21223.9i	0.0431667	−	0.575734i
$193$	44180.6			1.18609			0.593044	−	0.805170i	$-0.297926\pi$
$193$	44180.6			1.18609			0.593044	+	0.805170i	$0.297926\pi$
$194$	48473.3	+	604.629i	1.28795	+	0.0160652i
$195$		0			0
$196$	18490.6	+	461.355i	0.481326	+	0.0120094i
$197$	−8724.29			−0.224801			−0.112400	−	0.993663i	$-0.535854\pi$
$197$	−8724.29			−0.224801			−0.112400	+	0.993663i	$0.535854\pi$
$198$	5.32289	−	426.738i	0.000135774	−	0.0108851i
$199$			6720.98i			0.169717i	0.996393	+	0.0848587i	$0.0270439\pi$
$199$			6720.98i			0.169717i	−0.996393	+	0.0848587i	$0.972956\pi$
$200$		0			0
$201$	38927.3			0.963522
$202$	28762.6	+	358.768i	0.704896	+	0.00879248i
$203$			34557.7i			0.838596i
$204$	−387.291	+	15522.2i	−0.00930630	+	0.372987i
$205$		0			0
$206$	508.359	−	40755.3i	0.0119794	−	0.960395i
$207$			12753.1i			0.297628i
$208$	−10497.6	−	524.171i	−0.242640	−	0.0121156i
$209$	2295.60			0.0525537
$210$		0			0
$211$		−	8501.81i		−	0.190962i	−0.995431	−	0.0954808i	$-0.969561\pi$
$211$		−	8501.81i		−	0.190962i	0.995431	−	0.0954808i	$-0.0304389\pi$
$212$	−60494.8	−	1509.39i	−1.34600	−	0.0335839i
$213$	24006.5			0.529139
$214$	1080.06	−	86588.6i	0.0235841	−	1.89075i
$215$		0			0
$216$	335.900	−	8972.67i	0.00719949	−	0.192315i
$217$	−1174.49			−0.0249419
$218$	−42619.0	−	531.606i	−0.896790	−	0.0111861i
$219$		−	36160.7i		−	0.753961i
$220$		0			0
$221$	7667.90			0.156997
$222$	−161.569	+	12953.1i	−0.00327833	+	0.262825i
$223$			28886.8i			0.580883i	0.956893	+	0.290442i	$0.0938022\pi$
$223$			28886.8i			0.580883i	−0.956893	+	0.290442i	$0.906198\pi$
$224$	−2251.82	+	36060.8i	−0.0448784	+	0.718687i
$225$		0			0
$226$	39501.2	+	492.716i	0.773381	+	0.00964672i
$227$			17662.3i			0.342764i	0.985205	+	0.171382i	$0.0548233\pi$
$227$			17662.3i			0.342764i	−0.985205	+	0.171382i	$0.945177\pi$
$228$	48282.7	+	1204.69i	0.928800	+	0.0231743i
$229$	−99665.8			−1.90053			−0.950266	−	0.311439i	$-0.899189\pi$
$229$	−99665.8			−1.90053			−0.950266	+	0.311439i	$0.899189\pi$
$230$		0			0
$231$			724.492i			0.0135772i
$232$	62638.3	+	2344.92i	1.16376	+	0.0435664i
$233$	−72559.0			−1.33653			−0.668266	−	0.743922i	$-0.732963\pi$
$233$	−72559.0			−1.33653			−0.668266	+	0.743922i	$0.732963\pi$
$234$	−4433.84	−	55.3052i	−0.0809744	−	0.00101003i
$235$		0			0
$236$	−1391.85	+	55783.9i	−0.0249902	+	1.00158i
$237$	35107.9			0.625040
$238$	328.761	−	26356.9i	0.00580399	−	0.465307i
$239$		−	70208.6i		−	1.22912i	−0.788870	−	0.614560i	$-0.789334\pi$
$239$		−	70208.6i		−	1.22912i	0.788870	−	0.614560i	$-0.210666\pi$
$240$		0			0
$241$	−51440.5			−0.885668			−0.442834	−	0.896604i	$-0.646027\pi$
$241$	−51440.5			−0.885668			−0.442834	+	0.896604i	$0.646027\pi$
$242$	−58497.0	−	729.659i	−0.998856	−	0.0124592i
$243$		−	3788.00i		−	0.0641500i
$244$	−7814.19	−	194.970i	−0.131252	−	0.00327483i
$245$		0			0
$246$	−40.0462	+	3210.52i	−0.000661746	+	0.0530524i
$247$		−	23851.4i		−	0.390950i
$248$	−79.6951	+	2128.84i	−0.00129577	+	0.0346131i
$249$	25264.5			0.407485
$250$		0			0
$251$			72429.1i			1.14965i	0.818276	+	0.574825i	$0.194930\pi$
$251$			72429.1i			1.14965i	−0.818276	+	0.574825i	$0.805070\pi$
$252$	−380.201	+	15238.0i	−0.00598704	+	0.239954i
$253$	−1866.48			−0.0291596
$254$	996.436	−	79884.6i	0.0154448	−	1.23821i
$255$		0			0
$256$	65210.0	+	6528.49i	0.995026	+	0.0996169i
$257$	−77711.9			−1.17658			−0.588290	−	0.808650i	$-0.700199\pi$
$257$	−77711.9			−1.17658			−0.588290	+	0.808650i	$0.700199\pi$
$258$	55601.1	+	693.538i	0.835303	+	0.0104191i
$259$		−	21991.0i		−	0.327828i
$260$		0			0
$261$	26444.0			0.388192
$262$	−1533.30	+	122925.i	−0.0223369	+	1.79076i
$263$			2716.70i			0.0392763i	0.999807	+	0.0196382i	$0.00625142\pi$
$263$			2716.70i			0.0392763i	−0.999807	+	0.0196382i	$0.993749\pi$
$264$	1313.19	+	49.1606i	0.0188417	+	0.000705357i
$265$		0			0
$266$	−81984.5	−	1022.63i	−1.15869	−	0.0144529i
$267$		−	2669.30i		−	0.0374434i
$268$	−2989.79	+	119828.i	−0.0416266	+	1.66835i
$269$	66666.6			0.921306			0.460653	−	0.887580i	$-0.347615\pi$
$269$	66666.6			0.921306			0.460653	+	0.887580i	$0.347615\pi$
$270$		0			0
$271$			63959.9i			0.870902i	0.900212	+	0.435451i	$0.143411\pi$
$271$			63959.9i			0.870902i	−0.900212	+	0.435451i	$0.856589\pi$
$272$	−47751.4	−	2384.35i	−0.645429	−	0.0322280i
$273$	7527.53			0.101001
$274$	−28706.0	−	358.062i	−0.382359	−	0.00476933i
$275$		0			0
$276$	−39257.1	−	979.494i	−0.515347	−	0.0128583i
$277$	36446.7			0.475005			0.237502	−	0.971387i	$-0.423671\pi$
$277$	36446.7			0.475005			0.237502	+	0.971387i	$0.423671\pi$
$278$	230.930	−	18513.8i	0.00298808	−	0.239555i
$279$			898.734i			0.0115458i
$280$		0			0
$281$	83688.9			1.05988			0.529938	−	0.848036i	$-0.322215\pi$
$281$	83688.9			1.05988			0.529938	+	0.848036i	$0.322215\pi$
$282$	−60791.6	−	758.281i	−0.764443	−	0.00953524i
$283$		−	99210.9i		−	1.23876i	−0.785092	−	0.619379i	$-0.787384\pi$
$283$		−	99210.9i		−	1.23876i	0.785092	−	0.619379i	$-0.212616\pi$
$284$	−1843.81	+	73897.9i	−0.0228602	+	0.916211i
$285$		0			0
$286$	8.09419	−	648.914i	9.89558e−5	−	0.00793332i
$287$		−	5450.65i		−	0.0661735i
$288$	27594.3	+	1723.12i	0.332685	+	0.0207745i
$289$	−48641.2			−0.582383
$290$		0			0
$291$			62973.6i			0.743657i
$292$	111312.	+	2777.31i	1.30549	+	0.0325731i
$293$	−5554.90			−0.0647054			−0.0323527	−	0.999477i	$-0.510300\pi$
$293$	−5554.90			−0.0647054			−0.0323527	+	0.999477i	$0.510300\pi$
$294$	−299.682	+	24025.6i	−0.00346710	+	0.277958i
$295$		0			0
$296$	−39860.3	−	1492.20i	−0.454943	−	0.0170312i
$297$	554.392			0.00628498
$298$	−140504.	−	1752.57i	−1.58219	−	0.0197353i
