LMFDB - Embedded newform 74.7.d.a.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,7,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	74.d (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:	$17.0240021879$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 $ x^18 + 8470x^16 + 28007049x^14 + 45282701078x^12 + 36580026955844x^10 + 13599755691108102x^8 + 2140498199687229457x^6 + 117348928221103362406x^4 + 1596692663909213634249x^2 + 657611720884512028944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.5
Root			$0.651946i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 4.00000i) q^{2} +4.65195i q^{3} +32.0000i q^{4} +(-62.1985 + 62.1985i) q^{5} +(-18.6078 + 18.6078i) q^{6} +564.672 q^{7} +(-128.000 + 128.000i) q^{8} +707.359 q^{9} +O(q^{10})$	\(q+(4.00000 + 4.00000i) q^{2} +4.65195i q^{3} +32.0000i q^{4} +(-62.1985 + 62.1985i) q^{5} +(-18.6078 + 18.6078i) q^{6} +564.672 q^{7} +(-128.000 + 128.000i) q^{8} +707.359 q^{9} -497.588 q^{10} -447.353i q^{11} -148.862 q^{12} +(-2851.44 + 2851.44i) q^{13} +(2258.69 + 2258.69i) q^{14} +(-289.344 - 289.344i) q^{15} -1024.00 q^{16} +(-4948.00 + 4948.00i) q^{17} +(2829.44 + 2829.44i) q^{18} +(-749.331 + 749.331i) q^{19} +(-1990.35 - 1990.35i) q^{20} +2626.83i q^{21} +(1789.41 - 1789.41i) q^{22} +(4599.01 - 4599.01i) q^{23} +(-595.449 - 595.449i) q^{24} +7887.69i q^{25} -22811.5 q^{26} +6681.87i q^{27} +18069.5i q^{28} +(14323.9 + 14323.9i) q^{29} -2314.75i q^{30} +(-869.772 - 869.772i) q^{31} +(-4096.00 - 4096.00i) q^{32} +2081.06 q^{33} -39584.0 q^{34} +(-35121.8 + 35121.8i) q^{35} +22635.5i q^{36} +(-23486.3 - 44878.9i) q^{37} -5994.65 q^{38} +(-13264.7 - 13264.7i) q^{39} -15922.8i q^{40} +81678.3i q^{41} +(-10507.3 + 10507.3i) q^{42} +(101901. - 101901. i) q^{43} +14315.3 q^{44} +(-43996.7 + 43996.7i) q^{45} +36792.1 q^{46} -52628.1 q^{47} -4763.59i q^{48} +201206. q^{49} +(-31550.8 + 31550.8i) q^{50} +(-23017.8 - 23017.8i) q^{51} +(-91246.1 - 91246.1i) q^{52} -25583.6 q^{53} +(-26727.5 + 26727.5i) q^{54} +(27824.7 + 27824.7i) q^{55} +(-72278.1 + 72278.1i) q^{56} +(-3485.85 - 3485.85i) q^{57} +114591. i q^{58} +(-27162.1 + 27162.1i) q^{59} +(9259.01 - 9259.01i) q^{60} +(158791. + 158791. i) q^{61} -6958.18i q^{62} +399426. q^{63} -32768.0i q^{64} -354711. i q^{65} +(8324.24 + 8324.24i) q^{66} -419546. i q^{67} +(-158336. - 158336. i) q^{68} +(21394.4 + 21394.4i) q^{69} -280974. q^{70} +470162. q^{71} +(-90542.0 + 90542.0i) q^{72} +20202.9i