LMFDB - Embedded newform 35.5.g.a.8.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, 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("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.7
Character	$\chi$	$=$	35.8
Dual form			35.5.g.a.22.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.896879 - 0.896879i) q^{2} +(-9.60523 - 9.60523i) q^{3} +14.3912i q^{4} +(-20.2649 + 14.6401i) q^{5} -17.2295 q^{6} +(-13.0958 + 13.0958i) q^{7} +(27.2572 + 27.2572i) q^{8} +103.521i q^{9} +O(q^{10})$	\(q+(0.896879 - 0.896879i) q^{2} +(-9.60523 - 9.60523i) q^{3} +14.3912i q^{4} +(-20.2649 + 14.6401i) q^{5} -17.2295 q^{6} +(-13.0958 + 13.0958i) q^{7} +(27.2572 + 27.2572i) q^{8} +103.521i q^{9} +(-5.04483 + 31.3056i) q^{10} -106.380 q^{11} +(138.231 - 138.231i) q^{12} +(-222.204 - 222.204i) q^{13} +23.4907i q^{14} +(335.271 + 54.0282i) q^{15} -181.367 q^{16} +(163.879 - 163.879i) q^{17} +(92.8458 + 92.8458i) q^{18} +406.567i q^{19} +(-210.689 - 291.637i) q^{20} +251.576 q^{21} +(-95.4098 + 95.4098i) q^{22} +(492.730 + 492.730i) q^{23} -523.624i q^{24} +(196.336 - 593.361i) q^{25} -398.579 q^{26} +(216.320 - 216.320i) q^{27} +(-188.465 - 188.465i) q^{28} -371.475i q^{29} +(349.154 - 252.241i) q^{30} -315.550 q^{31} +(-598.780 + 598.780i) q^{32} +(1021.80 + 1021.80i) q^{33} -293.959i q^{34} +(73.6622 - 457.109i) q^{35} -1489.79 q^{36} +(-1113.90 + 1113.90i) q^{37} +(364.641 + 364.641i) q^{38} +4268.64i q^{39} +(-951.415 - 153.318i) q^{40} +273.917 q^{41} +(225.634 - 225.634i) q^{42} +(-739.107 - 739.107i) q^{43} -1530.94i q^{44} +(-1515.56 - 2097.85i) q^{45} +883.838 q^{46} +(326.912 - 326.912i) q^{47} +(1742.07 + 1742.07i) q^{48} -343.000i q^{49} +(-356.083 - 708.263i) q^{50} -3148.19 q^{51} +(3197.78 - 3197.78i) q^{52} +(502.049 + 502.049i) q^{53} -388.025i q^{54} +(2155.78 - 1557.41i) q^{55} -713.911 q^{56} +(3905.17 - 3905.17i) q^{57} +(-333.168 - 333.168i) q^{58} +5703.66i q^{59} +(-777.532 + 4824.96i) q^{60} -974.970 q^{61} +(-283.010 + 283.010i) q^{62} +(-1355.69 - 1355.69i) q^{63} -1827.80i q^{64} +(7756.02 + 1249.87i) q^{65} +1832.87 q^{66} +(-1635.67 + 1635.67i) q^{67} +(2358.42 + 2358.42i) q^{68} -9465.58i q^{69} +(-343.906 - 476.038i) q^{70} +586.493 q^{71} +(-2821.70 + 2821.70i) q^{72} +(-7096.31 - 7096.31i) q^{73} +1998.06i q^{74} +(-7585.22 + 3813.51i) q^{75} -5850.99 q^{76} +(1393.13 - 1393.13i) q^{77} +(3828.45 + 3828.45i) q^{78} -2389.81i q^{79} +(3675.38 - 2655.22i) q^{80} +4229.60 q^{81} +(245.671 - 245.671i) q^{82} +(-1297.02 - 1297.02i) q^{83} +3620.49i q^{84} +(-921.799 + 5720.20i) q^{85} -1325.78 q^{86} +(-3568.10 + 3568.10i) q^{87} +(-2899.62 - 2899.62i) q^{88} +11496.6i q^{89} +(-3240.78 - 522.246i) q^{90} +5819.87 q^{91} +(-7090.99 + 7090.99i) q^{92} +(3030.93 + 3030.93i) q^{93} -586.400i q^{94} +(-5952.17 - 8239.06i) q^{95} +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} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.896879	−	0.896879i	0.224220	−	0.224220i	−0.586053	−	0.810273i	$-0.699319\pi$
$2$	0.896879	−	0.896879i	0.224220	−	0.224220i	0.810273	+	0.586053i	$0.199319\pi$
$3$	−9.60523	−	9.60523i	−1.06725	−	1.06725i	−0.997569	−	0.0696786i	$-0.977803\pi$
$3$	−9.60523	−	9.60523i	−1.06725	−	1.06725i	−0.0696786	−	0.997569i	$-0.522197\pi$
$4$			14.3912i			0.899451i
$5$	−20.2649	+	14.6401i	−0.810598	+	0.585603i
$5$	−20.2649	+	14.6401i	−0.810598	+	0.585603i
$6$	−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
$10$	−5.04483	+	31.3056i	−0.0504483	+	0.313056i
$11$	−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	$-0.870054\pi$
$13$	−222.204	−	222.204i	−1.31481	−	1.31481i	−0.396993	−	0.917822i	$-0.629946\pi$
$14$			23.4907i			0.119850i
$15$	335.271	+	54.0282i	1.49009	+	0.240125i
$16$	−181.367			−0.708463
$17$	163.879	−	163.879i	0.567056	−	0.567056i	−0.364247	−	0.931302i	$-0.618674\pi$
$17$	163.879	−	163.879i	0.567056	−	0.567056i	0.931302	+	0.364247i	$0.118674\pi$
$18$	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	$0.809604\pi$
$20$	−210.689	−	291.637i	−0.526721	−	0.729093i
$21$	251.576			0.570468
$22$	−95.4098	+	95.4098i	−0.197128	+	0.197128i
$23$	492.730	+	492.730i	0.931437	+	0.931437i	0.997796	−	0.0663589i	$-0.0211382\pi$
$23$	492.730	+	492.730i	0.931437	+	0.931437i	−0.0663589	+	0.997796i	$0.521138\pi$
$24$		−	523.624i		−	0.909070i
$25$	196.336	−	593.361i	0.314138	−	0.949377i
$26$	−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	$-0.0708841\pi$
$30$	349.154	−	252.241i	0.387949	−	0.280267i
$31$	−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
$35$	73.6622	−	457.109i	0.0601324	−	0.373150i
$36$	−1489.79			−1.14953
$37$	−1113.90	+	1113.90i	−0.813657	+	0.813657i	−0.985180	−	0.171523i	$-0.945131\pi$
$37$	−1113.90	+	1113.90i	−0.813657	+	0.813657i	0.171523	+	0.985180i	$0.445131\pi$
$38$	364.641	+	364.641i	0.252522	+	0.252522i
$39$			4268.64i			2.80647i
$40$	−951.415	−	153.318i	−0.594634	−	0.0958240i
$41$	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	0.478406	−	0.878139i	$-0.341215\pi$
$43$	−739.107	−	739.107i	−0.399733	−	0.399733i	−0.878139	+	0.478406i	$0.841215\pi$
$44$		−	1530.94i		−	0.790773i
$45$	−1515.56	−	2097.85i	−0.748423	−	1.03597i
$46$	883.838			0.417693
$47$	326.912	−	326.912i	0.147991	−	0.147991i	−0.629229	−	0.777220i	$-0.716629\pi$
$47$	326.912	−	326.912i	0.147991	−	0.147991i	0.777220	+	0.629229i	$0.216629\pi$
$48$	1742.07	+	1742.07i	0.756106	+	0.756106i
$49$		−	343.000i		−	0.142857i
$50$	−356.083	−	708.263i	−0.142433	−	0.283305i
$51$	−3148.19			−1.21038
$52$	3197.78	−	3197.78i	1.18261	−	1.18261i
$53$	502.049	+	502.049i	0.178729	+	0.178729i	0.790802	−	0.612073i	$-0.209664\pi$
$53$	502.049	+	502.049i	0.178729	+	0.178729i	−0.612073	+	0.790802i	$0.709664\pi$
$54$		−	388.025i		−	0.133068i
$55$	2155.78	−	1557.41i	0.712655	−	0.514846i