$299$			19392.8i			0.216919i
$300$		0			0
$301$	−94396.6			−1.04189
$302$	−2060.94	+	165226.i	−0.0225971	+	1.81161i
$303$			37366.6i			0.407004i
$304$	−7416.67	+	148533.i	−0.0802531	+	1.60723i
$305$		0			0
$306$	−20168.6	−	251.573i	−0.215394	−	0.00268671i
$307$		−	25814.0i		−	0.273891i	−0.990579	−	0.136946i	$-0.956271\pi$
$307$		−	25814.0i		−	0.273891i	0.990579	−	0.136946i	$-0.0437286\pi$
$308$	−2230.16	−	55.6443i	−0.0235091	−	0.000586569i
$309$	52946.8			0.554527
$310$		0			0
$311$			106750.i			1.10369i	0.833947	+	0.551844i	$0.186076\pi$
$311$			106750.i			1.10369i	−0.833947	+	0.551844i	$0.813924\pi$
$312$	510.782	−	13644.2i	0.00524718	−	0.140165i
$313$	76334.9			0.779174			0.389587	−	0.920990i	$-0.372618\pi$
$313$	76334.9			0.779174			0.389587	+	0.920990i	$0.372618\pi$
$314$	14326.7	+	178.704i	0.145307	+	0.00181248i
$315$		0			0
$316$	−2696.44	+	108071.i	−0.0270033	+	1.08226i
$317$	108286.			1.07759			0.538794	−	0.842437i	$-0.318880\pi$
$317$	108286.			1.07759			0.538794	+	0.842437i	$0.318880\pi$
$318$	980.456	−	78603.4i	0.00969558	−	0.777298i
$319$			3870.22i			0.0380324i
$320$		0			0
$321$	112491.			1.09171
$322$	66658.9	+	831.466i	0.642904	+	0.00801923i
$323$		−	108496.i		−	1.03994i
$324$	11660.4	+	290.935i	0.111077	+	0.00277145i
$325$		0			0
$326$	746.830	−	59873.6i	0.00702727	−	0.563378i
$327$		−	55368.1i		−	0.517802i
$328$	−9879.69	−	369.855i	−0.0918323	−	0.00343782i
$329$	103209.			0.953508
$330$		0			0
$331$			109078.i			0.995590i	0.867295	+	0.497795i	$0.165857\pi$
$331$			109078.i			0.995590i	−0.867295	+	0.497795i	$0.834143\pi$
$332$	−1940.43	+	77770.3i	−0.0176044	+	0.705565i
$333$	−16827.8			−0.151754
$334$	−624.123	+	50036.1i	−0.00559471	+	0.448529i
$335$		0			0
$336$	−46877.2	−	2340.70i	−0.415225	−	0.0207333i
$337$	−152574.			−1.34345			−0.671725	−	0.740801i	$-0.734446\pi$
$337$	−152574.			−1.34345			−0.671725	+	0.740801i	$0.734446\pi$
$338$	107493.	+	1340.81i	0.940906	+	0.0117363i
$339$			51317.6i			0.446546i
$340$		0			0
$341$	−131.534			−0.00113118
$342$	−782.531	+	62735.7i	−0.00669036	+	0.536368i
$343$		−	125507.i		−	1.06679i
$344$	−6405.30	+	171101.i	−0.0541281	+	1.44589i
$345$		0			0
$346$	205448.	+	2562.64i	1.71612	+	0.0214060i
$347$		−	168701.i		−	1.40107i	−0.713618	−	0.700535i	$-0.752945\pi$
$347$		−	168701.i		−	1.40107i	0.713618	−	0.700535i	$-0.247055\pi$
$348$	−2031.02	+	81401.2i	−0.0167709	+	0.672159i
$349$	−19680.8			−0.161582			−0.0807910	−	0.996731i	$-0.525745\pi$
$349$	−19680.8			−0.161582			−0.0807910	+	0.996731i	$0.525745\pi$
$350$		0			0
$351$		−	5760.17i		−	0.0467542i
$352$	−252.187	+	4038.56i	−0.00203535	+	0.0325942i
$353$	−55058.2			−0.441848			−0.220924	−	0.975291i	$-0.570907\pi$
$353$	−55058.2			−0.441848			−0.220924	+	0.975291i	$0.570907\pi$
$354$	−72482.4	−	904.105i	−0.578397	−	0.00721460i
$355$		0			0
$356$	8216.75	+	205.014i	0.0648336	+	0.00161765i
$357$	34241.2			0.268666
$358$	1496.16	−	119948.i	0.0116738	−	0.935894i
$359$		−	73206.8i		−	0.568019i	−0.958822	−	0.284009i	$-0.908335\pi$
$359$		−	73206.8i		−	0.568019i	0.958822	−	0.284009i	$-0.0916647\pi$
$360$		0			0
$361$	−207161.			−1.58962
$362$	189650.	+	2365.59i	1.44722	+	0.0180519i
$363$		−	75995.7i		−	0.576735i
$364$	−578.148	+	23171.6i	−0.00436351	+	0.174885i
$365$		0			0
$366$	126.647	−	10153.3i	0.000945435	−	0.0757958i
$367$		−	156333.i		−	1.16069i	−0.814370	−	0.580346i	$-0.802917\pi$
$367$		−	156333.i		−	1.16069i	0.814370	−	0.580346i	$-0.197083\pi$
$368$	6030.24	−	120768.i	0.0445286	−	0.891774i
$369$	−4170.91			−0.0306322
$370$		0			0
$371$			133449.i			0.969542i
$372$	−2766.52	−	69.0269i	−0.0199916	−	0.000498807i
$373$	233763.			1.68019			0.840096	−	0.542438i	$-0.182499\pi$
$373$	233763.			1.68019			0.840096	+	0.542438i	$0.182499\pi$
$374$	36.8189	−	2951.78i	0.000263225	−	0.0211028i
$375$		0			0
$376$	7003.24	−	187073.i	0.0495363	−	1.32323i
$377$	40211.8			0.282925
$378$	−19799.4	−	246.967i	−0.138570	−	0.00172844i
$379$		−	25001.6i		−	0.174056i	−0.996206	−	0.0870282i	$-0.972263\pi$
$379$		−	25001.6i		−	0.174056i	0.996206	−	0.0870282i	$-0.0277370\pi$
$380$		0			0
$381$	103781.			0.714938
$382$	−2046.92	+	164102.i	−0.0140273	+	1.12457i
$383$		−	165132.i		−	1.12573i	−0.826549	−	0.562864i	$-0.809699\pi$
$383$		−	165132.i		−	1.12573i	0.826549	−	0.562864i	$-0.190301\pi$
$384$	−7423.55	+	84809.5i	−0.0503442	+	0.575151i
$385$		0			0
$386$	−176709.	−	2204.17i	−1.18600	−	0.0147935i
$387$			72233.6i			0.482300i
$388$	−193848.	−	4836.66i	−1.28765	−	0.0321279i
$389$	46311.3			0.306047			0.153023	−	0.988223i	$-0.451099\pi$
$389$	46311.3			0.306047			0.153023	+	0.988223i	$0.451099\pi$
$390$		0			0
$391$			88214.1i			0.577012i
$392$	−73933.7	−	2767.77i	−0.481138	−	0.0180118i
$393$	−159696.			−1.03398
$394$	34894.4	+	435.254i	0.224783	+	0.00280382i
$395$		0			0
$396$	−42.5798	+	1706.55i	−0.000271527	+	0.0108825i
$397$	−244029.			−1.54832			−0.774161	−	0.632989i	$-0.781828\pi$
$397$	−244029.			−1.54832			−0.774161	+	0.632989i	$0.781828\pi$
$398$	335.309	−	26881.8i	0.00211680	−	0.169704i
$399$		−	106509.i		−	0.669024i
$400$		0			0
$401$	102342.			0.636451			0.318225	−	0.948015i	$-0.396913\pi$
$401$	102342.			0.636451			0.318225	+	0.948015i	$0.396913\pi$
$402$	−155697.	−	1942.08i	−0.963447	−	0.0120175i
$403$			1366.65i			0.00841487i
$404$	−115023.	−	2869.92i	−0.704732	−	0.0175836i
$405$		0			0
$406$	1724.08	−	138220.i	0.0104594	−	0.838531i
$407$		−	2462.84i		−	0.0148678i
$408$	2323.45	−	62064.7i	0.0139576	−	0.372842i
$409$	−110640.			−0.661405			−0.330702	−	0.943735i	$-0.607286\pi$
$409$	−110640.			−0.661405			−0.330702	+	0.943735i	$0.607286\pi$
