LMFDB - Embedded newform 175.5.g.c.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(43,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("175.43");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	175.43
Dual form			175.5.g.c.57.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.896879 + 0.896879i) q^{2} +(9.60523 + 9.60523i) q^{3} +14.3912i q^{4} -17.2295 q^{6} +(13.0958 - 13.0958i) q^{7} +(-27.2572 - 27.2572i) q^{8} +103.521i q^{9} +O(q^{10})$	\(q+(-0.896879 + 0.896879i) q^{2} +(9.60523 + 9.60523i) q^{3} +14.3912i q^{4} -17.2295 q^{6} +(13.0958 - 13.0958i) q^{7} +(-27.2572 - 27.2572i) q^{8} +103.521i q^{9} -106.380 q^{11} +(-138.231 + 138.231i) q^{12} +(222.204 + 222.204i) q^{13} +23.4907i q^{14} -181.367 q^{16} +(-163.879 + 163.879i) q^{17} +(-92.8458 - 92.8458i) q^{18} +406.567i q^{19} +251.576 q^{21} +(95.4098 - 95.4098i) q^{22} +(-492.730 - 492.730i) q^{23} -523.624i q^{24} -398.579 q^{26} +(-216.320 + 216.320i) q^{27} +(188.465 + 188.465i) q^{28} -371.475i q^{29} -315.550 q^{31} +(598.780 - 598.780i) q^{32} +(-1021.80 - 1021.80i) q^{33} -293.959i q^{34} -1489.79 q^{36} +(1113.90 - 1113.90i) q^{37} +(-364.641 - 364.641i) q^{38} +4268.64i q^{39} +273.917 q^{41} +(-225.634 + 225.634i) q^{42} +(739.107 + 739.107i) q^{43} -1530.94i q^{44} +883.838 q^{46} +(-326.912 + 326.912i) q^{47} +(-1742.07 - 1742.07i) q^{48} -343.000i q^{49} -3148.19 q^{51} +(-3197.78 + 3197.78i) q^{52} +(-502.049 - 502.049i) q^{53} -388.025i q^{54} -713.911 q^{56} +(-3905.17 + 3905.17i) q^{57} +(333.168 + 333.168i) q^{58} +5703.66i q^{59} -974.970 q^{61} +(283.010 - 283.010i) q^{62} +(1355.69 + 1355.69i) q^{63} -1827.80i q^{64} +1832.87 q^{66} +(1635.67 - 1635.67i) q^{67} +(-2358.42 - 2358.42i) q^{68} -9465.58i q^{69} +586.493 q^{71} +(2821.70 - 2821.70i) q^{72} +(7096.31 + 7096.31i) q^{73} +1998.06i q^{74} -5850.99 q^{76} +(-1393.13 + 1393.13i) q^{77} +(-3828.45 - 3828.45i) q^{78} -2389.81i q^{79} +4229.60 q^{81} +(-245.671 + 245.671i) q^{82} +(1297.02 + 1297.02i) q^{83} +3620.49i q^{84} -1325.78 q^{86} +(3568.10 - 3568.10i) q^{87} +(2899.62 + 2899.62i) q^{88} +11496.6i q^{89} +5819.87 q^{91} +(7090.99 - 7090.99i) q^{92} +(-3030.93 - 3030.93i) q^{93} -586.400i q^{94} +11502.8 q^{96} +(6917.34 - 6917.34i) q^{97} +(307.629 + 307.629i) q^{98} -11012.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) $ 24 * q - 20 * q^3 + 72 * q^6	$ 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) $ 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.896879	+	0.896879i	−0.224220	+	0.224220i	−0.810273	−	0.586053i	$-0.800681\pi$
$2$	−0.896879	+	0.896879i	−0.224220	+	0.224220i	0.586053	+	0.810273i	$0.300681\pi$
$3$	9.60523	+	9.60523i	1.06725	+	1.06725i	0.997569	+	0.0696786i	$0.0221974\pi$
$3$	9.60523	+	9.60523i	1.06725	+	1.06725i	0.0696786	+	0.997569i	$0.477803\pi$
$4$			14.3912i			0.899451i
$5$		0			0
$5$		0			0
$6$	−17.2295			−0.478596
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$8$	−27.2572	−	27.2572i	−0.425894	−	0.425894i
$9$			103.521i			1.27804i
$10$		0			0
$11$	−106.380			−0.879173			−0.439586	−	0.898200i	$-0.644875\pi$
$11$	−106.380			−0.879173			−0.439586	+	0.898200i	$0.644875\pi$
$12$	−138.231	+	138.231i	−0.959937	+	0.959937i
$13$	222.204	+	222.204i	1.31481	+	1.31481i	0.917822	+	0.396993i	$0.129946\pi$
$13$	222.204	+	222.204i	1.31481	+	1.31481i	0.396993	+	0.917822i	$0.370054\pi$
$14$			23.4907i			0.119850i
$15$		0			0
$16$	−181.367			−0.708463
$17$	−163.879	+	163.879i	−0.567056	+	0.567056i	−0.931302	−	0.364247i	$-0.881326\pi$
$17$	−163.879	+	163.879i	−0.567056	+	0.567056i	0.364247	+	0.931302i	$0.381326\pi$
$18$	−92.8458	−	92.8458i	−0.286561	−	0.286561i
$19$			406.567i			1.12622i	0.826380	+	0.563112i	$0.190396\pi$
$19$			406.567i			1.12622i	−0.826380	+	0.563112i	$0.809604\pi$
$20$		0			0
$21$	251.576			0.570468
$22$	95.4098	−	95.4098i	0.197128	−	0.197128i
$23$	−492.730	−	492.730i	−0.931437	−	0.931437i	0.0663589	−	0.997796i	$-0.478862\pi$
$23$	−492.730	−	492.730i	−0.931437	−	0.931437i	−0.997796	+	0.0663589i	$0.978862\pi$
$24$		−	523.624i		−	0.909070i
$25$		0			0
$26$	−398.579			−0.589615
$27$	−216.320	+	216.320i	−0.296735	+	0.296735i
$28$	188.465	+	188.465i	0.240388	+	0.240388i
$29$		−	371.475i		−	0.441706i	−0.975307	−	0.220853i	$-0.929116\pi$
$29$		−	371.475i		−	0.441706i	0.975307	−	0.220853i	$-0.0708841\pi$
$30$		0			0
$31$	−315.550			−0.328356			−0.164178	−	0.986431i	$-0.552497\pi$
$31$	−315.550			−0.328356			−0.164178	+	0.986431i	$0.552497\pi$
$32$	598.780	−	598.780i	0.584746	−	0.584746i
$33$	−1021.80	−	1021.80i	−0.938295	−	0.938295i
$34$		−	293.959i		−	0.254290i
$35$		0			0
$36$	−1489.79			−1.14953
$37$	1113.90	−	1113.90i	0.813657	−	0.813657i	−0.171523	−	0.985180i	$-0.554869\pi$
$37$	1113.90	−	1113.90i	0.813657	−	0.813657i	0.985180	+	0.171523i	$0.0548689\pi$
$38$	−364.641	−	364.641i	−0.252522	−	0.252522i
$39$			4268.64i			2.80647i
$40$		0			0
$41$	273.917			0.162949			0.0814746	−	0.996675i	$-0.474037\pi$
$41$	273.917			0.162949			0.0814746	+	0.996675i	$0.474037\pi$
$42$	−225.634	+	225.634i	−0.127910	+	0.127910i
$43$	739.107	+	739.107i	0.399733	+	0.399733i	0.878139	−	0.478406i	$-0.158785\pi$
$43$	739.107	+	739.107i	0.399733	+	0.399733i	−0.478406	+	0.878139i	$0.658785\pi$
$44$		−	1530.94i		−	0.790773i
$45$		0			0
$46$	883.838			0.417693
$47$	−326.912	+	326.912i	−0.147991	+	0.147991i	−0.777220	−	0.629229i	$-0.783371\pi$
$47$	−326.912	+	326.912i	−0.147991	+	0.147991i	0.629229	+	0.777220i	$0.283371\pi$
$48$	−1742.07	−	1742.07i	−0.756106	−	0.756106i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	−3148.19			−1.21038
$52$	−3197.78	+	3197.78i	−1.18261	+	1.18261i
$53$	−502.049	−	502.049i	−0.178729	−	0.178729i	0.612073	−	0.790802i	$-0.290336\pi$
$53$	−502.049	−	502.049i	−0.178729	−	0.178729i	−0.790802	+	0.612073i	$0.790336\pi$
$54$		−	388.025i		−	0.133068i
$55$		0			0
$56$	−713.911			−0.227650
$57$	−3905.17	+	3905.17i	−1.20196	+	1.20196i
$58$	333.168	+	333.168i	0.0990392	+	0.0990392i
$59$			5703.66i			1.63851i	0.573427	+	0.819257i	$0.305614\pi$
$59$			5703.66i			1.63851i	−0.573427	+	0.819257i	$0.694386\pi$
$60$		0			0
$61$	−974.970			−0.262018			−0.131009	−	0.991381i	$-0.541822\pi$
$61$	−974.970			−0.262018			−0.131009	+	0.991381i	$0.541822\pi$
$62$	283.010	−	283.010i	0.0736239	−	0.0736239i
$63$	1355.69	+	1355.69i	0.341570	+	0.341570i
$64$		−	1827.80i		−	0.446240i
$65$		0			0
$66$	1832.87			0.420769
$67$	1635.67	−	1635.67i	0.364373	−	0.364373i	−0.501047	−	0.865420i	$-0.667052\pi$
$67$	1635.67	−	1635.67i	0.364373	−	0.364373i	0.865420	+	0.501047i	$0.167052\pi$
$68$	−2358.42	−	2358.42i	−0.510039	−	0.510039i
$69$		−	9465.58i		−	1.98815i
$70$		0			0
$71$	586.493			0.116345			0.0581723	−	0.998307i	$-0.481473\pi$
$71$	586.493			0.116345			0.0581723	+	0.998307i	$0.481473\pi$
$72$	2821.70	−	2821.70i	0.544309	−	0.544309i
$73$	7096.31	+	7096.31i	1.33164	+	1.33164i	0.903903	+	0.427737i	$0.140689\pi$
$73$	7096.31	+	7096.31i	1.33164	+	1.33164i	0.427737	+	0.903903i	$0.359311\pi$
$74$			1998.06i			0.364876i
$75$		0			0
$76$	−5850.99			−1.01298
$77$	−1393.13	+	1393.13i	−0.234969	+	0.234969i