$56$	−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	$0.694386\pi$
$60$	−777.532	+	4824.96i	−0.215981	+	1.34027i
$61$	−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
$65$	7756.02	+	1249.87i	1.83575	+	0.295827i
$66$	1832.87			0.420769
$67$	−1635.67	+	1635.67i	−0.364373	+	0.364373i	−0.865420	−	0.501047i	$-0.832948\pi$
$67$	−1635.67	+	1635.67i	−0.364373	+	0.364373i	0.501047	+	0.865420i	$0.332948\pi$
$68$	2358.42	+	2358.42i	0.510039	+	0.510039i
$69$		−	9465.58i		−	1.98815i
$70$	−343.906	−	476.038i	−0.0701848	−	0.0971505i
$71$	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	$-0.859311\pi$
$73$	−7096.31	−	7096.31i	−1.33164	−	1.33164i	−0.427737	−	0.903903i	$-0.640689\pi$
$74$			1998.06i			0.364876i
$75$	−7585.22	+	3813.51i	−1.34848	+	0.677958i
$76$	−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	$-0.0613225\pi$
$80$	3675.38	−	2655.22i	0.574279	−	0.414878i
$81$	4229.60			0.644658
$82$	245.671	−	245.671i	0.0365364	−	0.0365364i
$83$	−1297.02	−	1297.02i	−0.188274	−	0.188274i	0.606676	−	0.794950i	$-0.292503\pi$
$83$	−1297.02	−	1297.02i	−0.188274	−	0.188274i	−0.794950	+	0.606676i	$0.792503\pi$
$84$			3620.49i			0.513108i
$85$	−921.799	+	5720.20i	−0.127585	+	0.791724i
$86$	−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	$0.741513\pi$
$90$	−3240.78	−	522.246i	−0.400097	−	0.0644748i
$91$	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
$95$	−5952.17	−	8239.06i	−0.659520	−	0.912915i
$96$	11502.8			1.24814
$97$	−6917.34	+	6917.34i	−0.735183	+	0.735183i	−0.971642	−	0.236458i	$-0.924013\pi$
$97$	−6917.34	+	6917.34i	−0.735183	+	0.735183i	0.236458	+	0.971642i	$0.424013\pi$
$98$	−307.629	−	307.629i	−0.0320314	−	0.0320314i
$99$		−	11012.6i		−	1.12362i
$100$	8539.18	+	2825.52i	0.853918	+	0.282552i
$101$	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	0.311589	−	0.950217i	$-0.399139\pi$
$103$	−6775.21	−	6775.21i	−0.638629	−	0.638629i	−0.950217	+	0.311589i	$0.899139\pi$
$104$		−	12113.3i		−	1.11994i
$105$	−5098.18	+	3683.10i	−0.462420	+	0.334068i
$106$	900.555			0.0801490
$107$	−2458.26	+	2458.26i	−0.214714	+	0.214714i	−0.806267	−	0.591552i	$-0.798515\pi$
$107$	−2458.26	+	2458.26i	−0.214714	+	0.214714i	0.591552	+	0.806267i	$0.298515\pi$
$108$	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	$-0.0631351\pi$
$110$	536.668	−	3330.28i	0.0443527	−	0.275230i
$111$	21398.5			1.73675
$112$	2375.14	−	2375.14i	0.189345	−	0.189345i
$113$	−4239.96	−	4239.96i	−0.332051	−	0.332051i	0.521314	−	0.853365i	$-0.325442\pi$
$113$	−4239.96	−	4239.96i	−0.332051	−	0.332051i	−0.853365	+	0.521314i	$0.825442\pi$
$114$		−	7004.93i		−	0.539007i
$115$	−17198.8	−	2771.54i	−1.30047	−	0.209569i
$116$	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
$120$	7665.90	+	10611.2i	0.532354	+	0.736890i
$121$	−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
$125$	4708.10	+	14898.8i	0.301319	+	0.953524i
$126$	−2431.78			−0.153173
$127$	458.788	−	458.788i	0.0284449	−	0.0284449i	−0.692741	−	0.721186i	$-0.743597\pi$
$127$	458.788	−	458.788i	0.0284449	−	0.0284449i	0.721186	+	0.692741i	$0.243597\pi$
$128$	−11219.8	−	11219.8i	−0.684802	−	0.684802i
$129$			14198.6i			0.853229i
$130$	8077.19	−	5835.23i	0.477940	−	0.345280i
$131$	−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
$135$	−1216.77	+	7550.64i	−0.0667638	+	0.414301i
$136$	8933.78			0.483012
$137$	10186.1	−	10186.1i	0.542708	−	0.542708i	−0.381614	−	0.924322i	$-0.624631\pi$
$137$	10186.1	−	10186.1i	0.542708	−	0.542708i	0.924322	+	0.381614i	$0.124631\pi$
$138$	−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	$0.760222\pi$
$140$	6578.36	+	1060.09i	0.335631	+	0.0540862i
$141$	−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
$145$	5438.42	+	7527.92i	0.258664	+	0.358046i
$146$	−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	$-0.191232\pi$
$150$	−3382.77	+	10223.3i	−0.150345	+	0.454368i
$151$	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
$155$	6394.61	−	4619.68i	0.266165	−	0.192286i
$156$	−61430.9			−2.52428
$157$	12567.2	−	12567.2i	0.509847	−	0.509847i	−0.404633	−	0.914479i	$-0.632601\pi$
$157$	12567.2	−	12567.2i	0.509847	−	0.509847i	0.914479	+	0.404633i	$0.132601\pi$
$158$	−2143.37	−	2143.37i	−0.0858585	−	0.0858585i
$159$		−	9644.60i		−	0.381496i
$160$	3368.06	−	20900.4i	0.131565	−	0.816423i
$161$	−12905.4			−0.497874
$162$	3793.44	−	3793.44i	0.144545	−	0.144545i
$163$	21632.3	+	21632.3i	0.814193	+	0.814193i	0.985259	−	0.171067i	$-0.0547214\pi$
$163$	21632.3	+	21632.3i	0.814193	+	0.814193i	−0.171067	+	0.985259i	$0.554721\pi$
$164$			3942.01i			0.146565i
$165$	−35666.1	−	5747.51i	−1.31005	−	0.211112i
$166$	−2326.54			−0.0844295
$167$	−25526.2	+	25526.2i	−0.915280	+	0.915280i	−0.996681	−	0.0814016i	$-0.974060\pi$
$167$	−25526.2	+	25526.2i	−0.915280	+	0.915280i	0.0814016	+	0.996681i	$0.474060\pi$
$168$	6857.28	+	6857.28i	0.242959	+	0.242959i
$169$			70187.9i			2.45747i
$170$	4303.59	+	5957.07i	0.148913	+	0.206127i
$171$	−42088.2			−1.43936
$172$	10636.6	−	10636.6i	0.359540	−	0.359540i
$173$	−17054.0	−	17054.0i	−0.569815	−	0.569815i	0.362262	−	0.932076i	$-0.382005\pi$
$173$	−17054.0	−	17054.0i	−0.569815	−	0.569815i	−0.932076	+	0.362262i	$0.882005\pi$
$174$			6400.31i			0.211399i
$175$	5199.35	+	10341.7i	0.169775	+	0.337689i
$176$	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	$-0.185405\pi$
$180$	30190.6	−	21810.7i	0.931808	−	0.673169i
$181$	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
$185$	6265.52	−	38880.6i	0.183069	−	1.13603i
$186$	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
$190$	−12727.8	−	2051.06i	−0.352571	−	0.0568161i
$191$	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	0.680548	−	0.732703i	$-0.261742\pi$
$193$	−1942.74	−	1942.74i	−0.0521555	−	0.0521555i	−0.732703	+	0.680548i	$0.761742\pi$
$194$			12408.0i			0.329685i
$195$	−62493.2	−	86503.7i	−1.64348	−	2.27492i