$410$		0			0
$411$		−	37293.0i		−	0.220772i
$412$	−4066.56	+	162983.i	−0.0239570	+	0.960171i
$413$	123057.			0.721448
$414$	636.250	−	51008.3i	0.00371216	−	0.297605i
$415$		0			0
$416$	41960.9	+	2620.25i	0.242470	+	0.0151410i
$417$	24052.0			0.138318
$418$	−9181.69	−	114.527i	−0.0525497	−	0.000655475i
$419$			2345.08i			0.0133576i	0.999978	+	0.00667882i	$0.00212595\pi$
$419$			2345.08i			0.0133576i	−0.999978	+	0.00667882i	$0.997874\pi$
$420$		0			0
$421$	−158819.			−0.896062			−0.448031	−	0.894018i	$-0.647875\pi$
$421$	−158819.			−0.896062			−0.448031	+	0.894018i	$0.647875\pi$
$422$	−424.154	+	34004.6i	−0.00238176	+	0.190947i
$423$		−	78976.7i		−	0.441386i
$424$	241885.	+	9055.18i	1.34548	+	0.0503693i
$425$		0			0
$426$	−96018.6	−	1197.68i	−0.529098	−	0.00659968i
$427$			17237.7i			0.0945419i
$428$	−8639.79	+	346274.i	−0.0471646	+	1.89030i
$429$	843.029			0.00458066
$430$		0			0
$431$		−	269669.i		−	1.45170i	−0.687853	−	0.725850i	$-0.741447\pi$
$431$		−	269669.i		−	1.45170i	0.687853	−	0.725850i	$-0.258553\pi$
$432$	−1791.14	+	35871.1i	−0.00959758	+	0.192211i
$433$	−161609.			−0.861967			−0.430983	−	0.902360i	$-0.641833\pi$
$433$	−161609.			−0.861967			−0.430983	+	0.902360i	$0.641833\pi$
$434$	4697.58	+	58.5951i	0.0249399	+	0.000311087i
$435$		0			0
$436$	170436.	+	4252.52i	0.896580	+	0.0223704i
$437$	274395.			1.43686
$438$	−1804.06	+	144632.i	−0.00940376	+	0.753903i
$439$		−	171500.i		−	0.889885i	−0.895559	−	0.444943i	$-0.853224\pi$
$439$		−	171500.i		−	0.889885i	0.895559	−	0.444943i	$-0.146776\pi$
$440$		0			0
$441$	−31212.6			−0.160492
$442$	−30669.2	−	382.551i	−0.156985	−	0.00195814i
$443$			78491.9i			0.399961i	0.979800	+	0.199980i	$0.0640878\pi$
$443$			78491.9i			0.399961i	−0.979800	+	0.199980i	$0.935912\pi$
$444$	1292.45	−	51800.2i	0.00655616	−	0.262764i
$445$		0			0
$446$	1441.16	−	115538.i	0.00724505	−	0.580838i
$447$		−	182535.i		−	0.913546i
$448$	10805.6	−	144120.i	0.0538387	−	0.718071i
$449$	−256874.			−1.27417			−0.637085	−	0.770794i	$-0.719860\pi$
$449$	−256874.			−1.27417			−0.637085	+	0.770794i	$0.719860\pi$
$450$		0			0
$451$		−	610.434i		−	0.00300113i
$452$	−157968.	−	3941.42i	−0.773200	−	0.0192919i
$453$	−214652.			−1.04602
$454$	881.170	−	70643.7i	0.00427512	−	0.342738i
$455$		0			0
$456$	−193056.	−	7227.21i	−0.928438	−	0.0347569i
$457$	−182963.			−0.876053			−0.438027	−	0.898962i	$-0.644322\pi$
$457$	−182963.			−0.876053			−0.438027	+	0.898962i	$0.644322\pi$
$458$	398632.	+	4972.32i	1.90038	+	0.0237043i
$459$		−	26201.9i		−	0.124368i
$460$		0			0
$461$	328023.			1.54348			0.771742	−	0.635936i	$-0.219386\pi$
$461$	328023.			1.54348			0.771742	+	0.635936i	$0.219386\pi$
$462$	36.1449	−	2897.74i	0.000169341	−	0.0135761i
$463$			288300.i			1.34488i	0.740153	+	0.672439i	$0.234753\pi$
$463$			288300.i			1.34488i	−0.740153	+	0.672439i	$0.765247\pi$
$464$	−250417.	−	12504.0i	−1.16313	−	0.0580780i
$465$		0			0
$466$	290213.	+	3619.96i	1.33643	+	0.0166699i
$467$		−	187893.i		−	0.861542i	−0.902461	−	0.430771i	$-0.858242\pi$
$467$		−	187893.i		−	0.861542i	0.902461	−	0.430771i	$-0.141758\pi$
$468$	17731.2	+	442.407i	0.0809555	+	0.00201990i
$469$	264334.			1.20173
$470$		0			0
$471$			18612.4i			0.0838998i
$472$	8350.03	−	223049.i	0.0374804	−	1.00119i
$473$	−10571.7			−0.0472525
$474$	−140420.	−	1751.53i	−0.624991	−	0.00779579i
$475$		0			0
$476$	−2629.88	+	105403.i	−0.0116071	+	0.465199i
$477$	102117.			0.448808
$478$	−3502.70	+	280812.i	−0.0153302	+	1.22902i
$479$		−	42484.8i		−	0.185167i	−0.995705	−	0.0925833i	$-0.970488\pi$
$479$		−	42484.8i		−	0.185167i	0.995705	−	0.0925833i	$-0.0295125\pi$
$480$		0			0
$481$	−25589.1			−0.110602
$482$	205746.	+	2566.36i	0.885599	+	0.0110465i
$483$			86599.2i			0.371210i
$484$	233933.	+	5836.82i	0.998623	+	0.0249164i
$485$		0			0
$486$	−188.983	+	15150.8i	−0.000800110	+	0.0641450i
$487$		−	115941.i		−	0.488854i	−0.969668	−	0.244427i	$-0.921400\pi$
$487$		−	115941.i		−	0.488854i	0.969668	−	0.244427i	$-0.0785998\pi$
$488$	31244.6	+	1169.67i	0.131200	+	0.00491160i
$489$	77784.1			0.325292
$490$		0			0
$491$			254668.i			1.05636i	0.849133	+	0.528179i	$0.177125\pi$
$491$			254668.i			1.05636i	−0.849133	+	0.528179i	$0.822875\pi$
$492$	320.345	−	12839.1i	0.00132339	−	0.0530400i
$493$	182916.			0.752588
$494$	−1189.95	+	95398.3i	−0.00487611	+	0.390919i
$495$		0			0
$496$	424.963	−	8510.73i	0.00172738	−	0.0345942i
$497$	163015.			0.659956
$498$	−101050.	−	1260.44i	−0.407454	−	0.00508235i
$499$		−	139763.i		−	0.561296i	−0.959811	−	0.280648i	$-0.909451\pi$
$499$		−	139763.i		−	0.561296i	0.959811	−	0.280648i	$-0.0905494\pi$
$500$		0			0
$501$	−65003.9			−0.258979
$502$	3613.48	−	289694.i	0.0143390	−	1.14956i
$503$			416958.i			1.64800i	0.566592	+	0.823998i	$0.308261\pi$
$503$			416958.i			1.64800i	−0.566592	+	0.823998i	$0.691739\pi$
$504$	2280.91	−	60928.5i	0.00897940	−	0.239861i
$505$		0			0
$506$	7465.32	+	93.1183i	0.0291573	+	0.000363692i
$507$			139648.i			0.543275i
$508$	−7970.87	+	319464.i	−0.0308872	+	1.23792i
$509$	−414530.			−1.60000			−0.800000	−	0.600000i	$-0.795167\pi$
$509$	−414530.			−1.60000			−0.800000	+	0.600000i	$0.795167\pi$
$510$		0			0
$511$		−	245548.i		−	0.940360i
$512$	−260494.	−	29365.3i	−0.993706	−	0.112020i
$513$	−81502.5			−0.309696
$514$	310823.	+	3877.04i	1.17649	+	0.0146749i
$515$		0			0
$516$	−222353.	−	5547.87i	−0.835108	−	0.0208366i
$517$	11558.6			0.0432440
$518$	−1097.13	+	87957.2i	−0.00408882	+	0.327802i
$519$			266905.i			0.990882i
$520$		0			0
$521$	7651.52			0.0281885			0.0140943	−	0.999901i	$-0.495514\pi$