$78$	−3828.45	−	3828.45i	−0.629265	−	0.629265i
$79$		−	2389.81i		−	0.382921i	−0.981500	−	0.191461i	$-0.938678\pi$
$79$		−	2389.81i		−	0.382921i	0.981500	−	0.191461i	$-0.0613225\pi$
$80$		0			0
$81$	4229.60			0.644658
$82$	−245.671	+	245.671i	−0.0365364	+	0.0365364i
$83$	1297.02	+	1297.02i	0.188274	+	0.188274i	0.794950	−	0.606676i	$-0.207497\pi$
$83$	1297.02	+	1297.02i	0.188274	+	0.188274i	−0.606676	+	0.794950i	$0.707497\pi$
$84$			3620.49i			0.513108i
$85$		0			0
$86$	−1325.78			−0.179256
$87$	3568.10	−	3568.10i	0.471410	−	0.471410i
$88$	2899.62	+	2899.62i	0.374435	+	0.374435i
$89$			11496.6i			1.45141i	0.688005	+	0.725706i	$0.258487\pi$
$89$			11496.6i			1.45141i	−0.688005	+	0.725706i	$0.741513\pi$
$90$		0			0
$91$	5819.87			0.702798
$92$	7090.99	−	7090.99i	0.837782	−	0.837782i
$93$	−3030.93	−	3030.93i	−0.350438	−	0.350438i
$94$		−	586.400i		−	0.0663649i
$95$		0			0
$96$	11502.8			1.24814
$97$	6917.34	−	6917.34i	0.735183	−	0.735183i	−0.236458	−	0.971642i	$-0.575987\pi$
$97$	6917.34	−	6917.34i	0.735183	−	0.735183i	0.971642	+	0.236458i	$0.0759867\pi$
$98$	307.629	+	307.629i	0.0320314	+	0.0320314i
$99$		−	11012.6i		−	1.12362i
$100$		0			0
$101$	6151.41			0.603021			0.301510	−	0.953463i	$-0.402509\pi$
$101$	6151.41			0.603021			0.301510	+	0.953463i	$0.402509\pi$
$102$	2823.55	−	2823.55i	0.271391	−	0.271391i
$103$	6775.21	+	6775.21i	0.638629	+	0.638629i	0.950217	−	0.311589i	$-0.100861\pi$
$103$	6775.21	+	6775.21i	0.638629	+	0.638629i	−0.311589	+	0.950217i	$0.600861\pi$
$104$		−	12113.3i		−	1.11994i
$105$		0			0
$106$	900.555			0.0801490
$107$	2458.26	−	2458.26i	0.214714	−	0.214714i	−0.591552	−	0.806267i	$-0.701485\pi$
$107$	2458.26	−	2458.26i	0.214714	−	0.214714i	0.806267	+	0.591552i	$0.201485\pi$
$108$	−3113.10	−	3113.10i	−0.266898	−	0.266898i
$109$		−	4682.23i		−	0.394094i	−0.980394	−	0.197047i	$-0.936865\pi$
$109$		−	4682.23i		−	0.394094i	0.980394	−	0.197047i	$-0.0631351\pi$
$110$		0			0
$111$	21398.5			1.73675
$112$	−2375.14	+	2375.14i	−0.189345	+	0.189345i
$113$	4239.96	+	4239.96i	0.332051	+	0.332051i	0.853365	−	0.521314i	$-0.174558\pi$
$113$	4239.96	+	4239.96i	0.332051	+	0.332051i	−0.521314	+	0.853365i	$0.674558\pi$
$114$		−	7004.93i		−	0.539007i
$115$		0			0
$116$	5345.97			0.397293
$117$	−23002.7	+	23002.7i	−1.68038	+	1.68038i
$118$	−5115.50	−	5115.50i	−0.367387	−	0.367387i
$119$			4292.26i			0.303104i
$120$		0			0
$121$	−3324.32			−0.227056
$122$	874.430	−	874.430i	0.0587496	−	0.0587496i
$123$	2631.04	+	2631.04i	0.173907	+	0.173907i
$124$		−	4541.15i		−	0.295340i
$125$		0			0
$126$	−2431.78			−0.153173
$127$	−458.788	+	458.788i	−0.0284449	+	0.0284449i	−0.721186	−	0.692741i	$-0.756403\pi$
$127$	−458.788	+	458.788i	−0.0284449	+	0.0284449i	0.692741	+	0.721186i	$0.256403\pi$
$128$	11219.8	+	11219.8i	0.684802	+	0.684802i
$129$			14198.6i			0.853229i
$130$		0			0
$131$	−20987.2			−1.22296			−0.611479	−	0.791261i	$-0.709425\pi$
$131$	−20987.2			−1.22296			−0.611479	+	0.791261i	$0.709425\pi$
$132$	14705.0	−	14705.0i	0.843951	−	0.843951i
$133$	5324.32	+	5324.32i	0.300996	+	0.300996i
$134$			2934.00i			0.163399i
$135$		0			0
$136$	8933.78			0.483012
$137$	−10186.1	+	10186.1i	−0.542708	+	0.542708i	−0.924322	−	0.381614i	$-0.875369\pi$
$137$	−10186.1	+	10186.1i	−0.542708	+	0.542708i	0.381614	+	0.924322i	$0.375369\pi$
$138$	8489.47	+	8489.47i	0.445782	+	0.445782i
$139$			26432.6i			1.36808i	0.729445	+	0.684039i	$0.239778\pi$
$139$			26432.6i			1.36808i	−0.729445	+	0.684039i	$0.760222\pi$
$140$		0			0
$141$	−6280.13			−0.315886
$142$	−526.013	+	526.013i	−0.0260868	+	0.0260868i
$143$	−23638.0	−	23638.0i	−1.15595	−	1.15595i
$144$		−	18775.3i		−	0.905442i
$145$		0			0
$146$	−12729.1			−0.597160
$147$	3294.60	−	3294.60i	0.152464	−	0.152464i
$148$	16030.3	+	16030.3i	0.731844	+	0.731844i
$149$		−	25099.6i		−	1.13056i	−0.824899	−	0.565281i	$-0.808768\pi$
$149$		−	25099.6i		−	1.13056i	0.824899	−	0.565281i	$-0.191232\pi$
$150$		0			0
$151$	21114.9			0.926052			0.463026	−	0.886345i	$-0.346764\pi$
$151$	21114.9			0.926052			0.463026	+	0.886345i	$0.346764\pi$
$152$	11081.9	−	11081.9i	0.479653	−	0.479653i
$153$	−16964.9	−	16964.9i	−0.724718	−	0.724718i
$154$		−	2498.94i		−	0.105369i
$155$		0			0
$156$	−61430.9			−2.52428
$157$	−12567.2	+	12567.2i	−0.509847	+	0.509847i	−0.914479	−	0.404633i	$-0.867399\pi$
$157$	−12567.2	+	12567.2i	−0.509847	+	0.509847i	0.404633	+	0.914479i	$0.367399\pi$
$158$	2143.37	+	2143.37i	0.0858585	+	0.0858585i
$159$		−	9644.60i		−	0.381496i
$160$		0			0
$161$	−12905.4			−0.497874
$162$	−3793.44	+	3793.44i	−0.144545	+	0.144545i
$163$	−21632.3	−	21632.3i	−0.814193	−	0.814193i	0.171067	−	0.985259i	$-0.445279\pi$
$163$	−21632.3	−	21632.3i	−0.814193	−	0.814193i	−0.985259	+	0.171067i	$0.945279\pi$
$164$			3942.01i			0.146565i
$165$		0			0
$166$	−2326.54			−0.0844295
$167$	25526.2	−	25526.2i	0.915280	−	0.915280i	−0.0814016	−	0.996681i	$-0.525940\pi$
$167$	25526.2	−	25526.2i	0.915280	−	0.915280i	0.996681	+	0.0814016i	$0.0259396\pi$
$168$	−6857.28	−	6857.28i	−0.242959	−	0.242959i
$169$			70187.9i			2.45747i
$170$		0			0
$171$	−42088.2			−1.43936
$172$	−10636.6	+	10636.6i	−0.359540	+	0.359540i
$173$	17054.0	+	17054.0i	0.569815	+	0.569815i	0.932076	−	0.362262i	$-0.117995\pi$
$173$	17054.0	+	17054.0i	0.569815	+	0.569815i	−0.362262	+	0.932076i	$0.617995\pi$
$174$			6400.31i			0.211399i
$175$		0			0
$176$	19293.8			0.622861
$177$	−54785.0	+	54785.0i	−1.74870	+	1.74870i
$178$	−10311.1	−	10311.1i	−0.325435	−	0.325435i
$179$		−	35250.6i		−	1.10017i	−0.835109	−	0.550085i	$-0.814595\pi$
$179$		−	35250.6i		−	1.10017i	0.835109	−	0.550085i	$-0.185405\pi$
$180$		0			0
$181$	40099.9			1.22401			0.612007	−	0.790852i	$-0.290362\pi$
$181$	40099.9			1.22401			0.612007	+	0.790852i	$0.290362\pi$
$182$	−5219.72	+	5219.72i	−0.157581	+	0.157581i
$183$	−9364.81	−	9364.81i	−0.279638	−	0.279638i
$184$			26860.9i			0.793387i
$185$		0			0
$186$	5436.76			0.157150
$187$	17433.4	−	17433.4i	0.498540	−	0.498540i
$188$	−4704.66	−	4704.66i	−0.133110	−	0.133110i
$189$			5665.76i			0.158611i
$190$		0			0
$191$	53605.9			1.46942			0.734710	−	0.678381i	$-0.237318\pi$
$191$	53605.9			1.46942			0.734710	+	0.678381i	$0.237318\pi$
$192$	17556.4	−	17556.4i	0.476249	−	0.476249i
$193$	1942.74	+	1942.74i	0.0521555	+	0.0521555i	0.732703	−	0.680548i	$-0.238258\pi$
$193$	1942.74	+	1942.74i	0.0521555	+	0.0521555i	−0.680548	+	0.732703i	$0.738258\pi$
$194$			12408.0i			0.329685i
$195$		0			0
$196$	4936.19			0.128493
$197$	−18355.9	+	18355.9i	−0.472980	+	0.472980i	−0.902878	−	0.429897i	$-0.858550\pi$
$197$	−18355.9	+	18355.9i	−0.472980	+	0.472980i	0.429897	+	0.902878i	$0.358550\pi$
$198$	9876.92	+	9876.92i	0.251937	+	0.251937i
$199$		−	13384.8i		−	0.337992i	−0.985617	−	0.168996i	$-0.945947\pi$
$199$		−	13384.8i		−	0.337992i	0.985617	−	0.168996i	$-0.0540526\pi$
$200$		0			0
$201$	31422.0			0.777753
$202$	−5517.07	+	5517.07i	−0.135209	+	0.135209i
$203$	−4864.76	−	4864.76i	−0.118051	−	0.118051i
$204$		−	45306.3i		−	1.08868i
$205$		0			0
$206$	−12153.1			−0.286386
$207$	51007.9	−	51007.9i	1.19041	−	1.19041i
$208$	−40300.3	−	40300.3i	−0.931498	−	0.931498i