q^{73} +(85570.5 - 273461. i) q^{74} -36693.1 q^{75} +(-23978.6 - 23978.6i) q^{76} -252608. i q^{77} -106118. i q^{78} +(159040. - 159040. i) q^{79} +(63691.3 - 63691.3i) q^{80} +484581. q^{81} +(-326713. + 326713. i) q^{82} +115661. q^{83} -84058.4 q^{84} -615517. i q^{85} +815209. q^{86} +(-66633.8 + 66633.8i) q^{87} +(57261.1 + 57261.1i) q^{88} +(-768017. - 768017. i) q^{89} -351974. q^{90} +(-1.61013e6 + 1.61013e6i) q^{91} +(147168. + 147168. i) q^{92} +(4046.13 - 4046.13i) q^{93} +(-210512. - 210512. i) q^{94} -93214.6i q^{95} +(19054.4 - 19054.4i) q^{96} +(580932. - 580932. i) q^{97} +(804824. + 804824. i) q^{98} -316439. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) $ 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9 + 2352 * q^10 - 2048 * q^12 - 6766 * q^13 - 416 * q^14 - 2136 * q^15 - 18432 * q^16 - 9134 * q^17 - 16168 * q^18 + 7578 * q^19 + 9408 * q^20 + 8928 * q^22 - 50578 * q^23 - 8192 * q^24 - 54128 * q^26 - 42950 * q^29 - 17358 * q^31 - 73728 * q^32 - 11056 * q^33 - 73072 * q^34 + 62152 * q^35 - 238242 * q^37 + 60624 * q^38 + 31572 * q^39 + 229024 * q^42 - 65470 * q^43 + 71424 * q^44 - 482358 * q^45 - 404624 * q^46 + 232192 * q^47 + 791686 * q^49 + 93752 * q^50 - 386848 * q^51 - 216512 * q^52 + 49972 * q^53 - 144560 * q^54 + 160168 * q^55 + 13312 * q^56 + 488476 * q^57 - 181570 * q^59 + 68352 * q^60 + 508802 * q^61 + 404788 * q^63 - 44224 * q^66 - 292288 * q^68 + 604532 * q^69 + 497216 * q^70 - 202632 * q^71 + 517376 * q^72 - 1191224 * q^74 + 2476628 * q^75 + 242496 * q^76 + 1752858 * q^79 - 301056 * q^80 + 2760658 * q^81 - 145808 * q^82 + 2371616 * q^83 + 1832192 * q^84 - 523760 * q^86 - 4188080 * q^87 + 285696 * q^88 + 1148346 * q^89 - 3858864 * q^90 + 433120 * q^91 - 1618496 * q^92 + 1589664 * q^93 + 928768 * q^94 + 262144 * q^96 - 1670270 * q^97 + 3166744 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	4.00000	+	4.00000i	0.500000	+	0.500000i
$2$	4.00000	+	4.00000i	0.500000	+	0.500000i
$3$			4.65195i			0.172294i	0.996282	+	0.0861471i	$0.0274555\pi$
$3$			4.65195i			0.172294i	−0.996282	+	0.0861471i	$0.972544\pi$
$4$			32.0000i			0.500000i
$5$	−62.1985	+	62.1985i	−0.497588	+	0.497588i	−0.910686	−	0.413098i	$-0.864447\pi$
$5$	−62.1985	+	62.1985i	−0.497588	+	0.497588i	0.413098	+	0.910686i	$0.364447\pi$
$6$	−18.6078	+	18.6078i	−0.0861471	+	0.0861471i
$7$	564.672			1.64628			0.823138	−	0.567842i	$-0.192221\pi$
$7$	564.672			1.64628			0.823138	+	0.567842i	$0.192221\pi$