$196$	4936.19			0.128493
$197$	18355.9	−	18355.9i	0.472980	−	0.472980i	−0.429897	−	0.902878i	$-0.641450\pi$
$197$	18355.9	−	18355.9i	0.472980	−	0.472980i	0.902878	+	0.429897i	$0.141450\pi$
$198$	−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	$-0.0540526\pi$
$200$	21525.0	−	10821.8i	0.538124	−	0.270545i
$201$	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
$205$	−5550.92	+	4010.17i	−0.132086	+	0.0954235i
$206$	−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
$210$	−1269.16	+	7875.75i	−0.0287791	+	0.178588i
$211$	−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
$215$	25798.5	+	4157.38i	0.558108	+	0.0899379i
$216$	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
$220$	22413.0	+	31024.3i	0.463079	+	0.640999i
$221$	−72829.1			−1.49115
$222$	19191.8	−	19191.8i	0.389413	−	0.389413i
$223$	−64.2980	−	64.2980i	−0.00129297	−	0.00129297i	0.706460	−	0.707753i	$-0.250291\pi$
$223$	−64.2980	−	64.2980i	−0.00129297	−	0.00129297i	−0.707753	+	0.706460i	$0.750291\pi$
$224$		−	15683.0i		−	0.312560i
$225$	61425.3	+	20324.9i	1.21334	+	0.401480i
$226$	−7605.45			−0.148905
$227$	−27272.1	+	27272.1i	−0.529256	+	0.529256i	−0.920351	−	0.391094i	$-0.872097\pi$
$227$	−27272.1	+	27272.1i	−0.529256	+	0.529256i	0.391094	+	0.920351i	$0.372097\pi$
$228$	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	$0.909705\pi$
$230$	−17910.9	+	12939.5i	−0.338581	+	0.244602i
$231$	−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	$-0.991232\pi$
$233$	−55763.6	−	55763.6i	−1.02716	−	1.02716i	−0.0275419	−	0.999621i	$-0.508768\pi$
$234$		−	41261.3i		−	0.753549i
$235$	−1838.84	+	11410.9i	−0.0332972	+	0.206625i
$236$	−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	$0.977995\pi$
$240$	−60806.9	−	9798.91i	−1.05568	−	0.170120i
$241$	−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
$245$	5021.55	+	6950.88i	0.0836576	+	0.115800i
$246$	−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
$250$	17585.0	+	9139.82i	0.281360	+	0.146237i
$251$	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
$255$	63798.0	−	46089.8i	0.981130	−	0.708801i
$256$	9119.22			0.139148
$257$	−51789.3	+	51789.3i	−0.784105	+	0.784105i	−0.980521	−	0.196416i	$-0.937070\pi$
$257$	−51789.3	+	51789.3i	−0.784105	+	0.784105i	0.196416	+	0.980521i	$0.437070\pi$
$258$	12734.4	+	12734.4i	0.191311	+	0.191311i
$259$		−	29174.7i		−	0.434918i
$260$	−17987.1	+	111619.i	−0.266081	+	1.65116i
$261$	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	$0.130014\pi$
$263$	90952.1	+	90952.1i	1.31493	+	1.31493i	0.397189	+	0.917737i	$0.369986\pi$
$264$			55703.1i			0.799229i
$265$	−17524.0	−	2823.96i	−0.249541	−	0.0402131i
$266$	−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	$-0.242136\pi$
$270$	5680.71	+	7863.30i	0.0779247	+	0.107864i
$271$	−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
$275$	−20886.2	+	63121.7i	−0.276182	+	0.834666i
$276$	136221.			1.78824
$277$	−65998.2	+	65998.2i	−0.860147	+	0.860147i	−0.991355	−	0.131208i	$-0.958115\pi$
$277$	−65998.2	+	65998.2i	−0.860147	+	0.860147i	0.131208	+	0.991355i	$0.458115\pi$
$278$	23706.9	+	23706.9i	0.306750	+	0.306750i
$279$		−	32666.1i		−	0.419651i
$280$	14467.4	−	10451.7i	0.184533	−	0.133313i
$281$	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	0.655666	−	0.755051i	$-0.272388\pi$
$283$	−7959.64	−	7959.64i	−0.0993849	−	0.0993849i	−0.755051	+	0.655666i	$0.772388\pi$
$284$			8440.35i			0.104646i
$285$	−21966.1	+	136310.i	−0.270435	+	1.67818i
$286$	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
$290$	11629.2	+	1874.03i	0.138279	+	0.0222833i
$291$	132885.			1.56925
$292$	102125.	−	102125.i	1.19775	−	1.19775i
$293$	42977.6	+	42977.6i	0.500619	+	0.500619i	0.911630	−	0.411011i	$-0.134824\pi$
$293$	42977.6	+	42977.6i	0.500619	+	0.500619i	−0.411011	+	0.911630i	$0.634824\pi$
$294$			5909.70i			0.0683709i
$295$	−83502.1	−	115584.i	−0.959518	−	1.32818i
$296$	−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
$300$	−54881.1	−	109161.i	−0.609790	−	1.21290i
$301$	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
$305$	19757.7	−	14273.6i	0.212391	−	0.153439i
$306$	30431.0			0.324992
$307$	−45339.7	+	45339.7i	−0.481063	+	0.481063i	−0.905471	−	0.424408i	$-0.860482\pi$
$307$	−45339.7	+	45339.7i	−0.481063	+	0.481063i	0.424408	+	0.905471i	$0.360482\pi$
$308$	20048.8	+	20048.8i	0.211343	+	0.211343i
$309$			130155.i			1.36315i
$310$	1591.90	−	9878.48i	0.0165650	−	0.102794i
$311$	−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	0.976756	−	0.214353i	$-0.0687642\pi$
$313$	74691.9	+	74691.9i	0.762404	+	0.762404i	−0.214353	+	0.976756i	$0.568764\pi$
$314$		−	22542.5i		−	0.228635i
$315$	47320.4	+	7625.59i	0.476900	+	0.0768515i
$316$	34392.3			0.344419
$317$	−52291.4	+	52291.4i	−0.520370	+	0.520370i	−0.917683	−	0.397313i	$-0.869943\pi$
$317$	−52291.4	+	52291.4i	−0.520370	+	0.520370i	0.397313	+	0.917683i	$0.369943\pi$
$318$	−8650.04	−	8650.04i	−0.0855389	−	0.0855389i
$319$			39517.4i			0.388336i
$320$	26759.1	+	37040.3i	0.261320	+	0.361721i
$321$	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
$325$	−175474.	+	88220.3i	−1.66129	+	0.835222i
$326$	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
$330$	−37143.0	+	26833.3i	−0.341074	+	0.246403i
$331$	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
$335$	9200.43	−	57093.1i	0.0819820	−	0.508738i
$336$	−45627.6			−0.404156
$337$	−68383.2	+	68383.2i	−0.602129	+	0.602129i	−0.940877	−	0.338748i	$-0.889997\pi$
$337$	−68383.2	+	68383.2i	−0.602129	+	0.602129i	0.338748	+	0.940877i	$0.389997\pi$
$338$	62950.1	+	62950.1i	0.551014	+	0.551014i
$339$			81451.5i			0.708761i
$340$	−82320.7	−	13265.8i	−0.712117	−	0.114756i
$341$	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
$345$	138577.	+	191819.i	1.16427	+	1.61159i
$346$	−30590.7			−0.255527