$209$		−	43250.5i		−	0.990145i
$210$		0			0
$211$	−67277.6			−1.51114			−0.755571	−	0.655066i	$-0.772641\pi$
$211$	−67277.6			−1.51114			−0.755571	+	0.655066i	$0.772641\pi$
$212$	7225.10	−	7225.10i	0.160758	−	0.160758i
$213$	5633.40	+	5633.40i	0.124169	+	0.124169i
$214$			4409.52i			0.0962862i
$215$		0			0
$216$	11792.5			0.252755
$217$	−4132.38	+	4132.38i	−0.0877569	+	0.0877569i
$218$	4199.39	+	4199.39i	0.0883636	+	0.0883636i
$219$			136323.i			2.84238i
$220$		0			0
$221$	−72829.1			−1.49115
$222$	−19191.8	+	19191.8i	−0.389413	+	0.389413i
$223$	64.2980	+	64.2980i	0.00129297	+	0.00129297i	0.707753	−	0.706460i	$-0.249709\pi$
$223$	64.2980	+	64.2980i	0.00129297	+	0.00129297i	−0.706460	+	0.707753i	$0.749709\pi$
$224$		−	15683.0i		−	0.312560i
$225$		0			0
$226$	−7605.45			−0.148905
$227$	27272.1	−	27272.1i	0.529256	−	0.529256i	−0.391094	−	0.920351i	$-0.627903\pi$
$227$	27272.1	−	27272.1i	0.529256	−	0.529256i	0.920351	+	0.391094i	$0.127903\pi$
$228$	−56200.2	−	56200.2i	−1.08110	−	1.08110i
$229$			29354.6i			0.559765i	0.960034	+	0.279882i	$0.0902955\pi$
$229$			29354.6i			0.559765i	−0.960034	+	0.279882i	$0.909705\pi$
$230$		0			0
$231$	−26762.7			−0.501540
$232$	−10125.4	+	10125.4i	−0.188120	+	0.188120i
$233$	55763.6	+	55763.6i	1.02716	+	1.02716i	0.999621	+	0.0275419i	$0.00876798\pi$
$233$	55763.6	+	55763.6i	1.02716	+	1.02716i	0.0275419	+	0.999621i	$0.491232\pi$
$234$		−	41261.3i		−	0.753549i
$235$		0			0
$236$	−82082.7			−1.47376
$237$	22954.7	−	22954.7i	0.408672	−	0.408672i
$238$	−3849.63	−	3849.63i	−0.0679619	−	0.0679619i
$239$			7891.35i			0.138151i	0.997611	+	0.0690757i	$0.0220050\pi$
$239$			7891.35i			0.138151i	−0.997611	+	0.0690757i	$0.977995\pi$
$240$		0			0
$241$	−15610.7			−0.268775			−0.134387	−	0.990929i	$-0.542907\pi$
$241$	−15610.7			−0.268775			−0.134387	+	0.990929i	$0.542907\pi$
$242$	2981.51	−	2981.51i	0.0509103	−	0.0509103i
$243$	58148.2	+	58148.2i	0.984745	+	0.984745i
$244$		−	14031.0i		−	0.235673i
$245$		0			0
$246$	−4719.45			−0.0779868
$247$	−90340.7	+	90340.7i	−1.48078	+	1.48078i
$248$	8601.03	+	8601.03i	0.139845	+	0.139845i
$249$			24916.3i			0.401870i
$250$		0			0
$251$	110552.			1.75477			0.877384	−	0.479789i	$-0.159287\pi$
$251$	110552.			1.75477			0.877384	+	0.479789i	$0.159287\pi$
$252$	−19510.0	+	19510.0i	−0.307225	+	0.307225i
$253$	52416.6	+	52416.6i	0.818894	+	0.818894i
$254$		−	822.953i		−	0.0127558i
$255$		0			0
$256$	9119.22			0.139148
$257$	51789.3	−	51789.3i	0.784105	−	0.784105i	−0.196416	−	0.980521i	$-0.562930\pi$
$257$	51789.3	−	51789.3i	0.784105	−	0.784105i	0.980521	+	0.196416i	$0.0629302\pi$
$258$	−12734.4	−	12734.4i	−0.191311	−	0.191311i
$259$		−	29174.7i		−	0.434918i
$260$		0			0
$261$	38455.4			0.564517
$262$	18823.0	−	18823.0i	0.274211	−	0.274211i
$263$	−90952.1	−	90952.1i	−1.31493	−	1.31493i	−0.917737	−	0.397189i	$-0.869986\pi$
$263$	−90952.1	−	90952.1i	−1.31493	−	1.31493i	−0.397189	−	0.917737i	$-0.630014\pi$
$264$			55703.1i			0.799229i
$265$		0			0
$266$	−9550.54			−0.134979
$267$	−110428.	+	110428.i	−1.54902	+	1.54902i
$268$	23539.3	+	23539.3i	0.327736	+	0.327736i
$269$		−	99774.7i		−	1.37885i	−0.724359	−	0.689423i	$-0.757864\pi$
$269$		−	99774.7i		−	1.37885i	0.724359	−	0.689423i	$-0.242136\pi$
$270$		0			0
$271$	−54432.5			−0.741173			−0.370587	−	0.928798i	$-0.620843\pi$
$271$	−54432.5			−0.741173			−0.370587	+	0.928798i	$0.620843\pi$
$272$	29722.2	−	29722.2i	0.401738	−	0.401738i
$273$	55901.2	+	55901.2i	0.750060	+	0.750060i
$274$		−	18271.4i		−	0.243372i
$275$		0			0
$276$	136221.			1.78824
$277$	65998.2	−	65998.2i	0.860147	−	0.860147i	−0.131208	−	0.991355i	$-0.541885\pi$
$277$	65998.2	−	65998.2i	0.860147	−	0.860147i	0.991355	+	0.131208i	$0.0418855\pi$
$278$	−23706.9	−	23706.9i	−0.306750	−	0.306750i
$279$		−	32666.1i		−	0.419651i
$280$		0			0
$281$	14995.6			0.189911			0.0949556	−	0.995482i	$-0.469729\pi$
$281$	14995.6			0.189911			0.0949556	+	0.995482i	$0.469729\pi$
$282$	5632.51	−	5632.51i	0.0708278	−	0.0708278i
$283$	7959.64	+	7959.64i	0.0993849	+	0.0993849i	0.755051	−	0.655666i	$-0.227612\pi$
$283$	7959.64	+	7959.64i	0.0993849	+	0.0993849i	−0.655666	+	0.755051i	$0.727612\pi$
$284$			8440.35i			0.104646i
$285$		0			0
$286$	42400.8			0.518373
$287$	3587.17	−	3587.17i	0.0435500	−	0.0435500i
$288$	61986.3	+	61986.3i	0.747327	+	0.747327i
$289$			29808.3i			0.356896i
$290$		0			0
$291$	132885.			1.56925
$292$	−102125.	+	102125.i	−1.19775	+	1.19775i
$293$	−42977.6	−	42977.6i	−0.500619	−	0.500619i	0.411011	−	0.911630i	$-0.365176\pi$
$293$	−42977.6	−	42977.6i	−0.500619	−	0.500619i	−0.911630	+	0.411011i	$0.865176\pi$
$294$			5909.70i			0.0683709i
$295$		0			0
$296$	−60723.4			−0.693063
$297$	23012.0	−	23012.0i	0.260881	−	0.260881i
$298$	22511.3	+	22511.3i	0.253494	+	0.253494i
$299$		−	218973.i		−	2.44933i
$300$		0			0
$301$	19358.4			0.213666
$302$	−18937.5	+	18937.5i	−0.207639	+	0.207639i
$303$	59085.8	+	59085.8i	0.643573	+	0.643573i
$304$		−	73737.7i		−	0.797889i
$305$		0			0
$306$	30431.0			0.324992
$307$	45339.7	−	45339.7i	0.481063	−	0.481063i	−0.424408	−	0.905471i	$-0.639518\pi$
$307$	45339.7	−	45339.7i	0.481063	−	0.481063i	0.905471	+	0.424408i	$0.139518\pi$
$308$	−20048.8	−	20048.8i	−0.211343	−	0.211343i
$309$			130155.i			1.36315i
$310$		0			0
$311$	−17752.7			−0.183545			−0.0917727	−	0.995780i	$-0.529253\pi$
$311$	−17752.7			−0.183545			−0.0917727	+	0.995780i	$0.529253\pi$
$312$	116351.	−	116351.i	1.19526	−	1.19526i
$313$	−74691.9	−	74691.9i	−0.762404	−	0.762404i	0.214353	−	0.976756i	$-0.431236\pi$
$313$	−74691.9	−	74691.9i	−0.762404	−	0.762404i	−0.976756	+	0.214353i	$0.931236\pi$
$314$		−	22542.5i		−	0.228635i
$315$		0			0
$316$	34392.3			0.344419
$317$	52291.4	−	52291.4i	0.520370	−	0.520370i	−0.397313	−	0.917683i	$-0.630057\pi$
$317$	52291.4	−	52291.4i	0.520370	−	0.520370i	0.917683	+	0.397313i	$0.130057\pi$
$318$	8650.04	+	8650.04i	0.0855389	+	0.0855389i
$319$			39517.4i			0.388336i
$320$		0			0
$321$	47224.3			0.458306
$322$	11574.6	−	11574.6i	0.111633	−	0.111633i
$323$	−66627.8	−	66627.8i	−0.638632	−	0.638632i
$324$			60869.1i			0.579838i
$325$		0			0
$326$	38803.1			0.365116
$327$	44973.9	−	44973.9i	0.420596	−	0.420596i
$328$	−7466.23	−	7466.23i	−0.0693991	−	0.0693991i
$329$			8562.34i			0.0791044i
$330$		0			0
$331$	34704.7			0.316762			0.158381	−	0.987378i	$-0.449373\pi$
$331$	34704.7			0.316762			0.158381	+	0.987378i	$0.449373\pi$
$332$	−18665.7	+	18665.7i	−0.169343	+	0.169343i
$333$	115312.	+	115312.i	1.03988	+	1.03988i
$334$			45787.9i			0.410447i
$335$		0			0
$336$	−45627.6			−0.404156
$337$	68383.2	−	68383.2i	0.602129	−	0.602129i	−0.338748	−	0.940877i	$-0.610003\pi$
$337$	68383.2	−	68383.2i	0.602129	−	0.602129i	0.940877	+	0.338748i	$0.110003\pi$
$338$	−62950.1	−	62950.1i	−0.551014	−	0.551014i
$339$			81451.5i			0.708761i
$340$		0			0
$341$	33568.2			0.288682
$342$	37748.0	−	37748.0i	0.322732	−	0.322732i
$343$	−4491.86	−	4491.86i	−0.0381802	−	0.0381802i
$344$		−	40292.0i		−	0.340488i
$345$		0			0
$346$	−30590.7			−0.255527
$347$	−25167.8	+	25167.8i	−0.209019	+	0.209019i	−0.803851	−	0.594831i	$-0.797219\pi$