$8$	−128.000	+	128.000i	−0.250000	+	0.250000i
$9$	707.359			0.970315
$10$	−497.588			−0.497588
$11$		−	447.353i		−	0.336103i	−0.985778	−	0.168051i	$-0.946253\pi$
$11$		−	447.353i		−	0.336103i	0.985778	−	0.168051i	$-0.0537474\pi$
$12$	−148.862			−0.0861471
$13$	−2851.44	+	2851.44i	−1.29788	+	1.29788i	−0.368088	+	0.929791i	$0.619988\pi$
$13$	−2851.44	+	2851.44i	−1.29788	+	1.29788i	−0.929791	+	0.368088i	$0.880012\pi$
$14$	2258.69	+	2258.69i	0.823138	+	0.823138i
$15$	−289.344	−	289.344i	−0.0857316	−	0.0857316i
$16$	−1024.00			−0.250000
$17$	−4948.00	+	4948.00i	−1.00712	+	1.00712i	−0.00715051	+	0.999974i	$0.502276\pi$
$17$	−4948.00	+	4948.00i	−1.00712	+	1.00712i	−0.999974	+	0.00715051i	$0.997724\pi$
$18$	2829.44	+	2829.44i	0.485157	+	0.485157i
$19$	−749.331	+	749.331i	−0.109248	+	0.109248i	−0.759618	−	0.650370i	$-0.774614\pi$
$19$	−749.331	+	749.331i	−0.109248	+	0.109248i	0.650370	+	0.759618i	$0.274614\pi$
$20$	−1990.35	−	1990.35i	−0.248794	−	0.248794i
$21$			2626.83i			0.283644i
$22$	1789.41	−	1789.41i	0.168051	−	0.168051i
$23$	4599.01	−	4599.01i	0.377991	−	0.377991i	−0.492386	−	0.870377i	$-0.663875\pi$
$23$	4599.01	−	4599.01i	0.377991	−	0.377991i	0.870377	+	0.492386i	$0.163875\pi$
$24$	−595.449	−	595.449i	−0.0430736	−	0.0430736i
$25$			7887.69i			0.504812i
$26$	−22811.5			−1.29788
$27$			6681.87i			0.339474i
$28$			18069.5i			0.823138i
$29$	14323.9	+	14323.9i	0.587308	+	0.587308i	0.936902	−	0.349593i	$-0.113680\pi$
$29$	14323.9	+	14323.9i	0.587308	+	0.587308i	−0.349593	+	0.936902i	$0.613680\pi$
$30$		−	2314.75i		−	0.0857316i
$31$	−869.772	−	869.772i	−0.0291958	−	0.0291958i	0.692358	−	0.721554i	$-0.256572\pi$
$31$	−869.772	−	869.772i	−0.0291958	−	0.0291958i	−0.721554	+	0.692358i	$0.756572\pi$
$32$	−4096.00	−	4096.00i	−0.125000	−	0.125000i
$33$	2081.06			0.0579086
$34$	−39584.0			−1.00712
$35$	−35121.8	+	35121.8i	−0.819167	+	0.819167i
$36$			22635.5i			0.485157i
$37$	−23486.3	−	44878.9i	−0.463671	−	0.886008i
$37$	−23486.3	−	44878.9i	−0.463671	−	0.886008i
$38$	−5994.65			−0.109248
$39$	−13264.7	−	13264.7i	−0.223617	−	0.223617i
$40$		−	15922.8i		−	0.248794i
$41$			81678.3i			1.18510i	0.805533	+	0.592550i	$0.201879\pi$
$41$			81678.3i			1.18510i	−0.805533	+	0.592550i	$0.798121\pi$
$42$	−10507.3	+	10507.3i	−0.141822	+	0.141822i
$43$	101901.	−	101901.i	1.28166	−	1.28166i	0.341941	−	0.939721i	$-0.388916\pi$
$43$	101901.	−	101901.i	1.28166	−	1.28166i	0.939721	−	0.341941i	$-0.111084\pi$
$44$	14315.3			0.168051