$347$	25167.8	−	25167.8i	0.209019	−	0.209019i	−0.594831	−	0.803851i	$-0.702781\pi$
$347$	25167.8	−	25167.8i	0.209019	−	0.209019i	0.803851	+	0.594831i	$0.202781\pi$
$348$	−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	$-0.283550\pi$
$350$	13938.5	+	4612.07i	0.113783	+	0.0376496i
$351$	−96134.0			−0.780302
$352$	63698.1	−	63698.1i	0.514092	−	0.514092i
$353$	69986.0	+	69986.0i	0.561645	+	0.561645i	0.929775	−	0.368130i	$-0.120002\pi$
$353$	69986.0	+	69986.0i	0.561645	+	0.561645i	−0.368130	+	0.929775i	$0.620002\pi$
$354$		−	98271.1i		−	0.784186i
$355$	−11885.3	+	8586.31i	−0.0943087	+	0.0681318i
$356$	−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	$-0.0676694\pi$
$360$	15871.7	−	98491.4i	0.122467	−	0.759964i
$361$	−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
$365$	247697.	+	39915.8i	1.85924	+	0.299612i
$366$	16798.2			0.125401
$367$	4302.78	−	4302.78i	0.0319460	−	0.0319460i	−0.690953	−	0.722899i	$-0.742809\pi$
$367$	4302.78	−	4302.78i	0.0319460	−	0.0319460i	0.722899	+	0.690953i	$0.242809\pi$
$368$	−89364.8	−	89364.8i	−0.659889	−	0.659889i
$369$			28356.2i			0.208255i
$370$	−29251.7	−	40490.6i	−0.213672	−	0.295767i
$371$	−13149.5			−0.0955346
$372$	−43618.8	+	43618.8i	−0.315201	+	0.315201i
$373$	−70465.2	−	70465.2i	−0.506474	−	0.506474i	0.406968	−	0.913442i	$-0.366586\pi$
$373$	−70465.2	−	70465.2i	−0.506474	−	0.506474i	−0.913442	+	0.406968i	$0.866586\pi$
$374$			31271.4i			0.223565i
$375$	97884.1	−	188329.i	0.696064	−	1.33923i
$376$	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	$-0.101193\pi$
$380$	118570.	−	85659.0i	0.821122	−	0.593206i
$381$	−8813.52			−0.0607155
$382$	48078.0	−	48078.0i	0.329473	−	0.329473i
$383$	17747.1	+	17747.1i	0.120985	+	0.120985i	0.765007	−	0.644022i	$-0.222736\pi$
$383$	17747.1	+	17747.1i	0.120985	+	0.120985i	−0.644022	+	0.765007i	$0.722736\pi$
$384$			215537.i			1.46171i
$385$	−7836.18	+	48627.2i	−0.0528668	+	0.328064i
$386$	−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	$0.969403\pi$
$390$	−133632.	−	21534.5i	−0.878581	−	0.141581i
$391$	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
$395$	34987.0	+	48429.4i	0.224240	+	0.310395i
$396$	158484.			1.01064
$397$	175512.	−	175512.i	1.11359	−	1.11359i	0.120929	−	0.992661i	$-0.461413\pi$
$397$	175512.	−	175512.i	1.11359	−	1.11359i	0.992661	−	0.120929i	$-0.0385873\pi$
$398$	−12004.6	−	12004.6i	−0.0757845	−	0.0757845i
$399$			102283.i			0.642475i
$400$	−35608.8	+	107616.i	−0.222555	+	0.672599i
$401$	−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
$405$	−85712.7	+	61921.7i	−0.522559	+	0.377514i
$406$	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	$0.852350\pi$
$410$	−1381.87	+	8575.14i	−0.00822050	+	0.0510122i
$411$	−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
$415$	45272.5	+	7295.57i	0.262868	+	0.0423607i
$416$	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	$0.882629\pi$
$420$	−53004.3	−	73369.1i	−0.300478	−	0.415924i
$421$	−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
$425$	−65064.0	−	129415.i	−0.360216	−	0.716484i
$426$	−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
$430$	26866.8	−	19409.5i	0.145305	−	0.104973i
$431$	−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	0.989398	−	0.145230i	$-0.0463921\pi$
$433$	158272.	+	158272.i	0.844168	+	0.844168i	−0.145230	+	0.989398i	$0.546392\pi$
$434$		−	7412.50i		−	0.0393536i
$435$	20070.1	−	124545.i	0.106065	−	0.658183i
$436$	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	$0.897096\pi$
$440$	101211.	+	16310.0i	0.522786	+	0.0842459i
$441$	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	$0.0261670\pi$
$443$	211701.	+	211701.i	1.07874	+	1.07874i	0.0821136	+	0.996623i	$0.473833\pi$
$444$			307950.i			1.56212i
$445$	−168312.	−	232979.i	−0.849951	−	1.17651i
$446$	−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	$-0.0599357\pi$
$450$	73320.1	−	36862.1i	0.362074	−	0.182035i
$451$	−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
$455$	−117939.	+	85203.3i	−0.569687	+	0.411561i
$456$	212888.			1.02382
$457$	−227700.	+	227700.i	−1.09026	+	1.09026i	−0.0947612	+	0.995500i	$0.530209\pi$
$457$	−227700.	+	227700.i	−1.09026	+	1.09026i	−0.995500	+	0.0947612i	$0.969791\pi$
$458$	26327.5	+	26327.5i	0.125510	+	0.125510i
$459$		−	70900.5i		−	0.336530i
$460$	39885.9	−	247511.i	0.188497	−	1.16971i
$461$	−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	0.359376	−	0.933193i	$-0.382990\pi$
$463$	−123009.	−	123009.i	−0.573817	−	0.573817i	−0.933193	+	0.359376i	$0.882990\pi$
$464$			67373.1i			0.312933i
$465$	−105795.	−	17048.6i	−0.489281	−	0.0788467i
$466$	−100026.			−0.460620
$467$	61189.1	−	61189.1i	0.280569	−	0.280569i	−0.552767	−	0.833336i	$-0.686428\pi$
$467$	61189.1	−	61189.1i	0.280569	−	0.280569i	0.833336	+	0.552767i	$0.186428\pi$
$468$	331038.	+	331038.i	1.51142	+	1.51142i
$469$		−	42840.8i		−	0.194766i
$470$	8584.94	+	11883.4i	0.0388635	+	0.0537952i
$471$	−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
$475$	241241.	+	79823.8i	1.06921	+	0.353790i
$476$	−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	$-0.0990393\pi$
$480$	−233104.	+	168402.i	−1.01174	+	0.730913i
$481$	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
$485$	38909.1	−	241450.i	0.165412	−	1.02646i
$486$	−104304.			−0.441598
$487$	−139424.	+	139424.i	−0.587869	+	0.587869i	−0.937054	−	0.349185i	$-0.886459\pi$
$487$	−139424.	+	139424.i	−0.587869	+	0.587869i	0.349185	+	0.937054i	$0.386459\pi$
$488$	−26575.0	−	26575.0i	−0.111592	−	0.111592i
$489$		−	415566.i		−	1.73789i
$490$	10737.8	+	1730.38i	0.0447223	+	0.00720690i
$491$	−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
$495$	161225.	+	223169.i	0.657993	+	0.910800i
$496$	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	$0.974141\pi$
$500$	−214412.	+	67755.3i	−0.857648	+	0.271021i