$347$	−25167.8	+	25167.8i	−0.209019	+	0.209019i	0.594831	+	0.803851i	$0.297219\pi$
$348$	51349.3	+	51349.3i	0.424010	+	0.424010i
$349$		−	189419.i		−	1.55515i	−0.628792	−	0.777574i	$-0.716450\pi$
$349$		−	189419.i		−	1.55515i	0.628792	−	0.777574i	$-0.283550\pi$
$350$		0			0
$351$	−96134.0			−0.780302
$352$	−63698.1	+	63698.1i	−0.514092	+	0.514092i
$353$	−69986.0	−	69986.0i	−0.561645	−	0.561645i	0.368130	−	0.929775i	$-0.379998\pi$
$353$	−69986.0	−	69986.0i	−0.561645	−	0.561645i	−0.929775	+	0.368130i	$0.879998\pi$
$354$		−	98271.1i		−	0.784186i
$355$		0			0
$356$	−165451.			−1.30547
$357$	−41228.1	+	41228.1i	−0.323487	+	0.323487i
$358$	31615.5	+	31615.5i	0.246680	+	0.246680i
$359$		−	54385.7i		−	0.421984i	−0.977488	−	0.210992i	$-0.932331\pi$
$359$		−	54385.7i		−	0.421984i	0.977488	−	0.210992i	$-0.0676694\pi$
$360$		0			0
$361$	−34975.7			−0.268381
$362$	−35964.8	+	35964.8i	−0.274448	+	0.274448i
$363$	−31930.9	−	31930.9i	−0.242325	−	0.242325i
$364$			83755.0i			0.632132i
$365$		0			0
$366$	16798.2			0.125401
$367$	−4302.78	+	4302.78i	−0.0319460	+	0.0319460i	−0.722899	−	0.690953i	$-0.757191\pi$
$367$	−4302.78	+	4302.78i	−0.0319460	+	0.0319460i	0.690953	+	0.722899i	$0.257191\pi$
$368$	89364.8	+	89364.8i	0.659889	+	0.659889i
$369$			28356.2i			0.208255i
$370$		0			0
$371$	−13149.5			−0.0955346
$372$	43618.8	−	43618.8i	0.315201	−	0.315201i
$373$	70465.2	+	70465.2i	0.506474	+	0.506474i	0.913442	−	0.406968i	$-0.133414\pi$
$373$	70465.2	+	70465.2i	0.506474	+	0.506474i	−0.406968	+	0.913442i	$0.633414\pi$
$374$			31271.4i			0.223565i
$375$		0			0
$376$	17821.4			0.126057
$377$	82543.1	−	82543.1i	0.580762	−	0.580762i
$378$	−5081.50	−	5081.50i	−0.0355638	−	0.0355638i
$379$		−	89798.6i		−	0.625160i	−0.949891	−	0.312580i	$-0.898807\pi$
$379$		−	89798.6i		−	0.625160i	0.949891	−	0.312580i	$-0.101193\pi$
$380$		0			0
$381$	−8813.52			−0.0607155
$382$	−48078.0	+	48078.0i	−0.329473	+	0.329473i
$383$	−17747.1	−	17747.1i	−0.120985	−	0.120985i	0.644022	−	0.765007i	$-0.277264\pi$
$383$	−17747.1	−	17747.1i	−0.120985	−	0.120985i	−0.765007	+	0.644022i	$0.777264\pi$
$384$			215537.i			1.46171i
$385$		0			0
$386$	−3484.80			−0.0233886
$387$	−76513.1	+	76513.1i	−0.510874	+	0.510874i
$388$	99548.9	+	99548.9i	0.661261	+	0.661261i
$389$			29046.4i			0.191952i	0.995384	+	0.0959760i	$0.0305972\pi$
$389$			29046.4i			0.191952i	−0.995384	+	0.0959760i	$0.969403\pi$
$390$		0			0
$391$	161496.			1.05635
$392$	−9349.23	+	9349.23i	−0.0608420	+	0.0608420i
$393$	−201587.	−	201587.i	−1.30520	−	1.30520i
$394$		−	32926.0i		−	0.212103i
$395$		0			0
$396$	158484.			1.01064
$397$	−175512.	+	175512.i	−1.11359	+	1.11359i	−0.120929	+	0.992661i	$0.538587\pi$
$397$	−175512.	+	175512.i	−1.11359	+	1.11359i	−0.992661	+	0.120929i	$0.961413\pi$
$398$	12004.6	+	12004.6i	0.0757845	+	0.0757845i
$399$			102283.i			0.642475i
$400$		0			0
$401$	−283533.			−1.76325			−0.881626	−	0.471949i	$-0.843550\pi$
$401$	−283533.			−1.76325			−0.881626	+	0.471949i	$0.843550\pi$
$402$	−28181.7	+	28181.7i	−0.174387	+	0.174387i
$403$	−70116.4	−	70116.4i	−0.431728	−	0.431728i
$404$			88526.3i			0.542388i
$405$		0			0
$406$	8726.20			0.0529387
$407$	−118496.	+	118496.i	−0.715344	+	0.715344i
$408$	85811.1	+	85811.1i	0.515493	+	0.515493i
$409$			149683.i			0.894802i	0.894333	+	0.447401i	$0.147650\pi$
$409$			149683.i			0.894802i	−0.894333	+	0.447401i	$0.852350\pi$
$410$		0			0
$411$	−195680.			−1.15841
$412$	−97503.5	+	97503.5i	−0.574415	+	0.574415i
$413$	74694.1	+	74694.1i	0.437911	+	0.437911i
$414$			91495.8i			0.533827i
$415$		0			0
$416$	266102.			1.53766
$417$	−253892.	+	253892.i	−1.46008	+	1.46008i
$418$	38790.5	+	38790.5i	0.222010	+	0.222010i
$419$			126556.i			0.720867i	0.932785	+	0.360434i	$0.117371\pi$
$419$			126556.i			0.720867i	−0.932785	+	0.360434i	$0.882629\pi$
$420$		0			0
$421$	−335016.			−1.89017			−0.945087	−	0.326819i	$-0.894023\pi$
$421$	−335016.			−1.89017			−0.945087	+	0.326819i	$0.894023\pi$
$422$	60339.8	−	60339.8i	0.338828	−	0.338828i
$423$	−33842.2	−	33842.2i	−0.189138	−	0.189138i
$424$			27368.9i			0.152239i
$425$		0			0
$426$	−10105.0			−0.0556821
$427$	−12768.0	+	12768.0i	−0.0700273	+	0.0700273i
$428$	35377.4	+	35377.4i	0.193125	+	0.193125i
$429$		−	454097.i		−	2.46737i
$430$		0			0
$431$	−351739.			−1.89350			−0.946751	−	0.321967i	$-0.895656\pi$
$431$	−351739.			−1.89350			−0.946751	+	0.321967i	$0.895656\pi$
$432$	39233.1	−	39233.1i	0.210226	−	0.210226i
$433$	−158272.	−	158272.i	−0.844168	−	0.844168i	0.145230	−	0.989398i	$-0.453608\pi$
$433$	−158272.	−	158272.i	−0.844168	−	0.844168i	−0.989398	+	0.145230i	$0.953608\pi$
$434$		−	7412.50i		−	0.0393536i
$435$		0			0
$436$	67382.9			0.354468
$437$	200328.	−	200328.i	1.04901	−	1.04901i
$438$	−122266.	−	122266.i	−0.637318	−	0.637318i
$439$			122448.i			0.635362i	0.948198	+	0.317681i	$0.102904\pi$
$439$			122448.i			0.635362i	−0.948198	+	0.317681i	$0.897096\pi$
$440$		0			0
$441$	35507.7			0.182577
$442$	65318.8	−	65318.8i	0.334344	−	0.334344i
$443$	−211701.	−	211701.i	−1.07874	−	1.07874i	−0.996623	−	0.0821136i	$-0.973833\pi$
$443$	−211701.	−	211701.i	−1.07874	−	1.07874i	−0.0821136	−	0.996623i	$-0.526167\pi$
$444$			307950.i			1.56212i
$445$		0			0
$446$	−115.335			−0.000579817
$447$	241088.	−	241088.i	1.20659	−	1.20659i
$448$	−23936.5	−	23936.5i	−0.119263	−	0.119263i
$449$		−	75472.5i		−	0.374366i	−0.982325	−	0.187183i	$-0.940064\pi$
$449$		−	75472.5i		−	0.374366i	0.982325	−	0.187183i	$-0.0599357\pi$
$450$		0			0
$451$	−29139.3			−0.143260
$452$	−61018.1	+	61018.1i	−0.298663	+	0.298663i
$453$	202814.	+	202814.i	0.988327	+	0.988327i
$454$			48919.5i			0.237339i
$455$		0			0
$456$	212888.			1.02382
$457$	227700.	−	227700.i	1.09026	−	1.09026i	0.0947612	−	0.995500i	$-0.469791\pi$
$457$	227700.	−	227700.i	1.09026	−	1.09026i	0.995500	−	0.0947612i	$-0.0302087\pi$
$458$	−26327.5	−	26327.5i	−0.125510	−	0.125510i
$459$		−	70900.5i		−	0.336530i
$460$		0			0
$461$	−66408.2			−0.312478			−0.156239	−	0.987719i	$-0.549937\pi$
$461$	−66408.2			−0.312478			−0.156239	+	0.987719i	$0.549937\pi$
$462$	24002.9	−	24002.9i	0.112455	−	0.112455i
$463$	123009.	+	123009.i	0.573817	+	0.573817i	0.933193	−	0.359376i	$-0.117010\pi$
$463$	123009.	+	123009.i	0.573817	+	0.573817i	−0.359376	+	0.933193i	$0.617010\pi$
$464$			67373.1i			0.312933i
$465$		0			0
$466$	−100026.			−0.460620
$467$	−61189.1	+	61189.1i	−0.280569	+	0.280569i	−0.833336	−	0.552767i	$-0.813572\pi$
$467$	−61189.1	+	61189.1i	−0.280569	+	0.280569i	0.552767	+	0.833336i	$0.313572\pi$
$468$	−331038.	−	331038.i	−1.51142	−	1.51142i
$469$		−	42840.8i		−	0.194766i
$470$		0			0
$471$	−241422.			−1.08827
$472$	155466.	−	155466.i	0.697833	−	0.697833i
$473$	−78626.1	−	78626.1i	−0.351434	−	0.351434i
$474$			41175.2i			0.183265i
$475$		0			0
$476$	−61770.8			−0.272627
$477$	51972.6	−	51972.6i	0.228422	−	0.228422i
$478$	−7077.58	−	7077.58i	−0.0309763	−	0.0309763i
$479$		−	140484.i		−	0.612290i	−0.951985	−	0.306145i	$-0.900961\pi$
$479$		−	140484.i		−	0.612290i	0.951985	−	0.306145i	$-0.0990393\pi$
$480$		0			0
$481$	495023.			2.13961
$482$	14000.9	−	14000.9i	0.0602646	−	0.0602646i