$521$	7651.52			0.0281885			0.0140943	+	0.999901i	$0.495514\pi$
$522$	−105768.	−	1319.29i	−0.388162	−	0.00484172i
$523$			120269.i			0.439692i	0.975535	+	0.219846i	$0.0705555\pi$
$523$			120269.i			0.439692i	−0.975535	+	0.219846i	$0.929444\pi$
$524$	12265.4	−	491585.i	0.0446704	−	1.79034i
$525$		0			0
$526$	135.536	−	10866.0i	0.000489873	−	0.0392732i
$527$			6216.62i			0.0223838i
$528$	−5249.92	−	262.142i	−0.0188315	−	0.000940305i
$529$	56739.5			0.202756
$530$		0			0
$531$		−	94164.7i		−	0.333964i
$532$	327862.	+	8180.40i	1.15842	+	0.0289036i
$533$	−6342.45			−0.0223256
$534$	−133.171	+	10676.4i	−0.000467011	+	0.0374404i
$535$		0			0
$536$	17936.4	−	479124.i	0.0624319	−	1.66770i
$537$	155829.			0.540381
$538$	−266646.	−	3325.99i	−0.921234	−	0.0114910i
$539$		−	4568.12i		−	0.0157239i
$540$		0			0
$541$	−479201.			−1.63728			−0.818640	−	0.574307i	$-0.805272\pi$
$541$	−479201.			−1.63728			−0.818640	+	0.574307i	$0.805272\pi$
$542$	3190.95	−	255820.i	0.0108623	−	0.870834i
$543$			246382.i			0.835619i
$544$	190872.	+	11919.0i	0.644977	+	0.0402755i
$545$		0			0
$546$	−30107.8	−	375.547i	−0.100993	−	0.00125974i
$547$			327802.i			1.09556i	0.836622	+	0.547781i	$0.184527\pi$
$547$			327802.i			1.09556i	−0.836622	+	0.547781i	$0.815473\pi$
$548$	114797.	+	2864.28i	0.382269	+	0.00953792i
$549$	13190.6			0.0437641
$550$		0			0
$551$		−	568970.i		−	1.87407i
$552$	156967.	+	5876.20i	0.515147	+	0.0192850i
$553$	238398.			0.779566
$554$	−145775.	−	1818.32i	−0.474968	−	0.00592449i
$555$		0			0
$556$	−1847.30	+	74037.8i	−0.00597569	+	0.239499i
$557$	−131341.			−0.423342			−0.211671	−	0.977341i	$-0.567891\pi$
$557$	−131341.			−0.423342			−0.211671	+	0.977341i	$0.567891\pi$
$558$	44.8378	−	3594.66i	0.000144004	−	0.0115449i
$559$			109841.i			0.351513i
$560$		0			0
$561$	3834.78			0.0121847
$562$	−334730.	−	4175.23i	−1.05979	−	0.0132193i
$563$		−	137401.i		−	0.433485i	−0.976229	−	0.216742i	$-0.930457\pi$
$563$		−	137401.i		−	0.433485i	0.976229	−	0.216742i	$-0.0695432\pi$
$564$	243110.	+	6065.77i	0.764265	+	0.0190690i
$565$		0			0
$566$	−4949.62	+	396813.i	−0.0154504	+	1.23866i
$567$		−	25722.2i		−	0.0800096i
$568$	11061.4	−	295477.i	0.0342858	−	0.915855i
$569$	152095.			0.469775			0.234887	−	0.972023i	$-0.424528\pi$
$569$	152095.			0.469775			0.234887	+	0.972023i	$0.424528\pi$
$570$		0			0
$571$		−	150818.i		−	0.462573i	−0.972886	−	0.231286i	$-0.925707\pi$
$571$		−	150818.i		−	0.462573i	0.972886	−	0.231286i	$-0.0742935\pi$
$572$	−64.7485	+	2595.05i	−0.000197896	+	0.00793147i
$573$	−213191.			−0.649322
$574$	−271.932	+	21800.9i	−0.000825348	+	0.0661684i
$575$		0			0
$576$	−110282.	−	8268.63i	−0.332400	−	0.0249223i
$577$	−258173.			−0.775461			−0.387730	−	0.921773i	$-0.626741\pi$
$577$	−258173.			−0.775461			−0.387730	+	0.921773i	$0.626741\pi$
$578$	194550.	+	2426.71i	0.582338	+	0.00726376i
$579$		−	229569.i		−	0.684788i
$580$		0			0
$581$	171557.			0.508226
$582$	3141.75	−	251875.i	0.00927524	−	0.743599i
$583$			14945.3i			0.0439711i
$584$	−445073.	−	16661.7i	−1.30499	−	0.0488533i
$585$		0			0
$586$	22217.9	+	277.133i	0.0647004	+	0.000807037i
$587$			574134.i			1.66624i	0.553095	+	0.833118i	$0.313447\pi$
$587$			574134.i			1.66624i	−0.553095	+	0.833118i	$0.686553\pi$
$588$	2397.27	−	96080.0i	0.00693366	−	0.277894i
$589$	19337.2			0.0557394
$590$		0			0
$591$			45332.7i			0.129789i
$592$	159354.	+	7956.98i	0.454695	+	0.0227041i
$593$	275339.			0.782995			0.391497	−	0.920179i	$-0.371957\pi$
$593$	275339.			0.782995			0.391497	+	0.920179i	$0.371957\pi$
$594$	−2217.39	−	27.6586i	−0.00628449	−	7.83893e-5i
$595$		0			0
$596$	561886.	+	14019.5i	1.58182	+	0.0394675i
$597$	34923.2			0.0979864
$598$	967.506	−	77565.2i	0.00270552	−	0.216903i
$599$		−	86528.9i		−	0.241161i	−0.992704	−	0.120581i	$-0.961524\pi$
$599$		−	86528.9i		−	0.241161i	0.992704	−	0.120581i	$-0.0384756\pi$
$600$		0			0
$601$	−391085.			−1.08273			−0.541367	−	0.840786i	$-0.682093\pi$
$601$	−391085.			−1.08273			−0.541367	+	0.840786i	$0.682093\pi$
$602$	377557.	+	4709.44i	1.04181	+	0.0129950i
$603$		−	202272.i		−	0.556290i
$604$	16486.3	−	660752.i	0.0451906	−	1.81119i
$605$		0			0
$606$	1864.22	−	149455.i	0.00507634	−	0.406972i
$607$		−	86135.8i		−	0.233779i	−0.993145	−	0.116890i	$-0.962708\pi$
$607$		−	86135.8i		−	0.233779i	0.993145	−	0.116890i	$-0.0372924\pi$
$608$	37074.7	−	593718.i	0.100293	−	1.60610i
$609$	179567.			0.484164
$610$		0			0
$611$		−	120095.i		−	0.321694i
$612$	80655.8	+	2012.42i	0.215344	+	0.00537300i
$613$	−161510.			−0.429811			−0.214906	−	0.976635i	$-0.568944\pi$
$613$	−161510.			−0.429811			−0.214906	+	0.976635i	$0.568944\pi$
$614$	−1287.86	+	103248.i	−0.00341610	+	0.273870i
$615$		0			0
$616$	8917.19	+	333.823i	0.0234999	+	0.000879740i
$617$	3300.03			0.00866857			0.00433428	−	0.999991i	$-0.498620\pi$
$617$	3300.03			0.00866857			0.00433428	+	0.999991i	$0.498620\pi$
$618$	−211771.	−	2641.51i	−0.554484	−	0.00691633i
$619$			670945.i			1.75108i	0.483147	+	0.875539i	$0.339494\pi$
$619$			670945.i			1.75108i	−0.483147	+	0.875539i	$0.660506\pi$
$620$		0			0
$621$	66266.9			0.171836
$622$	5325.74	−	426966.i	0.0137657	−	1.10360i
$623$		−	18125.8i		−	0.0467003i
$624$	−2723.67	+	54547.0i	−0.00699497	+	0.140088i
$625$		0			0
$626$	−305316.	−	3808.34i	−0.779113	−	0.00971822i
$627$		−	11928.3i		−	0.0303419i
$628$	−57293.6	−	1429.52i	−0.145274	−	0.00362469i
$629$	−116400.			−0.294205
$630$		0			0
$631$		−	563090.i		−	1.41423i	−0.707100	−	0.707113i	$-0.749997\pi$
$631$		−	563090.i		−	1.41423i	0.707100	−	0.707113i	$-0.250003\pi$
$632$	16176.6	−	432114.i	0.0404997	−	1.08184i