$501$	490371.			1.95366
$502$	99151.9	−	99151.9i	0.393454	−	0.393454i
$503$	−302310.	−	302310.i	−1.19486	−	1.19486i	−0.975686	−	0.219173i	$-0.929664\pi$
$503$	−302310.	−	302310.i	−1.19486	−	1.19486i	−0.219173	−	0.975686i	$-0.570336\pi$
$504$		−	73904.8i		−	0.290945i
$505$	−124658.	+	90057.2i	−0.488807	+	0.353131i
$506$	−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	$-0.0307491\pi$
$510$	15882.1	−	98556.0i	0.0610615	−	0.378916i
$511$	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
$515$	236489.	+	38109.7i	0.891654	+	0.143688i
$516$	−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
$520$	177340.	+	245476.i	0.655843	+	0.907824i
$521$	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	0.899007	−	0.437935i	$-0.144290\pi$
$523$	126116.	+	126116.i	0.461071	+	0.461071i	−0.437935	+	0.899007i	$0.644290\pi$
$524$		−	302031.i		−	1.09999i
$525$	49393.6	−	149276.i	0.179206	−	0.541589i
$526$	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
$530$	−18249.7	+	13184.2i	−0.0649686	+	0.0469355i
$531$	−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
$535$	13827.4	−	85805.7i	0.0483096	−	0.299784i
$536$	−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
$540$	−108663.	−	17510.8i	−0.372644	−	0.0600507i
$541$	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
$545$	68548.2	+	94885.1i	0.230782	+	0.319452i
$546$	−100273.			−0.336356
$547$	−188558.	+	188558.i	−0.630187	+	0.630187i	−0.948115	−	0.317928i	$-0.897013\pi$
$547$	−188558.	+	188558.i	−0.630187	+	0.630187i	0.317928	+	0.948115i	$0.397013\pi$
$548$	146590.	+	146590.i	0.488140	+	0.488140i
$549$		−	100930.i		−	0.334869i
$550$	37880.1	+	75344.9i	0.125223	+	0.249074i
$551$	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
$555$	−433639.	+	313275.i	−1.40780	+	1.01704i
$556$	−380398.			−1.23052
$557$	−111586.	+	111586.i	−0.359665	+	0.359665i	−0.863689	−	0.504025i	$-0.831852\pi$
$557$	−111586.	+	111586.i	−0.359665	+	0.359665i	0.504025	+	0.863689i	$0.331852\pi$
$558$	−29297.5	−	29297.5i	−0.0940941	−	0.0940941i
$559$			328464.i			1.05115i
$560$	−13359.9	+	82904.4i	−0.0426016	+	0.264363i
$561$	334905.			1.06413
$562$	13449.2	−	13449.2i	0.0425818	−	0.0425818i
$563$	251019.	+	251019.i	0.791936	+	0.791936i	0.981809	−	0.189873i	$-0.0608076\pi$
$563$	251019.	+	251019.i	0.791936	+	0.791936i	−0.189873	+	0.981809i	$0.560808\pi$
$564$		−	90378.6i		−	0.284124i
$565$	147996.	+	23849.2i	0.463610	+	0.0747097i
$566$	−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	$-0.00676803\pi$
$570$	102553.	+	141955.i	0.315644	+	0.436918i
$571$	−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
$575$	389108.	−	195626.i	1.17688	−	0.591685i
$576$	189216.			0.570312
$577$	148330.	−	148330.i	0.445529	−	0.445529i	−0.448336	−	0.893865i	$-0.647983\pi$
$577$	148330.	−	148330.i	0.445529	−	0.445529i	0.893865	+	0.448336i	$0.147983\pi$
$578$	26734.4	+	26734.4i	0.0800230	+	0.0800230i
$579$			37320.9i			0.111326i
$580$	−108336.	+	78265.5i	−0.322045	+	0.232656i
$581$	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
$585$	−129387.	+	802911.i	−0.378077	+	2.34615i
$586$	77091.5			0.224497
$587$	208211.	−	208211.i	0.604266	−	0.604266i	−0.337175	−	0.941442i	$-0.609472\pi$
$587$	208211.	−	208211.i	0.604266	−	0.604266i	0.941442	+	0.337175i	$0.109472\pi$
$588$	−47413.2	−	47413.2i	−0.137134	−	0.137134i
$589$		−	128292.i		−	0.369803i
$590$	−178557.	−	28774.0i	−0.512946	−	0.0826602i
$591$	−352625.			−1.00957
$592$	202023.	−	202023.i	0.576446	−	0.576446i
$593$	−176624.	−	176624.i	−0.502273	−	0.502273i	0.409870	−	0.912144i	$-0.365574\pi$
$593$	−176624.	−	176624.i	−0.502273	−	0.502273i	−0.912144	+	0.409870i	$0.865574\pi$
$594$			41278.0i			0.116989i
$595$	−62839.0	−	86982.4i	−0.177499	−	0.245696i
$596$	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	$0.760247\pi$
$600$	−310698.	−	102806.i	−0.863050	−	0.285573i
$601$	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
$605$	67367.2	−	48668.3i	0.184051	−	0.132964i
$606$	−105986.			−0.288603
$607$	21818.0	−	21818.0i	0.0592159	−	0.0592159i	−0.676879	−	0.736095i	$-0.736668\pi$
$607$	21818.0	−	21818.0i	0.0592159	−	0.0592159i	0.736095	+	0.676879i	$0.236668\pi$
$608$	−243444.	−	243444.i	−0.658555	−	0.658555i
$609$		−	93454.3i		−	0.251979i
$610$	4918.55	−	30522.0i	0.0132184	−	0.0820263i
$611$	−145282.			−0.389161
$612$	−244146.	+	244146.i	−0.651849	+	0.651849i
$613$	257328.	+	257328.i	0.684804	+	0.684804i	0.961079	−	0.276275i	$-0.0891001\pi$
$613$	257328.	+	257328.i	0.684804	+	0.684804i	−0.276275	+	0.961079i	$0.589100\pi$
$614$			81328.4i			0.215728i
$615$	91836.6	+	14799.3i	0.242809	+	0.0391282i
$616$	75945.7			0.200144
$617$	−457425.	+	457425.i	−1.20157	+	1.20157i	−0.227883	+	0.973689i	$0.573180\pi$
$617$	−457425.	+	457425.i	−1.20157	+	1.20157i	−0.973689	+	0.227883i	$0.926820\pi$
$618$	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	$-0.178196\pi$
$620$	66482.8	+	92026.2i	0.172952	+	0.239402i
$621$	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
$625$	−313529.	−	232997.i	−0.802635	−	0.596471i
$626$	133979.			0.341892
$627$	−415432.	+	415432.i	−1.05673	+	1.05673i
$628$	180857.	+	180857.i	0.458582	+	0.458582i
$629$			365089.i			0.922777i
$630$	49279.9	−	35601.4i	0.124162	−	0.0896988i
$631$	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
$635$	−2580.62	+	16014.0i	−0.00639995	+	0.0397148i
$636$	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
$640$	391627.	+	63109.9i	0.956121	+	0.154077i
$641$	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	0.868759	−	0.495235i	$-0.164918\pi$
$643$	154433.	+	154433.i	0.373524	+	0.373524i	−0.495235	+	0.868759i	$0.664918\pi$
$644$		−	185724.i		−	0.447813i
$645$	−207868.	−	287734.i	−0.499654	−	0.691626i
$646$	119514.			0.286388
$647$	−172763.	+	172763.i	−0.412707	+	0.412707i	−0.882681	−	0.469973i	$-0.844264\pi$