$483$	−123959.	−	123959.i	−0.531355	−	0.531355i
$484$		−	47841.0i		−	0.204225i
$485$		0			0
$486$	−104304.			−0.441598
$487$	139424.	−	139424.i	0.587869	−	0.587869i	−0.349185	−	0.937054i	$-0.613541\pi$
$487$	139424.	−	139424.i	0.587869	−	0.587869i	0.937054	+	0.349185i	$0.113541\pi$
$488$	26575.0	+	26575.0i	0.111592	+	0.111592i
$489$		−	415566.i		−	1.73789i
$490$		0			0
$491$	−184604.			−0.765735			−0.382867	−	0.923803i	$-0.625063\pi$
$491$	−184604.			−0.765735			−0.382867	+	0.923803i	$0.625063\pi$
$492$	−37863.9	+	37863.9i	−0.156421	+	0.156421i
$493$	60877.0	+	60877.0i	0.250472	+	0.250472i
$494$		−	162049.i		−	0.664038i
$495$		0			0
$496$	57230.3			0.232628
$497$	7680.60	−	7680.60i	0.0310944	−	0.0310944i
$498$	−22346.9	−	22346.9i	−0.0901072	−	0.0901072i
$499$			40411.9i			0.162296i	0.996702	+	0.0811481i	$0.0258587\pi$
$499$			40411.9i			0.162296i	−0.996702	+	0.0811481i	$0.974141\pi$
$500$		0			0
$501$	490371.			1.95366
$502$	−99151.9	+	99151.9i	−0.393454	+	0.393454i
$503$	302310.	+	302310.i	1.19486	+	1.19486i	0.975686	+	0.219173i	$0.0703358\pi$
$503$	302310.	+	302310.i	1.19486	+	1.19486i	0.219173	+	0.975686i	$0.429664\pi$
$504$		−	73904.8i		−	0.290945i
$505$		0			0
$506$	−94022.6			−0.367224
$507$	−674171.	+	674171.i	−2.62273	+	2.62273i
$508$	−6602.51	−	6602.51i	−0.0255848	−	0.0255848i
$509$		−	49977.3i		−	0.192902i	−0.995338	−	0.0964511i	$-0.969251\pi$
$509$		−	49977.3i		−	0.192902i	0.995338	−	0.0964511i	$-0.0307491\pi$
$510$		0			0
$511$	185864.			0.711792
$512$	−187695.	+	187695.i	−0.716001	+	0.716001i
$513$	−87948.4	−	87948.4i	−0.334190	−	0.334190i
$514$			92897.5i			0.351624i
$515$		0			0
$516$	−204335.			−0.767438
$517$	34776.8	−	34776.8i	0.130109	−	0.130109i
$518$	26166.2	+	26166.2i	0.0975171	+	0.0975171i
$519$			327615.i			1.21627i
$520$		0			0
$521$	288617.			1.06328			0.531639	−	0.846971i	$-0.321576\pi$
$521$	288617.			1.06328			0.531639	+	0.846971i	$0.321576\pi$
$522$	−34489.9	+	34489.9i	−0.126576	+	0.126576i
$523$	−126116.	−	126116.i	−0.461071	−	0.461071i	0.437935	−	0.899007i	$-0.355710\pi$
$523$	−126116.	−	126116.i	−0.461071	−	0.461071i	−0.899007	+	0.437935i	$0.855710\pi$
$524$		−	302031.i		−	1.09999i
$525$		0			0
$526$	163146.			0.589664
$527$	51712.1	−	51712.1i	0.186196	−	0.186196i
$528$	185321.	+	185321.i	0.664748	+	0.664748i
$529$			205725.i			0.735150i
$530$		0			0
$531$	−590449.			−2.09408
$532$	−76623.4	+	76623.4i	−0.270731	+	0.270731i
$533$	60865.5	+	60865.5i	0.214248	+	0.214248i
$534$		−	198081.i		−	0.694640i
$535$		0			0
$536$	−89167.7			−0.310369
$537$	338590.	−	338590.i	1.17415	−	1.17415i
$538$	89485.8	+	89485.8i	0.309164	+	0.309164i
$539$			36488.3i			0.125596i
$540$		0			0
$541$	431340.			1.47375			0.736877	−	0.676027i	$-0.236300\pi$
$541$	431340.			1.47375			0.736877	+	0.676027i	$0.236300\pi$
$542$	48819.4	−	48819.4i	0.166186	−	0.166186i
$543$	385169.	+	385169.i	1.30633	+	1.30633i
$544$			196255.i			0.663167i
$545$		0			0
$546$	−100273.			−0.336356
$547$	188558.	−	188558.i	0.630187	−	0.630187i	−0.317928	−	0.948115i	$-0.602987\pi$
$547$	188558.	−	188558.i	0.630187	−	0.630187i	0.948115	+	0.317928i	$0.102987\pi$
$548$	−146590.	−	146590.i	−0.488140	−	0.488140i
$549$		−	100930.i		−	0.334869i
$550$		0			0
$551$	151029.			0.497460
$552$	−258005.	+	258005.i	−0.846741	+	0.846741i
$553$	−31296.5	−	31296.5i	−0.102340	−	0.102340i
$554$			118385.i			0.385724i
$555$		0			0
$556$	−380398.			−1.23052
$557$	111586.	−	111586.i	0.359665	−	0.359665i	−0.504025	−	0.863689i	$-0.668148\pi$
$557$	111586.	−	111586.i	0.359665	−	0.359665i	0.863689	+	0.504025i	$0.168148\pi$
$558$	29297.5	+	29297.5i	0.0940941	+	0.0940941i
$559$			328464.i			1.05115i
$560$		0			0
$561$	334905.			1.06413
$562$	−13449.2	+	13449.2i	−0.0425818	+	0.0425818i
$563$	−251019.	−	251019.i	−0.791936	−	0.791936i	0.189873	−	0.981809i	$-0.439192\pi$
$563$	−251019.	−	251019.i	−0.791936	−	0.791936i	−0.981809	+	0.189873i	$0.939192\pi$
$564$		−	90378.6i		−	0.284124i
$565$		0			0
$566$	−14277.7			−0.0445681
$567$	55390.0	−	55390.0i	0.172292	−	0.172292i
$568$	−15986.2	−	15986.2i	−0.0495505	−	0.0495505i
$569$		−	13766.8i		−	0.0425216i	−0.999774	−	0.0212608i	$-0.993232\pi$
$569$		−	13766.8i		−	0.0425216i	0.999774	−	0.0212608i	$-0.00676803\pi$
$570$		0			0
$571$	−149481.			−0.458473			−0.229236	−	0.973371i	$-0.573623\pi$
$571$	−149481.			−0.458473			−0.229236	+	0.973371i	$0.573623\pi$
$572$	340180.	−	340180.i	1.03972	−	1.03972i
$573$	514897.	+	514897.i	1.56824	+	1.56824i
$574$			6434.51i			0.0195295i
$575$		0			0
$576$	189216.			0.570312
$577$	−148330.	+	148330.i	−0.445529	+	0.445529i	−0.893865	−	0.448336i	$-0.852017\pi$
$577$	−148330.	+	148330.i	−0.445529	+	0.445529i	0.448336	+	0.893865i	$0.352017\pi$
$578$	−26734.4	−	26734.4i	−0.0800230	−	0.0800230i
$579$			37320.9i			0.111326i
$580$		0			0
$581$	33971.0			0.100637
$582$	−119182.	+	119182.i	−0.351856	+	0.351856i
$583$	53407.9	+	53407.9i	0.157133	+	0.157133i
$584$		−	386852.i		−	1.13428i
$585$		0			0
$586$	77091.5			0.224497
$587$	−208211.	+	208211.i	−0.604266	+	0.604266i	−0.941442	−	0.337175i	$-0.890528\pi$
$587$	−208211.	+	208211.i	−0.604266	+	0.604266i	0.337175	+	0.941442i	$0.390528\pi$
$588$	47413.2	+	47413.2i	0.137134	+	0.137134i
$589$		−	128292.i		−	0.369803i
$590$		0			0
$591$	−352625.			−1.00957
$592$	−202023.	+	202023.i	−0.576446	+	0.576446i
$593$	176624.	+	176624.i	0.502273	+	0.502273i	0.912144	−	0.409870i	$-0.134426\pi$
$593$	176624.	+	176624.i	0.502273	+	0.502273i	−0.409870	+	0.912144i	$0.634426\pi$
$594$			41278.0i			0.116989i
$595$		0			0
$596$	361214.			1.01688
$597$	128564.	−	128564.i	0.360722	−	0.360722i
$598$	196392.	+	196392.i	0.549189	+	0.549189i
$599$			490826.i			1.36796i	0.729501	+	0.683980i	$0.239753\pi$
$599$			490826.i			1.36796i	−0.729501	+	0.683980i	$0.760247\pi$
$600$		0			0
$601$	490280.			1.35736			0.678681	−	0.734434i	$-0.262552\pi$
$601$	490280.			1.35736			0.678681	+	0.734434i	$0.262552\pi$
$602$	−17362.1	+	17362.1i	−0.0479082	+	0.0479082i
$603$	169326.	+	169326.i	0.465682	+	0.465682i
$604$			303869.i			0.832938i
$605$		0			0
$606$	−105986.			−0.288603
$607$	−21818.0	+	21818.0i	−0.0592159	+	0.0592159i	−0.736095	−	0.676879i	$-0.763332\pi$
$607$	−21818.0	+	21818.0i	−0.0592159	+	0.0592159i	0.676879	+	0.736095i	$0.263332\pi$
$608$	243444.	+	243444.i	0.658555	+	0.658555i
$609$		−	93454.3i		−	0.251979i
$610$		0			0
$611$	−145282.			−0.389161
$612$	244146.	−	244146.i	0.651849	−	0.651849i
$613$	−257328.	−	257328.i	−0.684804	−	0.684804i	0.276275	−	0.961079i	$-0.410900\pi$
$613$	−257328.	−	257328.i	−0.684804	−	0.684804i	−0.961079	+	0.276275i	$0.910900\pi$
$614$			81328.4i			0.215728i
$615$		0			0
$616$	75945.7			0.200144
$617$	457425.	−	457425.i	1.20157	−	1.20157i	0.227883	−	0.973689i	$-0.426820\pi$
$617$	457425.	−	457425.i	1.20157	−	1.20157i	0.973689	−	0.227883i	$-0.0731803\pi$
$618$	−116733.	−	116733.i	−0.305645	−	0.305645i
$619$		−	406943.i		−	1.06207i	−0.847351	−	0.531033i	$-0.821804\pi$
$619$		−	406943.i		−	1.06207i	0.847351	−	0.531033i	$-0.178196\pi$
$620$		0			0
$621$	213174.			0.552779
$622$	15922.0	−	15922.0i	0.0411545	−	0.0411545i