$633$	−44176.7			−0.110252
$634$	−433110.	−	5402.37i	−1.07750	−	0.0134402i
$635$		0			0
$636$	−7843.04	+	314340.i	−0.0193897	+	0.777116i
$637$	−47463.1			−0.116971
$638$	193.085	−	15479.7i	0.000474358	−	0.0380295i
$639$		−	124742.i		−	0.305499i
$640$		0			0
$641$	758985.			1.84721			0.923607	−	0.383341i	$-0.125226\pi$
$641$	758985.			1.84721			0.923607	+	0.383341i	$0.125226\pi$
$642$	−449928.	−	5612.15i	−1.09162	−	0.0136163i
$643$		−	572545.i		−	1.38480i	−0.721513	−	0.692401i	$-0.756553\pi$
$643$		−	572545.i		−	1.38480i	0.721513	−	0.692401i	$-0.243447\pi$
$644$	−266573.	−	6651.21i	−0.642754	−	0.0160372i
$645$		0			0
$646$	−5412.83	+	433948.i	−0.0129706	+	1.03986i
$647$			263241.i			0.628847i	0.949283	+	0.314423i	$0.101811\pi$
$647$			263241.i			0.628847i	−0.949283	+	0.314423i	$0.898189\pi$
$648$	−46623.3	−	1745.39i	−0.111033	−	0.00415663i
$649$	13781.5			0.0327195
$650$		0			0
$651$			6102.82i			0.0144002i
$652$	−5974.18	+	239439.i	−0.0140534	+	0.563247i
$653$	224745.			0.527065			0.263532	−	0.964651i	$-0.415112\pi$
$653$	224745.			0.527065			0.263532	+	0.964651i	$0.415112\pi$
$654$	−2762.31	+	221455.i	−0.00645827	+	0.517762i
$655$		0			0
$656$	39497.2	+	1972.20i	0.0917823	+	0.00458293i
$657$	−187897.			−0.435300
$658$	−412803.	−	5149.07i	−0.953434	−	0.0118926i
$659$			778617.i			1.79289i	0.443158	+	0.896444i	$0.353858\pi$
$659$			778617.i			1.79289i	−0.443158	+	0.896444i	$0.646142\pi$
$660$		0			0
$661$	339420.			0.776844			0.388422	−	0.921482i	$-0.373020\pi$
$661$	339420.			0.776844			0.388422	+	0.921482i	$0.373020\pi$
$662$	5441.88	−	436277.i	0.0124175	−	0.995512i
$663$		−	39843.6i		−	0.0906424i
$664$	11641.1	−	310960.i	0.0264032	−	0.705291i
$665$		0			0
$666$	67306.1	+	839.539i	0.151742	+	0.00189275i
$667$			462610.i			1.03983i
$668$	4992.60	−	200098.i	0.0111885	−	0.448425i
$669$	150100.			0.335373
$670$		0			0
$671$			1930.50i			0.00428771i
$672$	187378.	+	11700.8i	0.414934	+	0.0259105i
$673$	20796.2			0.0459149			0.0229574	−	0.999736i	$-0.492692\pi$
$673$	20796.2			0.0459149			0.0229574	+	0.999736i	$0.492692\pi$
$674$	610250.	+	7611.92i	1.34335	+	0.0167561i
$675$		0			0
$676$	−429871.	−	10725.6i	−0.940686	−	0.0234709i
$677$	202957.			0.442820			0.221410	−	0.975181i	$-0.428934\pi$
$677$	202957.			0.442820			0.221410	+	0.975181i	$0.428934\pi$
$678$	2560.23	−	205254.i	0.00556954	−	0.446512i
$679$			427619.i			0.927508i
$680$		0			0
$681$	91776.0			0.197895
$682$	526.096	+	6.56223i	0.00113109	+	1.41086e-5i
$683$		−	74248.4i		−	0.159164i	−0.996828	−	0.0795821i	$-0.974641\pi$
$683$		−	74248.4i		−	0.159164i	0.996828	−	0.0795821i	$-0.0253586\pi$
$684$	6259.76	−	250884.i	0.0133797	−	0.536243i
$685$		0			0
$686$	−6261.52	+	501988.i	−0.0133055	+	1.06671i
$687$			517879.i			1.09727i
$688$	34155.4	−	684029.i	0.0721577	−	1.44510i
$689$	155283.			0.327103
$690$		0			0
$691$			628006.i			1.31525i	0.753346	+	0.657624i	$0.228438\pi$
$691$			628006.i			1.31525i	−0.753346	+	0.657624i	$0.771562\pi$
$692$	−821599.	−	20499.5i	−1.71572	−	0.0428086i
$693$	3764.57			0.00783879
$694$	−8416.50	+	674753.i	−0.0174748	+	1.40096i
$695$		0			0
$696$	12184.6	−	325478.i	0.0251531	−	0.671898i
$697$	−28850.6			−0.0593866
$698$	78717.3	+	981.876i	0.161569	+	0.00201533i
$699$			377028.i			0.771647i
$700$		0			0
$701$	−508002.			−1.03378			−0.516892	−	0.856051i	$-0.672911\pi$
$701$	−508002.			−1.03378			−0.516892	+	0.856051i	$0.672911\pi$
$702$	−287.374	+	23038.9i	−0.000583141	+	0.0467506i
$703$			362068.i			0.732620i
$704$	1210.15	−	16140.4i	0.00244172	−	0.0325663i
$705$		0			0
$706$	220216.	+	2746.85i	0.441813	+	0.00551094i
$707$			253736.i			0.507626i
$708$	289862.	+	7232.28i	0.578262	+	0.0144281i
$709$	−60762.6			−0.120877			−0.0604385	−	0.998172i	$-0.519250\pi$
$709$	−60762.6			−0.120877			−0.0604385	+	0.998172i	$0.519250\pi$
$710$		0			0
$711$		−	182426.i		−	0.360867i
$712$	−32854.2	−	1229.93i	−0.0648084	−	0.00242616i
$713$	−15722.4			−0.0309271
$714$	−136954.	−	1708.29i	−0.268645	−	0.00335093i
$715$		0			0
$716$	−11968.4	+	479680.i	−0.0233458	+	0.935676i
$717$	−364814.			−0.709633
$718$	−3652.28	+	292804.i	−0.00708460	+	0.567974i
$719$			240815.i			0.465828i	0.972497	+	0.232914i	$0.0748261\pi$
$719$			240815.i			0.465828i	−0.972497	+	0.232914i	$0.925174\pi$
$720$		0			0
$721$	359533.			0.691621
$722$	828578.	+	10335.2i	1.58949	+	0.0198265i
$723$			267292.i			0.511340i
$724$	−758422.	−	18923.2i	−1.44689	−	0.0361009i
$725$		0			0
$726$	−3791.42	+	303959.i	−0.00719331	+	0.576690i
$727$			447387.i			0.846476i	0.906018	+	0.423238i	$0.139107\pi$
$727$			447387.i			0.846476i	−0.906018	+	0.423238i	$0.860893\pi$
$728$	3468.44	−	92650.2i	0.00654442	−	0.174817i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			499646.i			0.935035i
$732$	−1013.09	+	40603.7i	−0.00189072	+	0.0757781i
$733$	−855174.			−1.59165			−0.795823	−	0.605529i	$-0.792961\pi$
$733$	−855174.			−1.59165			−0.795823	+	0.605529i	$0.792961\pi$
$734$	−7799.41	+	625282.i	−0.0144767	+	1.16060i
$735$		0			0
$736$	−30144.2	+	482732.i	−0.0556478	+	0.891149i
$737$	29603.5			0.0545015
$738$	16682.4	+	208.086i	0.0306298	+	0.000382059i
$739$		−	234148.i		−	0.428747i	−0.976752	−	0.214374i	$-0.931229\pi$
$739$		−	234148.i		−	0.428747i	0.976752	−	0.214374i	$-0.0687710\pi$
$740$		0			0
$741$	−123936.			−0.225715
$742$	6657.74	−	533753.i	0.0120926	−	0.969466i
$743$			242702.i			0.439639i	0.975541	+	0.219819i	$0.0705468\pi$
$743$			242702.i			0.439639i	−0.975541	+	0.219819i	$0.929453\pi$
$744$	11061.8	+	414.108i	0.0199839	+	0.000748113i
$745$		0			0
$746$	−934981.	−	11662.4i	−1.68006	−	0.0209562i