$647$	−172763.	+	172763.i	−0.412707	+	0.412707i	0.469973	+	0.882681i	$0.344264\pi$
$648$	115287.	+	115287.i	0.274556	+	0.274556i
$649$		−	606755.i		−	1.44054i
$650$	−78255.6	+	236501.i	−0.185220	+	0.559767i
$651$	−79385.0			−0.187317
$652$	−311315.	+	311315.i	−0.732326	+	0.732326i
$653$	−402102.	−	402102.i	−0.942995	−	0.942995i	0.0554657	−	0.998461i	$-0.482336\pi$
$653$	−402102.	−	402102.i	−0.942995	−	0.942995i	−0.998461	+	0.0554657i	$0.982336\pi$
$654$			80672.2i			0.188612i
$655$	425304.	−	307254.i	0.991327	−	0.716168i
$656$	−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	$-0.197476\pi$
$660$	82713.7	−	513278.i	0.189885	−	1.17832i
$661$	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
$665$	185846.	+	29948.6i	0.420251	+	0.0677226i
$666$	−206841.			−0.466325
$667$	183037.	−	183037.i	0.411421	−	0.411421i
$668$	−367354.	−	367354.i	−0.823249	−	0.823249i
$669$			1235.19i			0.00275983i
$670$	−42953.9	−	59457.3i	−0.0956870	−	0.132451i
$671$	103717.			0.230359
$672$	−150639.	+	150639.i	−0.333579	+	0.333579i
$673$	−159035.	−	159035.i	−0.351126	−	0.351126i	0.509403	−	0.860528i	$-0.329866\pi$
$673$	−159035.	−	159035.i	−0.351126	−	0.351126i	−0.860528	+	0.509403i	$0.829866\pi$
$674$			122663.i			0.270018i
$675$	−85884.2	−	170827.i	−0.188498	−	0.374929i
$676$	−1.01009e6			−2.21038
$677$	40160.9	−	40160.9i	0.0876247	−	0.0876247i	−0.661936	−	0.749561i	$-0.730265\pi$
$677$	40160.9	−	40160.9i	0.0876247	−	0.0876247i	0.749561	+	0.661936i	$0.230265\pi$
$678$	73052.1	+	73052.1i	0.158918	+	0.158918i
$679$		−	181176.i		−	0.392972i
$680$	−181043.	+	130791.i	−0.391528	+	0.282853i
$681$	523909.			1.12970
$682$	30106.6	−	30106.6i	0.0647281	−	0.0647281i
$683$	161353.	+	161353.i	0.345888	+	0.345888i	0.858575	−	0.512688i	$-0.171350\pi$
$683$	161353.	+	161353.i	0.345888	+	0.345888i	−0.512688	+	0.858575i	$0.671350\pi$
$684$		−	605701.i		−	1.29463i
$685$	−57295.5	+	355546.i	−0.122107	+	0.757730i
$686$	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
$690$	296325.	+	47752.2i	0.622401	+	0.100299i
$691$	−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
$695$	−386976.	−	535656.i	−0.801151	−	1.10896i
$696$	−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
$700$	−148830.	+	74825.0i	−0.303734	+	0.152704i
$701$	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
$705$	127266.	−	91941.5i	0.256056	−	0.184984i
$706$	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	$0.749303\pi$
$710$	−2958.76	+	18360.5i	−0.00586939	+	0.0364224i
$711$	247396.			0.489388
$712$	−313367.	+	313367.i	−0.618148	+	0.618148i
$713$	−155481.	−	155481.i	−0.305843	−	0.305843i
$714$		−	73953.3i		−	0.145064i
$715$	−825085.	−	132961.i	−1.61394	−	0.260083i
$716$	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	$0.737964\pi$
$720$	274871.	+	380480.i	0.530230	+	0.733950i
$721$	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
$725$	−220419.	−	72934.0i	−0.419346	−	0.138757i
$726$	57276.3			0.108668
$727$	351306.	−	351306.i	0.664687	−	0.664687i	−0.291794	−	0.956481i	$-0.594252\pi$
$727$	351306.	−	351306.i	0.664687	−	0.664687i	0.956481	+	0.291794i	$0.0942522\pi$
$728$	158634.	+	158634.i	0.299318	+	0.299318i
$729$			774456.i			1.45728i
$730$	257954.	−	186354.i	0.484057	−	0.349699i
$731$	−242248.			−0.453342
$732$	−134771.	+	134771.i	−0.251521	+	0.251521i
$733$	21457.1	+	21457.1i	0.0399358	+	0.0399358i	0.726793	−	0.686857i	$-0.241010\pi$
$733$	21457.1	+	21457.1i	0.0399358	+	0.0399358i	−0.686857	+	0.726793i	$0.741010\pi$
$734$		−	7718.14i		−	0.0143259i
$735$	18531.7	−	114998.i	0.0343036	−	0.212870i
$736$	−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	$-0.248647\pi$
$740$	559539.	+	90168.5i	1.02180	+	0.164661i
$741$	−1.73549e6			−3.16071
$742$	−11793.5	+	11793.5i	−0.0214207	+	0.0214207i
$743$	34898.0	+	34898.0i	0.0632154	+	0.0632154i	0.738008	−	0.674792i	$-0.235767\pi$
$743$	34898.0	+	34898.0i	0.0632154	+	0.0632154i	−0.674792	+	0.738008i	$0.735767\pi$
$744$			165230.i			0.298499i
$745$	367460.	+	508642.i	0.662060	+	0.916431i
$746$	−126398.			−0.227123
$747$	134269.	−	134269.i	0.240621	−	0.240621i
$748$	−250888.	−	250888.i	−0.448412	−	0.448412i
$749$		−	64385.8i		−	0.114770i
$750$	−81118.1	−	256698.i	−0.144210	−	0.456353i
$751$	−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
$755$	−427892.	+	309124.i	−0.750655	+	0.542299i
$756$	−81537.1			−0.142663
$757$	85156.4	−	85156.4i	0.148602	−	0.148602i	−0.628891	−	0.777493i	$-0.716491\pi$
$757$	85156.4	−	85156.4i	0.148602	−	0.148602i	0.777493	+	0.628891i	$0.216491\pi$
$758$	−80538.5	−	80538.5i	−0.140173	−	0.140173i
$759$			1.00695e6i			1.74793i
$760$	62334.2	−	386814.i	0.107919	−	0.669691i
$761$	−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
$765$	−592161.	−	95425.6i	−1.01185	−	0.163058i
$766$	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	$-0.299859\pi$
$770$	36584.6	+	50640.8i	0.0617045	+	0.0854121i
$771$	994898.			1.67367
$772$	27958.4	−	27958.4i	0.0469113	−	0.0469113i
$773$	429882.	+	429882.i	0.719433	+	0.719433i	0.968489	−	0.249056i	$-0.0801204\pi$
$773$	429882.	+	429882.i	0.719433	+	0.719433i	−0.249056	+	0.968489i	$0.580120\pi$
$774$		−	137246.i		−	0.229096i
$775$	−61954.0	+	187235.i	−0.103149	+	0.311734i
$776$	−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
$780$	1.24489e6	−	899353.i	2.04618	−	1.47823i
$781$	−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
$785$	−70688.9	+	438659.i	−0.114713	+	0.711848i
$786$	361598.			0.585303
$787$	−100130.	+	100130.i	−0.161665	+	0.161665i	−0.783304	−	0.621639i	$-0.786467\pi$
$787$	−100130.	+	100130.i	−0.161665	+	0.161665i	0.621639	+	0.783304i	$0.286467\pi$
$788$	264164.	+	264164.i	0.425423	+	0.425423i
$789$		−	1.74723e6i		−	2.80670i
$790$	74814.5	+	12056.2i	0.119876	+	0.0193177i
$791$	111051.			0.177489
$792$	300172.	−	300172.i	0.478541	−	0.478541i