$623$	150558.	+	150558.i	0.387906	+	0.387906i
$624$		−	774188.i		−	1.98828i
$625$		0			0
$626$	133979.			0.341892
$627$	415432.	−	415432.i	1.05673	−	1.05673i
$628$	−180857.	−	180857.i	−0.458582	−	0.458582i
$629$			365089.i			0.922777i
$630$		0			0
$631$	8371.29			0.0210249			0.0105124	−	0.999945i	$-0.496654\pi$
$631$	8371.29			0.0210249			0.0105124	+	0.999945i	$0.496654\pi$
$632$	−65139.7	+	65139.7i	−0.163084	+	0.163084i
$633$	−646217.	−	646217.i	−1.61276	−	1.61276i
$634$			93798.2i			0.233354i
$635$		0			0
$636$	138798.			0.343137
$637$	76215.9	−	76215.9i	0.187831	−	0.187831i
$638$	−35442.4	−	35442.4i	−0.0870725	−	0.0870725i
$639$			60714.4i			0.148693i
$640$		0			0
$641$	370935.			0.902780			0.451390	−	0.892327i	$-0.350928\pi$
$641$	370935.			0.902780			0.451390	+	0.892327i	$0.350928\pi$
$642$	−42354.5	+	42354.5i	−0.102761	+	0.102761i
$643$	−154433.	−	154433.i	−0.373524	−	0.373524i	0.495235	−	0.868759i	$-0.335082\pi$
$643$	−154433.	−	154433.i	−0.373524	−	0.373524i	−0.868759	+	0.495235i	$0.835082\pi$
$644$		−	185724.i		−	0.447813i
$645$		0			0
$646$	119514.			0.286388
$647$	172763.	−	172763.i	0.412707	−	0.412707i	−0.469973	−	0.882681i	$-0.655736\pi$
$647$	172763.	−	172763.i	0.412707	−	0.412707i	0.882681	+	0.469973i	$0.155736\pi$
$648$	−115287.	−	115287.i	−0.274556	−	0.274556i
$649$		−	606755.i		−	1.44054i
$650$		0			0
$651$	−79385.0			−0.187317
$652$	311315.	−	311315.i	0.732326	−	0.732326i
$653$	402102.	+	402102.i	0.942995	+	0.942995i	0.998461	−	0.0554657i	$-0.0176644\pi$
$653$	402102.	+	402102.i	0.942995	+	0.942995i	−0.0554657	+	0.998461i	$0.517664\pi$
$654$			80672.2i			0.188612i
$655$		0			0
$656$	−49679.5			−0.115443
$657$	−734617.	+	734617.i	−1.70189	+	1.70189i
$658$	−7679.38	−	7679.38i	−0.0177368	−	0.0177368i
$659$		−	504941.i		−	1.16271i	−0.813652	−	0.581353i	$-0.802524\pi$
$659$		−	504941.i		−	1.16271i	0.813652	−	0.581353i	$-0.197476\pi$
$660$		0			0
$661$	8701.61			0.0199157			0.00995787	−	0.999950i	$-0.496830\pi$
$661$	8701.61			0.0199157			0.00995787	+	0.999950i	$0.496830\pi$
$662$	−31125.9	+	31125.9i	−0.0710242	+	0.0710242i
$663$	−699540.	−	699540.i	−1.59142	−	1.59142i
$664$		−	70706.3i		−	0.160370i
$665$		0			0
$666$	−206841.			−0.466325
$667$	−183037.	+	183037.i	−0.411421	+	0.411421i
$668$	367354.	+	367354.i	0.823249	+	0.823249i
$669$			1235.19i			0.00275983i
$670$		0			0
$671$	103717.			0.230359
$672$	150639.	−	150639.i	0.333579	−	0.333579i
$673$	159035.	+	159035.i	0.351126	+	0.351126i	0.860528	−	0.509403i	$-0.170134\pi$
$673$	159035.	+	159035.i	0.351126	+	0.351126i	−0.509403	+	0.860528i	$0.670134\pi$
$674$			122663.i			0.270018i
$675$		0			0
$676$	−1.01009e6			−2.21038
$677$	−40160.9	+	40160.9i	−0.0876247	+	0.0876247i	−0.749561	−	0.661936i	$-0.769735\pi$
$677$	−40160.9	+	40160.9i	−0.0876247	+	0.0876247i	0.661936	+	0.749561i	$0.269735\pi$
$678$	−73052.1	−	73052.1i	−0.158918	−	0.158918i
$679$		−	181176.i		−	0.392972i
$680$		0			0
$681$	523909.			1.12970
$682$	−30106.6	+	30106.6i	−0.0647281	+	0.0647281i
$683$	−161353.	−	161353.i	−0.345888	−	0.345888i	0.512688	−	0.858575i	$-0.328650\pi$
$683$	−161353.	−	161353.i	−0.345888	−	0.345888i	−0.858575	+	0.512688i	$0.828650\pi$
$684$		−	605701.i		−	1.29463i
$685$		0			0
$686$	8057.31			0.0171215
$687$	−281958.	+	281958.i	−0.597408	+	0.597408i
$688$	−134049.	−	134049.i	−0.283196	−	0.283196i
$689$		−	223114.i		−	0.469990i
$690$		0			0
$691$	−836856.			−1.75265			−0.876324	−	0.481722i	$-0.840012\pi$
$691$	−836856.			−1.75265			−0.876324	+	0.481722i	$0.840012\pi$
$692$	−245428.	+	245428.i	−0.512521	+	0.512521i
$693$	−144218.	−	144218.i	−0.300299	−	0.300299i
$694$		−	45145.0i		−	0.0937325i
$695$		0			0
$696$	−194513.			−0.401542
$697$	−44889.4	+	44889.4i	−0.0924012	+	0.0924012i
$698$	169885.	+	169885.i	0.348695	+	0.348695i
$699$			1.07125e6i			2.19247i
$700$		0			0
$701$	359589.			0.731763			0.365881	−	0.930661i	$-0.380768\pi$
$701$	359589.			0.731763			0.365881	+	0.930661i	$0.380768\pi$
$702$	86220.5	−	86220.5i	0.174959	−	0.174959i
$703$	452873.	+	452873.i	0.916360	+	0.916360i
$704$			194441.i			0.392322i
$705$		0			0
$706$	125538.			0.251864
$707$	80557.7	−	80557.7i	0.161164	−	0.161164i
$708$	−788423.	−	788423.i	−1.57287	−	1.57287i
$709$			712454.i			1.41731i	0.705556	+	0.708654i	$0.250697\pi$
$709$			712454.i			1.41731i	−0.705556	+	0.708654i	$0.749303\pi$
$710$		0			0
$711$	247396.			0.489388
$712$	313367.	−	313367.i	0.618148	−	0.618148i
$713$	155481.	+	155481.i	0.305843	+	0.305843i
$714$		−	73953.3i		−	0.145064i
$715$		0			0
$716$	507298.			0.989549
$717$	−75798.2	+	75798.2i	−0.147442	+	0.147442i
$718$	48777.4	+	48777.4i	0.0946171	+	0.0946171i
$719$			758208.i			1.46666i	0.679871	+	0.733332i	$0.262036\pi$
$719$			758208.i			1.46666i	−0.679871	+	0.733332i	$0.737964\pi$
$720$		0			0
$721$	177454.			0.341361
$722$	31369.0	−	31369.0i	0.0601763	−	0.0601763i
$723$	−149945.	−	149945.i	−0.286850	−	0.286850i
$724$			577087.i			1.10094i
$725$		0			0
$726$	57276.3			0.108668
$727$	−351306.	+	351306.i	−0.664687	+	0.664687i	−0.956481	−	0.291794i	$-0.905748\pi$
$727$	−351306.	+	351306.i	−0.664687	+	0.664687i	0.291794	+	0.956481i	$0.405748\pi$
$728$	−158634.	−	158634.i	−0.299318	−	0.299318i
$729$			774456.i			1.45728i
$730$		0			0
$731$	−242248.			−0.453342
$732$	134771.	−	134771.i	0.251521	−	0.251521i
$733$	−21457.1	−	21457.1i	−0.0399358	−	0.0399358i	0.686857	−	0.726793i	$-0.258990\pi$
$733$	−21457.1	−	21457.1i	−0.0399358	−	0.0399358i	−0.726793	+	0.686857i	$0.758990\pi$
$734$		−	7718.14i		−	0.0143259i
$735$		0			0
$736$	−590074.			−1.08931
$737$	−174002.	+	174002.i	−0.320347	+	0.320347i
$738$	−25432.1	−	25432.1i	−0.0466949	−	0.0466949i
$739$		−	769042.i		−	1.40819i	−0.710106	−	0.704095i	$-0.751353\pi$
$739$		−	769042.i		−	1.40819i	0.710106	−	0.704095i	$-0.248647\pi$
$740$		0			0
$741$	−1.73549e6			−3.16071
$742$	11793.5	−	11793.5i	0.0214207	−	0.0214207i
$743$	−34898.0	−	34898.0i	−0.0632154	−	0.0632154i	0.674792	−	0.738008i	$-0.264233\pi$
$743$	−34898.0	−	34898.0i	−0.0632154	−	0.0632154i	−0.738008	+	0.674792i	$0.764233\pi$
$744$			165230.i			0.298499i
$745$		0			0
$746$	−126398.			−0.227123
$747$	−134269.	+	134269.i	−0.240621	+	0.240621i
$748$	250888.	+	250888.i	0.448412	+	0.448412i
$749$		−	64385.8i		−	0.114770i
$750$		0			0
$751$	−623181.			−1.10493			−0.552464	−	0.833536i	$-0.686312\pi$
$751$	−623181.			−1.10493			−0.552464	+	0.833536i	$0.686312\pi$
$752$	59290.9	−	59290.9i	0.104846	−	0.104846i
$753$	1.06188e6	+	1.06188e6i	1.87277	+	1.87277i
$754$			148062.i			0.260436i
$755$		0			0
$756$	−81537.1			−0.142663
$757$	−85156.4	+	85156.4i	−0.148602	+	0.148602i	−0.777493	−	0.628891i	$-0.783509\pi$
$757$	−85156.4	+	85156.4i	−0.148602	+	0.148602i	0.628891	+	0.777493i	$0.283509\pi$
$758$	80538.5	+	80538.5i	0.140173	+	0.140173i
$759$			1.00695e6i			1.74793i
$760$		0			0
$761$	−823768.			−1.42245			−0.711223	−	0.702966i	$-0.751858\pi$
$761$	−823768.			−1.42245			−0.711223	+	0.702966i	$0.751858\pi$
$762$	7904.66	−	7904.66i	0.0136136	−	0.0136136i
$763$	−61317.5	−	61317.5i	−0.105326	−	0.105326i
$764$			771455.i			1.32167i