$747$		−	131278.i		−	0.235262i
$748$	−294.528	+	11804.4i	−0.000526409	+	0.0210979i
$749$	763863.			1.36161
$750$		0			0
$751$		−	328095.i		−	0.581728i	−0.956764	−	0.290864i	$-0.906057\pi$
$751$		−	328095.i		−	0.581728i	0.956764	−	0.290864i	$-0.0939428\pi$
$752$	−37343.9	+	747885.i	−0.0660364	+	1.32251i
$753$	376353.			0.663751
$754$	−160835.	−	2006.16i	−0.282903	−	0.00352877i
$755$		0			0
$756$	79179.2	+	1975.58i	0.138538	+	0.00345662i
$757$	270737.			0.472450			0.236225	−	0.971698i	$-0.424090\pi$
$757$	270737.			0.472450			0.236225	+	0.971698i	$0.424090\pi$
$758$	−1247.33	+	99998.8i	−0.00217092	+	0.174043i
$759$			9698.49i			0.0168353i
$760$		0			0
$761$	−718672.			−1.24097			−0.620485	−	0.784218i	$-0.713064\pi$
$761$	−718672.			−1.24097			−0.620485	+	0.784218i	$0.713064\pi$
$762$	−415092.	−	5177.63i	−0.714883	−	0.00891705i
$763$		−	375974.i		−	0.645816i
$764$	16374.0	−	656254.i	0.0280524	−	1.12431i
$765$		0			0
$766$	−8238.42	+	660476.i	−0.0140406	+	1.12564i
$767$		−	143190.i		−	0.243401i
$768$	33923.0	−	338841.i	0.0575138	−	0.574478i
$769$	−654646.			−1.10702			−0.553508	−	0.832844i	$-0.686711\pi$
$769$	−654646.			−1.10702			−0.553508	+	0.832844i	$0.686711\pi$
$770$		0			0
$771$			403803.i			0.679298i
$772$	706670.	+	17632.0i	1.18572	+	0.0295846i
$773$	547589.			0.916423			0.458211	−	0.888843i	$-0.348490\pi$
$773$	547589.			0.916423			0.458211	+	0.888843i	$0.348490\pi$
$774$	3603.73	−	288912.i	0.00601548	−	0.482263i
$775$		0			0
$776$	775091.	+	29016.2i	1.28715	+	0.0481856i
$777$	−114269.			−0.189271
$778$	−185231.	−	2310.46i	−0.306023	−	0.00381716i
$779$			89741.3i			0.147883i
$780$		0			0
$781$	18256.5			0.0299307
$782$	4400.99	−	352829.i	0.00719676	−	0.576967i
$783$		−	137407.i		−	0.224123i
$784$	295574.	+	14758.8i	0.480876	+	0.0240114i
$785$		0			0
$786$	638736.	+	7967.24i	1.03389	+	0.0128962i
$787$			709361.i			1.14530i	0.819801	+	0.572648i	$0.194084\pi$
$787$			709361.i			1.14530i	−0.819801	+	0.572648i	$0.805916\pi$
$788$	−139545.	−	3481.76i	−0.224731	−	0.00560721i
$789$	14116.4			0.0226762
$790$		0			0
$791$			348470.i			0.556944i
$792$	255.446	−	6823.56i	0.000407238	−	0.0108783i
$793$	20058.1			0.0318965
$794$	976042.	+	12174.6i	1.54820	+	0.0193114i
$795$		0			0
$796$	−2682.26	+	107502.i	−0.00423327	+	0.169665i
$797$	−431065.			−0.678620			−0.339310	−	0.940675i	$-0.610194\pi$
$797$	−431065.			−0.678620			−0.339310	+	0.940675i	$0.610194\pi$
$798$	−5313.74	+	426004.i	−0.00834439	+	0.668972i
$799$		−	546289.i		−	0.855714i
$800$		0			0
$801$	−13870.1			−0.0216179
$802$	−409336.	−	5105.83i	−0.636401	−	0.00793811i
$803$		−	27499.6i		−	0.0426477i
$804$	622642.	+	15535.4i	0.963223	+	0.0240331i
$805$		0			0
$806$	68.1820	−	5466.17i	0.000104954	−	0.00841421i
$807$		−	346410.i		−	0.531916i
$808$	459915.	+	17217.3i	0.704457	+	0.0263720i
$809$	−179022.			−0.273533			−0.136767	−	0.990603i	$-0.543671\pi$
$809$	−179022.			−0.273533			−0.136767	+	0.990603i	$0.543671\pi$
$810$		0			0
$811$			979088.i			1.48861i	0.667841	+	0.744304i	$0.267218\pi$
$811$			979088.i			1.48861i	−0.667841	+	0.744304i	$0.732782\pi$
$812$	−13791.6	+	552751.i	−0.0209171	+	0.838335i
$813$	332345.			0.502815
$814$	−122.871	+	9850.58i	−0.000185438	+	0.0148667i
$815$		0			0
$816$	−12389.5	+	248124.i	−0.0186068	+	0.372638i
$817$	1.55418e6			2.32839
$818$	442528.	+	5519.84i	0.661354	+	0.00824936i
$819$		−	39114.2i		−	0.0583131i
$820$		0			0
$821$	154045.			0.228540			0.114270	−	0.993450i	$-0.463547\pi$
$821$	154045.			0.228540			0.114270	+	0.993450i	$0.463547\pi$
$822$	−1860.55	+	149161.i	−0.00275357	+	0.220755i
$823$			844036.i			1.24612i	0.782173	+	0.623062i	$0.214111\pi$
$823$			844036.i			1.24612i	−0.782173	+	0.623062i	$0.785889\pi$
$824$	24396.2	−	651679.i	0.0359309	−	0.959797i
$825$		0			0
$826$	−492188.	−	6139.28i	−0.721392	−	0.00899824i
$827$			1.00992e6i			1.47665i	0.674445	+	0.738325i	$0.264383\pi$
$827$			1.00992e6i			1.47665i	−0.674445	+	0.738325i	$0.735617\pi$
$828$	−5089.60	+	203986.i	−0.00742375	+	0.297536i
$829$	−617007.			−0.897803			−0.448901	−	0.893581i	$-0.648185\pi$
$829$	−617007.			−0.897803			−0.448901	+	0.893581i	$0.648185\pi$
$830$		0			0
$831$		−	189382.i		−	0.274244i
$832$	−167700.	−	12573.6i	−0.242262	−	0.0181640i
$833$	−215900.			−0.311145
$834$	−96200.3	−	1199.95i	−0.138307	−	0.00172517i
$835$		0			0
$836$	36718.2	+	916.147i	0.0525374	+	0.00131085i
$837$	4669.96			0.00666595
$838$	116.996	−	9379.60i	0.000166603	−	0.0133566i
$839$		−	1.04364e6i		−	1.48261i	−0.671171	−	0.741303i	$-0.734208\pi$
$839$		−	1.04364e6i		−	1.48261i	0.671171	−	0.741303i	$-0.265792\pi$
$840$		0			0
$841$	251961.			0.356239
$842$	635227.	+	7923.46i	0.895993	+	0.0111761i
$843$		−	434860.i		−	0.611920i
$844$	3392.97	−	135987.i	0.00476316	−	0.190902i
$845$		0			0
$846$	−3940.14	+	315882.i	−0.00550518	+	0.441352i
$847$		−	516046.i		−	0.719318i
$848$	−967014.	−	48285.6i	−1.34475	−	0.0671468i
$849$	−515515.			−0.715197
$850$		0			0
$851$		−	294385.i		−	0.406496i
$852$	383985.	+	9580.72i	0.528975	+	0.0131983i
$853$	−103215.			−0.141856			−0.0709278	−	0.997481i	$-0.522596\pi$
$853$	−103215.			−0.141856			−0.0709278	+	0.997481i	$0.522596\pi$
$854$	859.988	−	68945.5i	0.00117917	−	0.0945345i
$855$		0			0
$856$	51832.0	−	1.38456e6i	0.0707377	−	1.88957i
$857$	240186.			0.327029			0.163515	−	0.986541i	$-0.447717\pi$
$857$	240186.			0.327029			0.163515	+	0.986541i	$0.447717\pi$
$858$	−3371.86	−	42.0587i	−0.00458030	−	5.71322e-5i
$859$			75055.7i			0.101718i	0.998706	+	0.0508590i	$0.0161959\pi$
$859$			75055.7i			0.101718i	−0.998706	+	0.0508590i	$0.983804\pi$