$793$	216642.	+	216642.i	0.344505	+	0.344505i
$794$		−	314826.i		−	0.499378i
$795$	141198.	+	195447.i	0.223405	+	0.309240i
$796$	192624.			0.304008
$797$	72885.6	−	72885.6i	0.114743	−	0.114743i	−0.647404	−	0.762147i	$-0.724145\pi$
$797$	72885.6	−	72885.6i	0.114743	−	0.114743i	0.762147	+	0.647404i	$0.224145\pi$
$798$	91735.2	+	91735.2i	0.144056	+	0.144056i
$799$		−	107148.i		−	0.167838i
$800$	237730.	+	472855.i	0.371453	+	0.738835i
$801$	−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
$805$	261527.	−	188936.i	0.403576	−	0.291557i
$806$	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	$0.927105\pi$
$810$	−21337.6	+	132410.i	−0.0325219	+	0.201814i
$811$	−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
$815$	−755075.	−	121679.i	−1.13678	−	0.183189i
$816$	570977.			0.857509
$817$	300496.	−	300496.i	0.450189	−	0.450189i
$818$	134248.	+	134248.i	0.200632	+	0.200632i
$819$			602479.i			0.898202i
$820$	−57711.3	−	79884.5i	−0.0858288	−	0.118805i
$821$	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	0.484440	−	0.874824i	$-0.339023\pi$
$823$	−264418.	−	264418.i	−0.390384	−	0.390384i	−0.874824	+	0.484440i	$0.839023\pi$
$824$		−	369347.i		−	0.543977i
$825$	806915.	−	405681.i	1.18555	−	0.596042i
$826$	−133983.			−0.196377
$827$	24449.6	−	24449.6i	0.0357488	−	0.0357488i	−0.689006	−	0.724755i	$-0.741953\pi$
$827$	24449.6	−	24449.6i	0.0357488	−	0.0357488i	0.724755	+	0.689006i	$0.241953\pi$
$828$	−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	$-0.0614418\pi$
$830$	47147.2	−	34060.7i	0.0684383	−	0.0494422i
$831$	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
$835$	143582.	−	890994.i	0.205933	−	1.27791i
$836$	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	$0.749991\pi$
$840$	−239353.	−	38571.3i	−0.339220	−	0.0546646i
$841$	569287.			0.804896
$842$	−300469.	+	300469.i	−0.423814	+	0.423814i
$843$	−144036.	−	144036.i	−0.202682	−	0.202682i
$844$		−	968206.i		−	1.35920i
$845$	−1.02756e6	−	1.42235e6i	−1.43910	−	1.99202i
$846$	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
$850$	−174424.	−	57714.9i	−0.241417	−	0.0798822i
$851$	−1.09770e6			−1.51574
$852$	81071.5	−	81071.5i	0.111684	−	0.111684i
$853$	−139414.	−	139414.i	−0.191606	−	0.191606i	0.604784	−	0.796390i	$-0.293260\pi$
$853$	−139414.	−	139414.i	−0.191606	−	0.191606i	−0.796390	+	0.604784i	$0.793260\pi$
$854$		−	22902.7i		−	0.0314030i
$855$	852916.	−	616175.i	1.16674	−	0.842892i
$856$	−134011.			−0.182891
$857$	124172.	−	124172.i	0.169068	−	0.169068i	−0.617501	−	0.786570i	$-0.711855\pi$
$857$	124172.	−	124172.i	0.169068	−	0.169068i	0.786570	+	0.617501i	$0.211855\pi$
$858$	−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	$0.940829\pi$
$860$	−59829.8	+	371272.i	−0.0808948	+	0.501991i
$861$	68911.2			0.0929573
$862$	−315467.	+	315467.i	−0.424560	+	0.424560i
$863$	762399.	+	762399.i	1.02367	+	1.02367i	0.999713	+	0.0239590i	$0.00762713\pi$
$863$	762399.	+	762399.i	1.02367	+	1.02367i	0.0239590	+	0.999713i	$0.492373\pi$
$864$			259055.i			0.347029i
$865$	595270.	+	95926.5i	0.795576	+	0.128205i
$866$	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
$870$	−93701.0	−	129702.i	−0.123796	−	0.171359i
$871$	726904.			0.958166
$872$	127625.	−	127625.i	0.167842	−	0.167842i
$873$	−716090.	−	716090.i	−0.939591	−	0.939591i
$874$			359339.i			0.470416i
$875$	−256768.	−	133455.i	−0.335371	−	0.174309i
$876$	−1.96186e6			−2.55658
$877$	978873.	−	978873.i	1.27270	−	1.27270i	0.328038	−	0.944664i	$-0.393613\pi$
$877$	978873.	−	978873.i	1.27270	−	1.27270i	0.944664	−	0.328038i	$-0.106387\pi$
$878$	109821.	+	109821.i	0.142461	+	0.142461i
$879$		−	825620.i		−	1.06857i
$880$	−390987.	+	282462.i	−0.504890	+	0.364750i
$881$	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	0.327528	−	0.944841i	$-0.393784\pi$
$883$	−481312.	−	481312.i	−0.617313	−	0.617313i	−0.944841	+	0.327528i	$0.893784\pi$
$884$		−	1.04810e6i		−	1.34121i
$885$	−308159.	+	1.91227e6i	−0.393449	+	2.44154i
$886$	379740.			0.483748
$887$	−816109.	+	816109.i	−1.03729	+	1.03729i	−0.0380150	+	0.999277i	$0.512103\pi$
$887$	−816109.	+	816109.i	−1.03729	+	1.03729i	−0.999277	+	0.0380150i	$0.987897\pi$
$888$	583263.	+	583263.i	0.739671	+	0.739671i
$889$			12016.4i			0.0152044i
$890$	−359909.	−	57998.5i	−0.454373	−	0.0732212i
$891$	−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
$895$	516071.	+	714351.i	0.644263	+	0.891796i
$896$	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
$900$	−292500.	+	883985.i	−0.361112	+	1.09134i
$901$	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
$905$	−812623.	+	587066.i	−0.992183	+	0.716786i
$906$	−363798.			−0.443205
$907$	159574.	−	159574.i	0.193975	−	0.193975i	−0.603436	−	0.797411i	$-0.706202\pi$
$907$	159574.	−	159574.i	0.193975	−	0.193975i	0.797411	+	0.603436i	$0.206202\pi$
$908$	−392478.	−	392478.i	−0.476040	−	0.476040i
$909$			636801.i			0.770683i
$910$	−29360.2	+	182194.i	−0.0354549	+	0.220015i
$911$	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
$915$	−326879.	−	52675.9i	−0.390431	−	0.0629172i
$916$	−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	$-0.343258\pi$
$920$	−393246.	−	544335.i	−0.464610	−	0.643118i
$921$	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
$925$	442244.	+	879640.i	0.516867	+	1.02807i
$926$	−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	$0.682900\pi$
$930$	−110176.	+	79594.6i	−0.127385	+	0.0920275i
$931$	139452.			0.160889
$932$	802506.	−	802506.i	0.923882	−	0.923882i
$933$	170519.	+	170519.i	0.195888	+	0.195888i
$934$		−	109758.i		−	0.125818i
$935$	98060.9	−	608515.i	0.112169	−	0.696062i
$936$	1.25398e6			1.43133
$937$	−716769.	+	716769.i	−0.816395	+	0.816395i	−0.985584	−	0.169189i	$-0.945885\pi$
$937$	−716769.	+	716769.i	−0.816395	+	0.816395i	0.169189	+	0.985584i	$0.445885\pi$