$765$		0			0
$766$	31834.1			0.0542544
$767$	−1.26738e6	+	1.26738e6i	−2.15434	+	2.15434i
$768$	87592.3	+	87592.3i	0.148506	+	0.148506i
$769$		−	956534.i		−	1.61751i	−0.588144	−	0.808756i	$-0.700141\pi$
$769$		−	956534.i		−	1.61751i	0.588144	−	0.808756i	$-0.299859\pi$
$770$		0			0
$771$	994898.			1.67367
$772$	−27958.4	+	27958.4i	−0.0469113	+	0.0469113i
$773$	−429882.	−	429882.i	−0.719433	−	0.719433i	0.249056	−	0.968489i	$-0.419880\pi$
$773$	−429882.	−	429882.i	−0.719433	−	0.719433i	−0.968489	+	0.249056i	$0.919880\pi$
$774$		−	137246.i		−	0.229096i
$775$		0			0
$776$	−377095.			−0.626221
$777$	280230.	−	280230.i	0.464165	−	0.464165i
$778$	−26051.1	−	26051.1i	−0.0430394	−	0.0430394i
$779$			111366.i			0.183517i
$780$		0			0
$781$	−62391.1			−0.102287
$782$	−144843.	+	144843.i	−0.236855	+	0.236855i
$783$	80357.3	+	80357.3i	0.131070	+	0.131070i
$784$			62208.7i			0.101209i
$785$		0			0
$786$	361598.			0.585303
$787$	100130.	−	100130.i	0.161665	−	0.161665i	−0.621639	−	0.783304i	$-0.713533\pi$
$787$	100130.	−	100130.i	0.161665	−	0.161665i	0.783304	+	0.621639i	$0.213533\pi$
$788$	−264164.	−	264164.i	−0.425423	−	0.425423i
$789$		−	1.74723e6i		−	2.80670i
$790$		0			0
$791$	111051.			0.177489
$792$	−300172.	+	300172.i	−0.478541	+	0.478541i
$793$	−216642.	−	216642.i	−0.344505	−	0.344505i
$794$		−	314826.i		−	0.499378i
$795$		0			0
$796$	192624.			0.304008
$797$	−72885.6	+	72885.6i	−0.114743	+	0.114743i	−0.762147	−	0.647404i	$-0.775855\pi$
$797$	−72885.6	+	72885.6i	−0.114743	+	0.114743i	0.647404	+	0.762147i	$0.275855\pi$
$798$	−91735.2	−	91735.2i	−0.144056	−	0.144056i
$799$		−	107148.i		−	0.167838i
$800$		0			0
$801$	−1.19014e6			−1.85496
$802$	254294.	−	254294.i	0.395356	−	0.395356i
$803$	−754905.	−	754905.i	−1.17074	−	1.17074i
$804$			452201.i			0.699550i
$805$		0			0
$806$	125772.			0.193604
$807$	958359.	−	958359.i	1.47157	−	1.47157i
$808$	−167671.	−	167671.i	−0.256823	−	0.256823i
$809$			297145.i			0.454017i	0.973893	+	0.227008i	$0.0728945\pi$
$809$			297145.i			0.454017i	−0.973893	+	0.227008i	$0.927105\pi$
$810$		0			0
$811$	−347268.			−0.527987			−0.263993	−	0.964524i	$-0.585040\pi$
$811$	−347268.			−0.527987			−0.263993	+	0.964524i	$0.585040\pi$
$812$	70009.8	−	70009.8i	0.106181	−	0.106181i
$813$	−522837.	−	522837.i	−0.791016	−	0.791016i
$814$		−	212553.i		−	0.320789i
$815$		0			0
$816$	570977.			0.857509
$817$	−300496.	+	300496.i	−0.450189	+	0.450189i
$818$	−134248.	−	134248.i	−0.200632	−	0.200632i
$819$			602479.i			0.898202i
$820$		0			0
$821$	960848.			1.42550			0.712752	−	0.701416i	$-0.247449\pi$
$821$	960848.			1.42550			0.712752	+	0.701416i	$0.247449\pi$
$822$	175501.	−	175501.i	0.259738	−	0.259738i
$823$	264418.	+	264418.i	0.390384	+	0.390384i	0.874824	−	0.484440i	$-0.160977\pi$
$823$	264418.	+	264418.i	0.390384	+	0.390384i	−0.484440	+	0.874824i	$0.660977\pi$
$824$		−	369347.i		−	0.543977i
$825$		0			0
$826$	−133983.			−0.196377
$827$	−24449.6	+	24449.6i	−0.0357488	+	0.0357488i	−0.724755	−	0.689006i	$-0.758047\pi$
$827$	−24449.6	+	24449.6i	−0.0357488	+	0.0357488i	0.689006	+	0.724755i	$0.258047\pi$
$828$	734066.	+	734066.i	1.07072	+	1.07072i
$829$		−	263665.i		−	0.383657i	−0.981428	−	0.191829i	$-0.938558\pi$
$829$		−	263665.i		−	0.383657i	0.981428	−	0.191829i	$-0.0614418\pi$
$830$		0			0
$831$	1.26786e6			1.83598
$832$	406144.	−	406144.i	0.586723	−	0.586723i
$833$	56210.5	+	56210.5i	0.0810080	+	0.0810080i
$834$		−	455420.i		−	0.654757i
$835$		0			0
$836$	622428.			0.890587
$837$	68259.7	−	68259.7i	0.0974347	−	0.0974347i
$838$	−113506.	−	113506.i	−0.161633	−	0.161633i
$839$			995523.i			1.41425i	0.707086	+	0.707127i	$0.250009\pi$
$839$			995523.i			1.41425i	−0.707086	+	0.707127i	$0.749991\pi$
$840$		0			0
$841$	569287.			0.804896
$842$	300469.	−	300469.i	0.423814	−	0.423814i
$843$	144036.	+	144036.i	0.202682	+	0.202682i
$844$		−	968206.i		−	1.35920i
$845$		0			0
$846$	60704.7			0.0848168
$847$	−43534.7	+	43534.7i	−0.0606832	+	0.0606832i
$848$	91055.0	+	91055.0i	0.126623	+	0.126623i
$849$			152908.i			0.212137i
$850$		0			0
$851$	−1.09770e6			−1.51574
$852$	−81071.5	+	81071.5i	−0.111684	+	0.111684i
$853$	139414.	+	139414.i	0.191606	+	0.191606i	0.796390	−	0.604784i	$-0.206740\pi$
$853$	139414.	+	139414.i	0.191606	+	0.191606i	−0.604784	+	0.796390i	$0.706740\pi$
$854$		−	22902.7i		−	0.0314030i
$855$		0			0
$856$	−134011.			−0.182891
$857$	−124172.	+	124172.i	−0.169068	+	0.169068i	−0.786570	−	0.617501i	$-0.788145\pi$
$857$	−124172.	+	124172.i	−0.169068	+	0.169068i	0.617501	+	0.786570i	$0.288145\pi$
$858$	407270.	+	407270.i	0.553233	+	0.553233i
$859$			272752.i			0.369642i	0.982772	+	0.184821i	$0.0591705\pi$
$859$			272752.i			0.369642i	−0.982772	+	0.184821i	$0.940829\pi$
$860$		0			0
$861$	68911.2			0.0929573
$862$	315467.	−	315467.i	0.424560	−	0.424560i
$863$	−762399.	−	762399.i	−1.02367	−	1.02367i	−0.999713	−	0.0239590i	$-0.992373\pi$
$863$	−762399.	−	762399.i	−1.02367	−	1.02367i	−0.0239590	−	0.999713i	$-0.507627\pi$
$864$			259055.i			0.347029i
$865$		0			0
$866$	283902.			0.378558
$867$	−286315.	+	286315.i	−0.380896	+	0.380896i
$868$	−59470.0	−	59470.0i	−0.0789330	−	0.0789330i
$869$			254228.i			0.336654i
$870$		0			0
$871$	726904.			0.958166
$872$	−127625.	+	127625.i	−0.167842	+	0.167842i
$873$	716090.	+	716090.i	0.939591	+	0.939591i
$874$			359339.i			0.470416i
$875$		0			0
$876$	−1.96186e6			−2.55658
$877$	−978873.	+	978873.i	−1.27270	+	1.27270i	−0.328038	+	0.944664i	$0.606387\pi$
$877$	−978873.	+	978873.i	−1.27270	+	1.27270i	−0.944664	+	0.328038i	$0.893613\pi$
$878$	−109821.	−	109821.i	−0.142461	−	0.142461i
$879$		−	825620.i		−	1.06857i
$880$		0			0
$881$	1.01046e6			1.30186			0.650932	−	0.759136i	$-0.274378\pi$
$881$	1.01046e6			1.30186			0.650932	+	0.759136i	$0.274378\pi$
$882$	−31846.1	+	31846.1i	−0.0409373	+	0.0409373i
$883$	481312.	+	481312.i	0.617313	+	0.617313i	0.944841	−	0.327528i	$-0.106216\pi$
$883$	481312.	+	481312.i	0.617313	+	0.617313i	−0.327528	+	0.944841i	$0.606216\pi$
$884$		−	1.04810e6i		−	1.34121i
$885$		0			0
$886$	379740.			0.483748
$887$	816109.	−	816109.i	1.03729	−	1.03729i	0.0380150	−	0.999277i	$-0.487897\pi$
$887$	816109.	−	816109.i	1.03729	−	1.03729i	0.999277	−	0.0380150i	$-0.0121035\pi$
$888$	−583263.	−	583263.i	−0.739671	−	0.739671i
$889$			12016.4i			0.0152044i
$890$		0			0
$891$	−449945.			−0.566766
$892$	−925.326	+	925.326i	−0.00116296	+	0.00116296i
$893$	−132911.	−	132911.i	−0.166671	−	0.166671i
$894$			432453.i			0.541082i
$895$		0			0
$896$	293864.			0.366042
$897$	2.10329e6	−	2.10329e6i	2.61405	−	2.61405i
$898$	67689.7	+	67689.7i	0.0839402	+	0.0839402i
$899$			117219.i			0.145037i
$900$		0			0
$901$	164551.			0.202698
$902$	26134.4	−	26134.4i	0.0321218	−	0.0321218i
$903$	185942.	+	185942.i	0.228035	+	0.228035i
$904$		−	231139.i		−	0.282837i
$905$		0			0
$906$	−363798.			−0.443205
$907$	−159574.	+	159574.i	−0.193975	+	0.193975i	−0.797411	−	0.603436i	$-0.793798\pi$
$907$	−159574.	+	159574.i	−0.193975	+	0.193975i	0.603436	+	0.797411i	$0.293798\pi$
$908$	392478.	+	392478.i	0.476040	+	0.476040i
$909$			636801.i			0.770683i
$910$		0			0