$45$	−43996.7	+	43996.7i	−0.482817	+	0.482817i
$46$	36792.1			0.377991
$47$	−52628.1			−0.506902			−0.253451	−	0.967348i	$-0.581566\pi$
$47$	−52628.1			−0.506902			−0.253451	+	0.967348i	$0.581566\pi$
$48$		−	4763.59i		−	0.0430736i
$49$	201206.			1.71022
$50$	−31550.8	+	31550.8i	−0.252406	+	0.252406i
$51$	−23017.8	−	23017.8i	−0.173522	−	0.173522i
$52$	−91246.1	−	91246.1i	−0.648940	−	0.648940i
$53$	−25583.6			−0.171844			−0.0859219	−	0.996302i	$-0.527384\pi$
$53$	−25583.6			−0.171844			−0.0859219	+	0.996302i	$0.527384\pi$
$54$	−26727.5	+	26727.5i	−0.169737	+	0.169737i
$55$	27824.7	+	27824.7i	0.167241	+	0.167241i
$56$	−72278.1	+	72278.1i	−0.411569	+	0.411569i
$57$	−3485.85	−	3485.85i	−0.0188228	−	0.0188228i
$58$			114591.i			0.587308i
$59$	−27162.1	+	27162.1i	−0.132254	+	0.132254i	−0.770135	−	0.637881i	$-0.779811\pi$
$59$	−27162.1	+	27162.1i	−0.132254	+	0.132254i	0.637881	+	0.770135i	$0.279811\pi$
$60$	9259.01	−	9259.01i	0.0428658	−	0.0428658i
$61$	158791.	+	158791.i	0.699580	+	0.699580i	0.964320	−	0.264740i	$-0.0852861\pi$
$61$	158791.	+	158791.i	0.699580	+	0.699580i	−0.264740	+	0.964320i	$0.585286\pi$
$62$		−	6958.18i		−	0.0291958i
$63$	399426.			1.59741
$64$		−	32768.0i		−	0.125000i
$65$		−	354711.i		−	1.29162i
$66$	8324.24	+	8324.24i	0.0289543	+	0.0289543i
$67$		−	419546.i		−	1.39494i	−0.716614	−	0.697470i	$-0.754309\pi$
$67$		−	419546.i		−	1.39494i	0.716614	−	0.697470i	$-0.245691\pi$
$68$	−158336.	−	158336.i	−0.503562	−	0.503562i
$69$	21394.4	+	21394.4i	0.0651256	+	0.0651256i
$70$	−280974.			−0.819167
$71$	470162.			1.31363			0.656814	−	0.754052i	$-0.271904\pi$
$71$	470162.			1.31363			0.656814	+	0.754052i	$0.271904\pi$
$72$	−90542.0	+	90542.0i	−0.242579	+	0.242579i
$73$			20202.9i			0.0519331i	0.999663	+	0.0259666i	$0.00826634\pi$
$73$			20202.9i			0.0519331i	−0.999663	+	0.0259666i	$0.991734\pi$
$74$	85570.5	−	273461.i	0.211168	−	0.674839i
$75$	−36693.1			−0.0869763
$76$	−23978.6	−	23978.6i	−0.0546240	−	0.0546240i
$77$		−	252608.i		−	0.553318i
$78$		−	106118.i		−	0.223617i
$79$	159040.	−	159040.i	0.322571	−	0.322571i	−0.527182	−	0.849753i	$-0.676751\pi$
$79$	159040.	−	159040.i	0.322571	−	0.322571i	0.849753	+	0.527182i	$0.176751\pi$
$80$	63691.3	−	63691.3i	0.124397	−	0.124397i
$81$	484581.			0.911825
$82$	−326713.	+	326713.i	−0.592550	+	0.592550i
$83$	115661.			0.202279			0.101140	−	0.994872i	$-0.467751\pi$
$83$	115661.			0.202279			0.101140	+	0.994872i	$0.467751\pi$
$84$	−84058.4			−0.141822