$860$		0			0
$861$	−28322.4			−0.0382053
$862$	−13453.8	+	1.07859e6i	−0.0181063	+	1.45159i
$863$		−	539137.i		−	0.723898i	−0.932198	−	0.361949i	$-0.882111\pi$
$863$		−	539137.i		−	0.723898i	0.932198	−	0.361949i	$-0.117889\pi$
$864$	8953.61	−	143384.i	0.0119942	−	0.192076i
$865$		0			0
$866$	646387.	+	8062.67i	0.861900	+	0.0107509i
$867$			252747.i			0.336239i
$868$	−18786.0	−	468.724i	−0.0249341	−	0.000622125i
$869$	26698.9			0.0353553
$870$		0			0
$871$		−	307583.i		−	0.405439i
$872$	−681480.	−	25511.8i	−0.896232	−	0.0335512i
$873$	327220.			0.429350
$874$	−1.09749e6	−	13689.5i	−1.43674	−	0.0179212i
$875$		0			0
$876$	14431.3	−	578392.i	0.0188061	−	0.753727i
$877$	−851207.			−1.10672			−0.553358	−	0.832944i	$-0.686654\pi$
$877$	−851207.			−1.10672			−0.553358	+	0.832944i	$0.686654\pi$
$878$	−8556.10	+	685945.i	−0.0110991	+	0.889816i
$879$			28864.1i			0.0373577i
$880$		0			0
$881$	−1.32290e6			−1.70442			−0.852209	−	0.523201i	$-0.824738\pi$
$881$	−1.32290e6			−1.70442			−0.852209	+	0.523201i	$0.824738\pi$
$882$	124841.	+	1557.19i	0.160479	+	0.00200173i
$883$			222639.i			0.285548i	0.989755	+	0.142774i	$0.0456023\pi$
$883$			222639.i			0.285548i	−0.989755	+	0.142774i	$0.954398\pi$
$884$	122648.	+	3060.17i	0.156948	+	0.00391598i
$885$		0			0
$886$	3915.95	−	313943.i	0.00498850	−	0.399929i
$887$		−	1.27431e6i		−	1.61967i	−0.586655	−	0.809837i	$-0.699555\pi$
$887$		−	1.27431e6i		−	1.61967i	0.586655	−	0.809837i	$-0.300445\pi$
$888$	−7753.72	+	207120.i	−0.00983296	+	0.262661i
$889$	704721.			0.891690
$890$		0			0
$891$		−	2880.70i		−	0.00362864i
$892$	−11528.4	+	462044.i	−0.0144890	+	0.580703i
$893$	−1.69926e6			−2.13087
$894$	−9106.64	+	730082.i	−0.0113942	+	0.913475i
$895$		0			0
$896$	−50409.3	+	575895.i	−0.0627906	+	0.717344i
$897$	100768.			0.125238
$898$	1.02742e6	+	12815.4i	1.27407	+	0.0158920i
$899$			32601.1i			0.0403378i
$900$		0			0
$901$	706351.			0.870103
$902$	−30.4545	+	2441.54i	−3.74316e−5	+	0.00300090i
$903$			490499.i			0.601537i
$904$	631626.	+	23645.5i	0.772900	+	0.0289342i
$905$		0			0
$906$	858542.	+	10709.0i	1.04594	+	0.0130464i
$907$		−	1.23551e6i		−	1.50187i	−0.660377	−	0.750934i	$-0.729604\pi$
$907$		−	1.23551e6i		−	1.50187i	0.660377	−	0.750934i	$-0.270396\pi$
$908$	−7048.81	+	282509.i	−0.00854957	+	0.342658i
$909$	194162.			0.234984
$910$		0			0
$911$		−	830747.i		−	1.00100i	−0.865738	−	0.500498i	$-0.833150\pi$
$911$		−	830747.i		−	1.00100i	0.865738	−	0.500498i	$-0.166850\pi$
$912$	771802.	+	38538.1i	0.927933	+	0.0463341i
$913$	19213.2			0.0230493
$914$	731795.	+	9128.00i	0.875985	+	0.0109266i
$915$		0			0
$916$	−1.59416e6	−	39775.4i	−1.89994	−	0.0474050i
$917$	−1.08441e6			−1.28960
$918$	−1307.21	+	104799.i	−0.00155117	+	0.124358i
$919$		−	189522.i		−	0.224403i	−0.993685	−	0.112201i	$-0.964210\pi$
$919$		−	189522.i		−	0.224403i	0.993685	−	0.112201i	$-0.0357902\pi$
$920$		0			0
$921$	−134133.			−0.158131
$922$	−1.31199e6	−	16365.0i	−1.54336	−	0.0192511i
$923$		−	189687.i		−	0.222656i
$924$	−289.136	+	11588.3i	−0.000338656	+	0.0135730i
$925$		0			0
$926$	14383.3	−	1.15311e6i	0.0167739	−	1.34477i
$927$		−	275120.i		−	0.320157i
$928$	1.00097e6	+	62505.2i	1.16231	+	0.0725806i
$929$	125410.			0.145312			0.0726558	−	0.997357i	$-0.476853\pi$
$929$	125410.			0.145312			0.0726558	+	0.997357i	$0.476853\pi$
$930$		0			0
$931$			671570.i			0.774804i
$932$	−1.16058e6	−	28957.4i	−1.33612	−	0.0333371i
$933$	554689.			0.637215
$934$	−9373.96	+	751513.i	−0.0107456	+	0.861475i
$935$		0			0
$936$	−70897.2	−	2654.10i	−0.0809240	−	0.00302946i
$937$	1.18087e6			1.34500			0.672502	−	0.740095i	$-0.265220\pi$
$937$	1.18087e6			1.34500			0.672502	+	0.740095i	$0.265220\pi$
$938$	−1.05725e6	−	13187.6i	−1.20164	−	0.0149886i
$939$		−	396648.i		−	0.449856i
$940$		0			0
$941$	259343.			0.292883			0.146442	−	0.989219i	$-0.453218\pi$
$941$	259343.			0.292883			0.146442	+	0.989219i	$0.453218\pi$
$942$	928.572	−	74443.9i	0.00104644	−	0.0838933i
$943$		−	72965.7i		−	0.0820531i
$944$	−44525.4	+	891710.i	−0.0499648	+	1.00064i
$945$		0			0
$946$	42283.7	+	527.423i	0.0472488	+	0.000589355i
$947$		−	658326.i		−	0.734076i	−0.930206	−	0.367038i	$-0.880372\pi$
$947$		−	658326.i		−	0.734076i	0.930206	−	0.367038i	$-0.119628\pi$
$948$	561551.	+	14011.1i	0.624845	+	0.0155904i
$949$	−285723.			−0.317258
$950$		0			0
$951$		−	562670.i		−	0.622146i
$952$	15777.3	−	421447.i	0.0174083	−	0.465018i
$953$	−710654.			−0.782478			−0.391239	−	0.920289i	$-0.627953\pi$
$953$	−710654.			−0.782478			−0.391239	+	0.920289i	$0.627953\pi$
$954$	−408435.	−	5094.60i	−0.448773	−	0.00559775i
$955$		0			0
$956$	28019.4	−	1.12299e6i	0.0306580	−	1.22874i
$957$	20110.2			0.0219580
$958$	−2119.56	+	169926.i	−0.00230949	+	0.185152i
$959$		−	253237.i		−	0.275353i
$960$		0			0
$961$	922413.			0.998800
$962$	102348.	+	1276.64i	0.110594	+	0.00137948i
$963$		−	584519.i		−	0.630298i
$964$	−822791.	−	20529.3i	−0.885392	−	0.0220912i
$965$		0			0
$966$	4320.42	−	346370.i	0.00462991	−	0.371181i
$967$		−	1.34932e6i		−	1.44298i	−0.692423	−	0.721491i	$-0.743457\pi$
$967$		−	1.34932e6i		−	1.44298i	0.692423	−	0.721491i	$-0.256543\pi$
$968$	−935369.	−	35016.4i	−0.998234	−	0.0373698i
$969$	−563759.			−0.600408
$970$		0			0
$971$			1.17569e6i			1.24696i	0.781838	+	0.623482i	$0.214282\pi$
$971$			1.17569e6i			1.24696i	−0.781838	+	0.623482i	$0.785718\pi$
$972$	1511.74	−	60589.1i	0.00160009	−	0.0641301i
$973$	163324.			0.172514
$974$	−5784.28	+	463728.i	−0.00609722	+	0.488816i
$975$		0			0
$976$	−124910.	−	6237.10i	−0.131129	−	0.00654762i