$911$	332313.			0.400415			0.200207	−	0.979754i	$-0.435838\pi$
$911$	332313.			0.400415			0.200207	+	0.979754i	$0.435838\pi$
$912$	708268.	−	708268.i	0.851545	−	0.851545i
$913$	−137977.	−	137977.i	−0.165525	−	0.165525i
$914$			408439.i			0.488916i
$915$		0			0
$916$	−422449.			−0.503481
$917$	−274844.	+	274844.i	−0.326849	+	0.326849i
$918$	63589.2	+	63589.2i	0.0754567	+	0.0754567i
$919$		−	1.48844e6i		−	1.76238i	−0.472760	−	0.881191i	$-0.656742\pi$
$919$		−	1.48844e6i		−	1.76238i	0.472760	−	0.881191i	$-0.343258\pi$
$920$		0			0
$921$	870997.			1.02683
$922$	59560.1	−	59560.1i	0.0700638	−	0.0700638i
$923$	130321.	+	130321.i	0.152972	+	0.152972i
$924$		−	385147.i		−	0.451111i
$925$		0			0
$926$	−220648.			−0.257322
$927$	−701377.	+	701377.i	−0.816191	+	0.816191i
$928$	−222432.	−	222432.i	−0.258286	−	0.258286i
$929$			1.44889e6i			1.67882i	0.543497	+	0.839411i	$0.317100\pi$
$929$			1.44889e6i			1.67882i	−0.543497	+	0.839411i	$0.682900\pi$
$930$		0			0
$931$	139452.			0.160889
$932$	−802506.	+	802506.i	−0.923882	+	0.923882i
$933$	−170519.	−	170519.i	−0.195888	−	0.195888i
$934$		−	109758.i		−	0.125818i
$935$		0			0
$936$	1.25398e6			1.43133
$937$	716769.	−	716769.i	0.816395	−	0.816395i	−0.169189	−	0.985584i	$-0.554115\pi$
$937$	716769.	−	716769.i	0.816395	−	0.816395i	0.985584	+	0.169189i	$0.0541148\pi$
$938$	38423.0	+	38423.0i	0.0436703	+	0.0436703i
$939$		−	1.43487e6i		−	1.62735i
$940$		0			0
$941$	217842.			0.246015			0.123008	−	0.992406i	$-0.460746\pi$
$941$	217842.			0.246015			0.123008	+	0.992406i	$0.460746\pi$
$942$	216526.	−	216526.i	0.244011	−	0.244011i
$943$	−134967.	−	134967.i	−0.151777	−	0.151777i
$944$		−	1.03445e6i		−	1.16083i
$945$		0			0
$946$	141036.			0.157597
$947$	5869.34	−	5869.34i	0.00654469	−	0.00654469i	−0.703827	−	0.710372i	$-0.748527\pi$
$947$	5869.34	−	5869.34i	0.00654469	−	0.00654469i	0.710372	+	0.703827i	$0.248527\pi$
$948$	330346.	+	330346.i	0.367581	+	0.367581i
$949$			3.15365e6i			3.50172i
$950$		0			0
$951$	1.00454e6			1.11073
$952$	116995.	−	116995.i	0.129090	−	0.129090i
$953$	1.14966e6	+	1.14966e6i	1.26586	+	1.26586i	0.948208	+	0.317649i	$0.102893\pi$
$953$	1.14966e6	+	1.14966e6i	1.26586	+	1.26586i	0.317649	+	0.948208i	$0.397107\pi$
$954$			93226.3i			0.102433i
$955$		0			0
$956$	−113566.			−0.124260
$957$	−379574.	+	379574.i	−0.414451	+	0.414451i
$958$	125998.	+	125998.i	0.137287	+	0.137287i
$959$			266790.i			0.290090i
$960$		0			0
$961$	−823949.			−0.892182
$962$	−443976.	+	443976.i	−0.479744	+	0.479744i
$963$	254482.	+	254482.i	0.274413	+	0.274413i
$964$		−	224657.i		−	0.241750i
$965$		0			0
$966$	222353.			0.238281
$967$	−642923.	+	642923.i	−0.687553	+	0.687553i	−0.961691	−	0.274137i	$-0.911608\pi$
$967$	−642923.	+	642923.i	−0.687553	+	0.687553i	0.274137	+	0.961691i	$0.411608\pi$
$968$	90611.8	+	90611.8i	0.0967017	+	0.0967017i
$969$		−	1.27995e6i		−	1.36316i
$970$		0			0
$971$	−646397.			−0.685585			−0.342792	−	0.939411i	$-0.611373\pi$
$971$	−646397.			−0.685585			−0.342792	+	0.939411i	$0.611373\pi$
$972$	−836823.	+	836823.i	−0.885730	+	0.885730i
$973$	346157.	+	346157.i	0.365634	+	0.365634i
$974$			250093.i			0.263624i
$975$		0			0
$976$	176827.			0.185630
$977$	−435906.	+	435906.i	−0.456672	+	0.456672i	−0.897561	−	0.440890i	$-0.854663\pi$
$977$	−435906.	+	435906.i	−0.456672	+	0.456672i	0.440890	+	0.897561i	$0.354663\pi$
$978$	372713.	+	372713.i	0.389669	+	0.389669i
$979$		−	1.22301e6i		−	1.27604i
$980$		0			0
$981$	484709.			0.503666
$982$	165568.	−	165568.i	0.171693	−	0.171693i
$983$	592997.	+	592997.i	0.613685	+	0.613685i	0.943904	−	0.330219i	$-0.107123\pi$
$983$	592997.	+	592997.i	0.613685	+	0.613685i	−0.330219	+	0.943904i	$0.607123\pi$
$984$		−	143430.i		−	0.148132i
$985$		0			0
$986$	−109199.			−0.112321
$987$	−82243.3	+	82243.3i	−0.0844240	+	0.0844240i
$988$	−1.30011e6	−	1.30011e6i	−1.33189	−	1.33189i
$989$		−	728360.i		−	0.744653i
$990$		0			0
$991$	−648180.			−0.660007			−0.330003	−	0.943980i	$-0.607050\pi$
$991$	−648180.			−0.660007			−0.330003	+	0.943980i	$0.607050\pi$
$992$	−188945.	+	188945.i	−0.192005	+	0.192005i
$993$	333347.	+	333347.i	0.338063	+	0.338063i
$994$			13777.1i			0.0139440i
$995$		0			0
$996$	−358577.			−0.361462
$997$	103914.	−	103914.i	0.104540	−	0.104540i	−0.652902	−	0.757442i	$-0.726449\pi$
$997$	103914.	−	103914.i	0.104540	−	0.104540i	0.757442	+	0.652902i	$0.226449\pi$
$998$	−36244.6	−	36244.6i	−0.0363900	−	0.0363900i
$999$			481915.i			0.482880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.c.43.6		24
5.2	odd	4	inner	175.5.g.c.57.6		24
5.3	odd	4		35.5.g.a.22.7	yes	24
5.4	even	2		35.5.g.a.8.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.7	✓	24	5.4	even	2
35.5.g.a.22.7	yes	24	5.3	odd	4
175.5.g.c.43.6		24	1.1	even	1	trivial
175.5.g.c.57.6		24	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.896879 + 0.896879i) q^{2} +(9.60523 + 9.60523i) q^{3} +14.3912i q^{4} -17.2295 q^{6} +(13.0958 - 13.0958i) q^{7} +(-27.2572 - 27.2572i) q^{8} +103.521i q^{9} +O(q^{10})\)	\(q+(-0.896879 + 0.896879i) q^{2} +(9.60523 + 9.60523i) q^{3} +14.3912i q^{4} -17.2295 q^{6} +(13.0958 - 13.0958i) q^{7} +(-27.2572 - 27.2572i) q^{8} +103.521i q^{9} -106.380 q^{11} +(-138.231 + 138.231i) q^{12} +(222.204 + 222.204i) q^{13} +23.4907i q^{14} -181.367 q^{16} +(-163.879 + 163.879i) q^{17} +(-92.8458 - 92.8458i) q^{18} +406.567i q^{19} +251.576 q^{21} +(95.4098 - 95.4098i) q^{22} +(-492.730 - 492.730i) q^{23} -523.624i q^{24} -398.579 q^{26} +(-216.320 + 216.320i) q^{27} +(188.465 + 188.465i) q^{28} -371.475i q^{29} -315.550 q^{31} +(598.780 - 598.780i) q^{32} +(-1021.80 - 1021.80i) q^{33} -293.959i q^{34} -1489.79 q^{36} +(1113.90 - 1113.90i) q^{37} +(-364.641 - 364.641i) q^{38} +4268.64i q^{39} +273.917 q^{41} +(-225.634 + 225.634i) q^{42} +(739.107 + 739.107i) q^{43} -1530.94i q^{44} +883.838 q^{46} +(-326.912 + 326.912i) q^{47} +(-1742.07 - 1742.07i) q^{48} -343.000i q^{49} -3148.19 q^{51} +(-3197.78 + 3197.78i) q^{52} +(-502.049 - 502.049i) q^{53} -388.025i q^{54} -713.911 q^{56} +(-3905.17 + 3905.17i) q^{57} +(333.168 + 333.168i) q^{58} +5703.66i q^{59} -974.970 q^{61} +(283.010 - 283.010i) q^{62} +(1355.69 + 1355.69i) q^{63} -1827.80i q^{64} +1832.87 q^{66} +(1635.67 - 1635.67i) q^{67} +(-2358.42 - 2358.42i) q^{68} -9465.58i q^{69} +586.493 q^{71} +(2821.70 - 2821.70i) q^{72} +(7096.31 + 7096.31i) q^{73} +1998.06i q^{74} -5850.99 q^{76} +(-1393.13 + 1393.13i) q^{77} +(-3828.45 - 3828.45i) q^{78} -2389.81i q^{79} +4229.60 q^{81} +(-245.671 + 245.671i) q^{82} +(1297.02 + 1297.02i) q^{83} +3620.49i q^{84} -1325.78 q^{86} +(3568.10 - 3568.10i) q^{87} +(2899.62 + 2899.62i) q^{88} +11496.6i q^{89} +5819.87 q^{91} +(7090.99 - 7090.99i) q^{92} +(-3030.93 - 3030.93i) q^{93} -586.400i q^{94} +11502.8 q^{96} +(6917.34 - 6917.34i) q^{97} +(307.629 + 307.629i) q^{98} -11012.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 24 * q - 20 * q^3 + 72 * q^6	\( 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) \) 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Introduction

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