$85$		−	615517.i		−	1.00227i
$86$	815209.			1.28166
$87$	−66633.8	+	66633.8i	−0.101190	+	0.101190i
$88$	57261.1	+	57261.1i	0.0840257	+	0.0840257i
$89$	−768017.	−	768017.i	−1.08943	−	1.08943i	−0.995587	−	0.0938470i	$-0.970084\pi$
$89$	−768017.	−	768017.i	−1.08943	−	1.08943i	−0.0938470	−	0.995587i	$-0.529916\pi$
$90$	−351974.			−0.482817
$91$	−1.61013e6	+	1.61013e6i	−2.13667	+	2.13667i
$92$	147168.	+	147168.i	0.188995	+	0.188995i
$93$	4046.13	−	4046.13i	0.00503027	−	0.00503027i
$94$	−210512.	−	210512.i	−0.253451	−	0.253451i
$95$		−	93214.6i		−	0.108721i
$96$	19054.4	−	19054.4i	0.0215368	−	0.0215368i
$97$	580932.	−	580932.i	0.636517	−	0.636517i	−0.313177	−	0.949695i	$-0.601393\pi$
$97$	580932.	−	580932.i	0.636517	−	0.636517i	0.949695	+	0.313177i	$0.101393\pi$
$98$	804824.	+	804824.i	0.855111	+	0.855111i
$99$		−	316439.i		−	0.326125i
$100$	−252406.			−0.252406
$101$		−	114954.i		−	0.111573i	−0.998443	−	0.0557865i	$-0.982233\pi$
$101$		−	114954.i		−	0.111573i	0.998443	−	0.0557865i	$-0.0177666\pi$
$102$		−	184143.i		−	0.173522i
$103$	1.47116e6	+	1.47116e6i	1.34632	+	1.34632i	0.889619	+	0.456703i	$0.150970\pi$
$103$	1.47116e6	+	1.47116e6i	1.34632	+	1.34632i	0.456703	+	0.889619i	$0.349030\pi$
$104$		−	729969.i		−	0.648940i
$105$	−163385.	−	163385.i	−0.141138	−	0.141138i
$106$	−102334.	−	102334.i	−0.0859219	−	0.0859219i
$107$	−636333.			−0.519437			−0.259719	−	0.965684i	$-0.583630\pi$
$107$	−636333.			−0.519437			−0.259719	+	0.965684i	$0.583630\pi$
$108$	−213820.			−0.169737
$109$	−707487.	+	707487.i	−0.546310	+	0.546310i	−0.925371	−	0.379062i	$-0.876247\pi$
$109$	−707487.	+	707487.i	−0.546310	+	0.546310i	0.379062	+	0.925371i	$0.376247\pi$
$110$			222597.i			0.167241i
$111$	208774.	−	109257.i	0.152654	−	0.0798878i
$112$	−578225.			−0.411569
$113$	960416.	+	960416.i	0.665617	+	0.665617i	0.956698	−	0.291082i	$-0.0940151\pi$
$113$	960416.	+	960416.i	0.665617	+	0.665617i	−0.291082	+	0.956698i	$0.594015\pi$
$114$		−	27886.8i		−	0.0188228i
$115$			572103.i			0.376167i
$116$	−458363.	+	458363.i	−0.293654	+	0.293654i
$117$	−2.01699e6	+	2.01699e6i	−1.25935	+	1.25935i
$118$	−217297.			−0.132254
$119$	−2.79400e6	+	2.79400e6i	−1.65800	+	1.65800i
$120$	74072.1			0.0428658
$121$	1.57144e6			0.887035
$122$			1.27033e6i			0.699580i
$123$	−379963.			−0.204186
$124$	27832.7	−	27832.7i	0.0145979	−	0.0145979i
$125$	−1.46245e6	−	1.46245e6i	−0.748777	−	0.748777i
$126$	1.59771e6	+	1.59771e6i	0.798703	+	0.798703i