$938$	−38423.0	−	38423.0i	−0.0436703	−	0.0436703i
$939$		−	1.43487e6i		−	1.62735i
$940$	−164216.	−	26463.1i	−0.185849	−	0.0299492i
$941$	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
$945$	−82947.1	−	114816.i	−0.0928833	−	0.128570i
$946$	141036.			0.157597
$947$	−5869.34	+	5869.34i	−0.00654469	+	0.00654469i	−0.710372	−	0.703827i	$-0.751473\pi$
$947$	−5869.34	+	5869.34i	−0.00654469	+	0.00654469i	0.703827	+	0.710372i	$0.251473\pi$
$948$	−330346.	−	330346.i	−0.367581	−	0.367581i
$949$			3.15365e6i			3.50172i
$950$	287956.	−	144772.i	0.319065	−	0.160412i
$951$	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	$-0.897107\pi$
$953$	−1.14966e6	−	1.14966e6i	−1.26586	−	1.26586i	−0.317649	−	0.948208i	$-0.602893\pi$
$954$			93226.3i			0.102433i
$955$	−1.08632e6	+	784795.i	−1.19111	+	0.860497i
$956$	−113566.			−0.124260
$957$	379574.	−	379574.i	0.414451	−	0.414451i
$958$	−125998.	−	125998.i	−0.137287	−	0.137287i
$959$			266790.i			0.290090i
$960$	98752.8	−	612808.i	0.107154	−	0.664940i
$961$	−823949.			−0.892182
$962$	443976.	−	443976.i	0.479744	−	0.479744i
$963$	−254482.	−	254482.i	−0.274413	−	0.274413i
$964$		−	224657.i		−	0.241750i
$965$	67811.4	+	10927.7i	0.0728195	+	0.0117347i
$966$	222353.			0.238281
$967$	642923.	−	642923.i	0.687553	−	0.687553i	−0.274137	−	0.961691i	$-0.588392\pi$
$967$	642923.	−	642923.i	0.687553	−	0.687553i	0.961691	+	0.274137i	$0.0883923\pi$
$968$	−90611.8	−	90611.8i	−0.0967017	−	0.0967017i
$969$		−	1.27995e6i		−	1.36316i
$970$	−181654.	−	251448.i	−0.193065	−	0.267242i
$971$	−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
$975$	2.53284e6	+	838088.i	2.66440	+	0.881618i
$976$	176827.			0.185630
$977$	435906.	−	435906.i	0.456672	−	0.456672i	−0.440890	−	0.897561i	$-0.645337\pi$
$977$	435906.	−	435906.i	0.456672	−	0.456672i	0.897561	+	0.440890i	$0.145337\pi$
$978$	−372713.	−	372713.i	−0.389669	−	0.389669i
$979$		−	1.22301e6i		−	1.27604i
$980$	−100032.	+	72266.2i	−0.104156	+	0.0752459i
$981$	484709.			0.503666
$982$	−165568.	+	165568.i	−0.171693	+	0.171693i
$983$	−592997.	−	592997.i	−0.613685	−	0.613685i	0.330219	−	0.943904i	$-0.392877\pi$
$983$	−592997.	−	592997.i	−0.613685	−	0.613685i	−0.943904	+	0.330219i	$0.892877\pi$
$984$		−	143430.i		−	0.148132i
$985$	−103250.	+	640713.i	−0.106418	+	0.660376i
$986$	−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
$990$	344754.	+	55556.4i	0.351754	+	0.0566845i
$991$	−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
$995$	195955.	+	271243.i	0.197929	+	0.273976i
$996$	−358577.			−0.361462
$997$	−103914.	+	103914.i	−0.104540	+	0.104540i	−0.757442	−	0.652902i	$-0.773551\pi$
$997$	−103914.	+	103914.i	−0.104540	+	0.104540i	0.652902	+	0.757442i	$0.273551\pi$
$998$	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	35.5.g.a.8.7	✓	24
5.2	odd	4	inner	35.5.g.a.22.7	yes	24
5.3	odd	4		175.5.g.c.57.6		24
5.4	even	2		175.5.g.c.43.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.7	✓	24	1.1	even	1	trivial
35.5.g.a.22.7	yes	24	5.2	odd	4	inner
175.5.g.c.43.6		24	5.4	even	2
175.5.g.c.57.6		24	5.3	odd	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.896879 - 0.896879i) q^{2} +(-9.60523 - 9.60523i) q^{3} +14.3912i q^{4} +(-20.2649 + 14.6401i) q^{5} -17.2295 q^{6} +(-13.0958 + 13.0958i) q^{7} +(27.2572 + 27.2572i) q^{8} +103.521i q^{9} +O(q^{10})\)	\(q+(0.896879 - 0.896879i) q^{2} +(-9.60523 - 9.60523i) q^{3} +14.3912i q^{4} +(-20.2649 + 14.6401i) q^{5} -17.2295 q^{6} +(-13.0958 + 13.0958i) q^{7} +(27.2572 + 27.2572i) q^{8} +103.521i q^{9} +(-5.04483 + 31.3056i) q^{10} -106.380 q^{11} +(138.231 - 138.231i) q^{12} +(-222.204 - 222.204i) q^{13} +23.4907i q^{14} +(335.271 + 54.0282i) q^{15} -181.367 q^{16} +(163.879 - 163.879i) q^{17} +(92.8458 + 92.8458i) q^{18} +406.567i q^{19} +(-210.689 - 291.637i) q^{20} +251.576 q^{21} +(-95.4098 + 95.4098i) q^{22} +(492.730 + 492.730i) q^{23} -523.624i q^{24} +(196.336 - 593.361i) q^{25} -398.579 q^{26} +(216.320 - 216.320i) q^{27} +(-188.465 - 188.465i) q^{28} -371.475i q^{29} +(349.154 - 252.241i) q^{30} -315.550 q^{31} +(-598.780 + 598.780i) q^{32} +(1021.80 + 1021.80i) q^{33} -293.959i q^{34} +(73.6622 - 457.109i) q^{35} -1489.79 q^{36} +(-1113.90 + 1113.90i) q^{37} +(364.641 + 364.641i) q^{38} +4268.64i q^{39} +(-951.415 - 153.318i) q^{40} +273.917 q^{41} +(225.634 - 225.634i) q^{42} +(-739.107 - 739.107i) q^{43} -1530.94i q^{44} +(-1515.56 - 2097.85i) q^{45} +883.838 q^{46} +(326.912 - 326.912i) q^{47} +(1742.07 + 1742.07i) q^{48} -343.000i q^{49} +(-356.083 - 708.263i) q^{50} -3148.19 q^{51} +(3197.78 - 3197.78i) q^{52} +(502.049 + 502.049i) q^{53} -388.025i q^{54} +(2155.78 - 1557.41i) q^{55} -713.911 q^{56} +(3905.17 - 3905.17i) q^{57} +(-333.168 - 333.168i) q^{58} +5703.66i q^{59} +(-777.532 + 4824.96i) q^{60} -974.970 q^{61} +(-283.010 + 283.010i) q^{62} +(-1355.69 - 1355.69i) q^{63} -1827.80i q^{64} +(7756.02 + 1249.87i) q^{65} +1832.87 q^{66} +(-1635.67 + 1635.67i) q^{67} +(2358.42 + 2358.42i) q^{68} -9465.58i q^{69} +(-343.906 - 476.038i) q^{70} +586.493 q^{71} +(-2821.70 + 2821.70i) q^{72} +(-7096.31 - 7096.31i) q^{73} +1998.06i q^{74} +(-7585.22 + 3813.51i) q^{75} -5850.99 q^{76} +(1393.13 - 1393.13i) q^{77} +(3828.45 + 3828.45i) q^{78} -2389.81i q^{79} +(3675.38 - 2655.22i) q^{80} +4229.60 q^{81} +(245.671 - 245.671i) q^{82} +(-1297.02 - 1297.02i) q^{83} +3620.49i q^{84} +(-921.799 + 5720.20i) q^{85} -1325.78 q^{86} +(-3568.10 + 3568.10i) q^{87} +(-2899.62 - 2899.62i) q^{88} +11496.6i q^{89} +(-3240.78 - 522.246i) q^{90} +5819.87 q^{91} +(-7090.99 + 7090.99i) q^{92} +(3030.93 + 3030.93i) q^{93} -586.400i q^{94} +(-5952.17 - 8239.06i) q^{95} +11502.8 q^{96} +(-6917.34 + 6917.34i) q^{97} +(-307.629 - 307.629i) q^{98} -11012.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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