$977$	−1.31383e6			−1.37642			−0.688211	−	0.725511i	$-0.741604\pi$
$977$	−1.31383e6			−1.37642			−0.688211	+	0.725511i	$0.741604\pi$
$978$	−311112.	−	3880.64i	−0.325267	−	0.00405720i
$979$		−	2029.96i		−	0.00211798i
$980$		0			0
$981$	−287701.			−0.298953
$982$	12705.3	−	1.01859e6i	0.0131754	−	1.05628i
$983$			915869.i			0.947821i	0.880573	+	0.473911i	$0.157158\pi$
$983$			915869.i			0.947821i	−0.880573	+	0.473911i	$0.842842\pi$
$984$	−1921.82	+	51336.4i	−0.00198483	+	0.0530194i
$985$		0			0
$986$	−731606.	−	9125.64i	−0.752529	−	0.00938663i
$987$		−	536288.i		−	0.550508i
$988$	9518.83	−	381504.i	0.00975146	−	0.390828i
$989$	−1.26365e6			−1.29192
$990$		0			0
$991$		−	1.25784e6i		−	1.28079i	−0.768046	−	0.640394i	$-0.778771\pi$
$991$		−	1.25784e6i		−	1.28079i	0.768046	−	0.640394i	$-0.221229\pi$
$992$	−2124.32	+	34019.1i	−0.00215872	+	0.0345700i
$993$	566785.			0.574804
$994$	−652010.	−	8132.81i	−0.659905	−	0.00823129i
$995$		0			0
$996$	404106.	+	10082.8i	0.407358	+	0.0101639i
$997$	1.20780e6			1.21508			0.607538	−	0.794291i	$-0.292157\pi$
$997$	1.20780e6			1.21508			0.607538	+	0.794291i	$0.292157\pi$
$998$	−6972.78	+	559010.i	−0.00700075	+	0.561253i
$999$			87440.0i			0.0876152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.b.151.1	✓	16
4.3	odd	2	inner	300.5.c.b.151.2	yes	16
5.2	odd	4		300.5.f.c.199.17		32
5.3	odd	4		300.5.f.c.199.16		32
5.4	even	2		300.5.c.c.151.16	yes	16
20.3	even	4		300.5.f.c.199.18		32
20.7	even	4		300.5.f.c.199.15		32
20.19	odd	2		300.5.c.c.151.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.1	✓	16	1.1	even	1	trivial
300.5.c.b.151.2	yes	16	4.3	odd	2	inner
300.5.c.c.151.15	yes	16	20.19	odd	2
300.5.c.c.151.16	yes	16	5.4	even	2
300.5.f.c.199.15		32	20.7	even	4
300.5.f.c.199.16		32	5.3	odd	4
300.5.f.c.199.17		32	5.2	odd	4
300.5.f.c.199.18		32	20.3	even	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.99969 - 0.0498899i) q^{2} -5.19615i q^{3} +(15.9950 + 0.399088i) q^{4} +(-0.259236 + 20.7830i) q^{6} -35.2842i q^{7} +(-63.9552 - 2.39422i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-3.99969 - 0.0498899i) q^{2} -5.19615i q^{3} +(15.9950 + 0.399088i) q^{4} +(-0.259236 + 20.7830i) q^{6} -35.2842i q^{7} +(-63.9552 - 2.39422i) q^{8} -27.0000 q^{9} -3.95158i q^{11} +(2.07372 - 83.1126i) q^{12} -41.0572 q^{13} +(-1.76033 + 141.126i) q^{14} +(255.681 + 12.7668i) q^{16} -186.761 q^{17} +(107.992 + 1.34703i) q^{18} +580.932i q^{19} -183.342 q^{21} +(-0.197144 + 15.8051i) q^{22} -472.336i q^{23} +(-12.4407 + 332.321i) q^{24} +(164.216 + 2.04834i) q^{26} +140.296i q^{27} +(14.0815 - 564.372i) q^{28} -979.409 q^{29} -33.2865i q^{31} +(-1022.01 - 63.8193i) q^{32} -20.5330 q^{33} +(746.987 + 9.31750i) q^{34} +(-431.866 - 10.7754i) q^{36} +623.253 q^{37} +(28.9826 - 2323.55i) q^{38} +213.340i q^{39} +154.478 q^{41} +(733.312 + 9.14693i) q^{42} -2675.32i q^{43} +(1.57703 - 63.2057i) q^{44} +(-23.5648 + 1889.20i) q^{46} +2925.06i q^{47} +(66.3385 - 1328.56i) q^{48} +1156.02 q^{49} +970.440i q^{51} +(-656.711 - 16.3855i) q^{52} -3782.10 q^{53} +(6.99936 - 561.141i) q^{54} +(-84.4782 + 2256.61i) q^{56} +3018.61 q^{57} +(3917.33 + 48.8626i) q^{58} +3487.58i q^{59} -488.539 q^{61} +(-1.66066 + 133.135i) q^{62} +952.674i q^{63} +(4084.54 + 306.245i) q^{64} +(82.1257 + 1.02439i) q^{66} +7491.56i q^{67} +(-2987.25 - 74.5342i) q^{68} -2454.33 q^{69} +4620.06i q^{71} +(1726.79 + 64.6439i) q^{72} +6959.14 q^{73} +(-2492.82 - 31.0940i) q^{74} +(-231.843 + 9292.01i) q^{76} -139.429 q^{77} +(10.6435 - 853.292i) q^{78} +6756.51i q^{79} +729.000 q^{81} +(-617.865 - 7.70690i) q^{82} +4862.15i q^{83} +(-2932.56 - 73.1697i) q^{84} +(-133.471 + 10700.4i) q^{86} +5089.16i q^{87} +(-9.46096 + 252.724i) q^{88} +513.707 q^{89} +1448.67i q^{91} +(188.504 - 7555.03i) q^{92} -172.962 q^{93} +(145.931 - 11699.3i) q^{94} +(-331.615 + 5310.52i) q^{96} -12119.3 q^{97} +(-4623.73 - 57.6739i) q^{98} +106.693i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	\( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} - 176 q^{13} + 78 q^{14} - 376 q^{16} + 162 q^{18} - 144 q^{21} + 788 q^{22} + 108 q^{24} + 678 q^{26} - 3368 q^{28} + 1728 q^{29} - 2016 q^{32} - 2932 q^{34} - 216 q^{36} + 1568 q^{37} + 6990 q^{38} + 1248 q^{41} - 162 q^{42} + 8088 q^{44} + 5956 q^{46} - 2088 q^{48} - 10720 q^{49} - 3128 q^{52} + 288 q^{53} - 486 q^{54} - 10236 q^{56} - 5616 q^{57} + 16164 q^{58} - 3760 q^{61} + 12714 q^{62} + 10544 q^{64} + 8100 q^{66} - 26136 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} - 17004 q^{74} - 28344 q^{76} - 768 q^{77} + 16830 q^{78} + 11664 q^{81} + 21280 q^{82} + 15120 q^{84} + 24414 q^{86} - 52840 q^{88} - 768 q^{89} - 23736 q^{92} + 9936 q^{93} - 45156 q^{94} - 11088 q^{96} - 7248 q^{97} + 58140 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 - 176 * q^13 + 78 * q^14 - 376 * q^16 + 162 * q^18 - 144 * q^21 + 788 * q^22 + 108 * q^24 + 678 * q^26 - 3368 * q^28 + 1728 * q^29 - 2016 * q^32 - 2932 * q^34 - 216 * q^36 + 1568 * q^37 + 6990 * q^38 + 1248 * q^41 - 162 * q^42 + 8088 * q^44 + 5956 * q^46 - 2088 * q^48 - 10720 * q^49 - 3128 * q^52 + 288 * q^53 - 486 * q^54 - 10236 * q^56 - 5616 * q^57 + 16164 * q^58 - 3760 * q^61 + 12714 * q^62 + 10544 * q^64 + 8100 * q^66 - 26136 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 - 17004 * q^74 - 28344 * q^76 - 768 * q^77 + 16830 * q^78 + 11664 * q^81 + 21280 * q^82 + 15120 * q^84 + 24414 * q^86 - 52840 * q^88 - 768 * q^89 - 23736 * q^92 + 9936 * q^93 - 45156 * q^94 - 11088 * q^96 - 7248 * q^97 + 58140 * q^98

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