$127$	1.63807e6			0.799688			0.399844	−	0.916583i	$-0.369064\pi$
$127$	1.63807e6			0.799688			0.399844	+	0.916583i	$0.369064\pi$
$128$	131072.	−	131072.i	0.0625000	−	0.0625000i
$129$	474039.	+	474039.i	0.220823	+	0.220823i
$130$	1.41884e6	−	1.41884e6i	0.645809	−	0.645809i
$131$	−2.46727e6	−	2.46727e6i	−1.09750	−	1.09750i	−0.994703	−	0.102793i	$-0.967222\pi$
$131$	−2.46727e6	−	2.46727e6i	−1.09750	−	1.09750i	−0.102793	−	0.994703i	$-0.532778\pi$
$132$			66593.9i			0.0289543i
$133$	−423127.	+	423127.i	−0.179852	+	0.179852i
$134$	1.67818e6	−	1.67818e6i	0.697470	−	0.697470i
$135$	−415602.	−	415602.i	−0.168918	−	0.168918i
$136$		−	1.26669e6i		−	0.503562i
$137$	1.85122e6			0.719941			0.359970	−	0.932964i	$-0.382787\pi$
$137$	1.85122e6			0.719941			0.359970	+	0.932964i	$0.382787\pi$
$138$			171155.i			0.0651256i
$139$		−	147469.i		−	0.0549106i	−0.999623	−	0.0274553i	$-0.991260\pi$
$139$		−	147469.i		−	0.0549106i	0.999623	−	0.0274553i	$-0.00874040\pi$
$140$	−1.12390e6	−	1.12390e6i	−0.409583	−	0.409583i
$141$		−	244823.i		−	0.0873363i
$142$	1.88065e6	+	1.88065e6i	0.656814	+	0.656814i
$143$	1.27560e6	+	1.27560e6i	0.436221	+	0.436221i
$144$	−724336.			−0.242579
$145$	−1.78185e6			−0.584475
$146$	−80811.5	+	80811.5i	−0.0259666	+	0.0259666i
$147$			935999.i			0.294662i
$148$	1.43613e6	−	751562.i	0.443004	−	0.231835i
$149$	−4.05100e6			−1.22462			−0.612312	−	0.790616i	$-0.709761\pi$
$149$	−4.05100e6			−1.22462			−0.612312	+	0.790616i	$0.709761\pi$
$150$	−146772.	−	146772.i	−0.0434881	−	0.0434881i
$151$		−	4.50298e6i		−	1.30788i	−0.756545	−	0.653941i	$-0.773114\pi$
$151$		−	4.50298e6i		−	1.30788i	0.756545	−	0.653941i	$-0.226886\pi$
$152$		−	191829.i		−	0.0546240i
$153$	−3.50002e6	+	3.50002e6i	−0.977228	+	0.977228i
$154$	1.01043e6	−	1.01043e6i	0.276659	−	0.276659i
$155$	108197.			0.0290550
$156$	424472.	−	424472.i	0.111809	−	0.111809i
$157$	1.70734e6			0.441185			0.220592	−	0.975366i	$-0.429201\pi$
$157$	1.70734e6			0.441185			0.220592	+	0.975366i	$0.429201\pi$
$158$	1.27232e6			0.322571
$159$		−	119013.i		−	0.0296077i
$160$	509530.			0.124397
$161$	2.59694e6	−	2.59694e6i	0.622277	−	0.622277i
$162$	1.93833e6	+	1.93833e6i	0.455913	+	0.455913i
$163$	−1.88528e6	−	1.88528e6i	−0.435324	−	0.435324i	0.455111	−	0.890435i	$-0.349600\pi$
$163$	−1.88528e6	−	1.88528e6i	−0.435324	−	0.435324i	−0.890435	+	0.455111i	$0.849600\pi$
$164$	−2.61371e6			−0.592550
$165$	−129439.	+	129439.i	−0.0288146	+	0.0288146i
$166$	462642.	+	462642.i	0.101140	+	0.101140i
$167$	5.71148e6	−	5.71148e6i	1.22631	−	1.22631i	0.260956	−	0.965351i	$-0.415962\pi$
$167$	5.71148e6	−	5.71148e6i	1.22631	−	1.22631i	0.965351	−	0.260956i	$-0.0840377\pi$
$168$	−336234.	−	336234.i	−0.0709110	−	0.0709110i
$169$		−	1.14346e7i		−	2.36898i
$170$	2.46207e6	−	2.46207e6i	0.501133	−	0.501133i
$171$	−530047.	+	530047.i	−0.106005	+	0.106005i
$172$	3.26084e6	+	3.26084e6i	0.640831	+	0.640831i
$173$		−	8.07343e6i		−	1.55926i	−0.626237	−	0.779632i	$-0.715406\pi$
$173$		−	8.07343e6i		−	1.55926i	0.626237	−	0.779632i	$-0.284594\pi$
$174$	−533070.			−0.101190
$175$			4.45396e6i			0.831060i
$176$			458089.i			0.0840257i
$177$	−126357.	−	126357.i	−0.0227866	−	0.0227866i
$178$		−	6.14414e6i		−	1.08943i
$179$	7.03144e6	+	7.03144e6i	1.22599	+	1.22599i	0.965470	+	0.260516i	$0.0838927\pi$
$179$	7.03144e6	+	7.03144e6i	1.22599	+	1.22599i	0.260516	+	0.965470i	$0.416107\pi$
$180$	−1.40789e6	−	1.40789e6i	−0.241409	−	0.241409i
$181$	2.49584e6			0.420902			0.210451	−	0.977604i	$-0.432507\pi$
$181$	2.49584e6			0.420902			0.210451	+	0.977604i	$0.432507\pi$
$182$	−1.28810e7			−2.13667
$183$	−738689.	+	738689.i	−0.120534	+	0.120534i
$184$			1.17735e6i			0.188995i
$185$	4.25222e6	+	1.33059e6i	0.671584	+	0.210150i
$186$	32369.1			0.00503027
$187$	2.21350e6	+	2.21350e6i	0.338497	+	0.338497i
$188$		−	1.68410e6i		−	0.253451i
$189$			3.77307e6i			0.558868i
$190$	372858.	−	372858.i	0.0543605	−	0.0543605i
$191$	−8.88871e6	+	8.88871e6i	−1.27567	+	1.27567i	−0.332604	+	0.943067i	$0.607927\pi$
$191$	−8.88871e6	+	8.88871e6i	−1.27567	+	1.27567i	−0.943067	+	0.332604i	$0.892073\pi$
$192$	152435.			0.0215368
$193$	1.80279e6	−	1.80279e6i	0.250769	−	0.250769i	−0.570517	−	0.821286i	$-0.693257\pi$
$193$	1.80279e6	−	1.80279e6i	0.250769	−	0.250769i	0.821286	+	0.570517i	$0.193257\pi$
$194$	4.64746e6			0.636517
$195$	1.65009e6			0.222538
$196$			6.43859e6i			0.855111i
$197$	−1.27623e7			−1.66929			−0.834643	−	0.550791i	$-0.814326\pi$
$197$	−1.27623e7			−1.66929			−0.834643	+	0.550791i	$0.814326\pi$
$198$	1.26576e6	−	1.26576e6i	0.163063	−	0.163063i
$199$	1.61419e6	+	1.61419e6i	0.204831	+	0.204831i	0.802066	−	0.597235i	$-0.203734\pi$
$199$	1.61419e6	+	1.61419e6i	0.204831	+	0.204831i	−0.597235	+	0.802066i	$0.703734\pi$
$200$	−1.00962e6	−	1.00962e6i	−0.126203	−	0.126203i
$201$	1.95171e6			0.240340
$202$	459815.	−	459815.i	0.0557865	−	0.0557865i
$203$	8.08829e6	+	8.08829e6i	0.966871	+	0.966871i
$204$	736571.	−	736571.i	0.0867609	−	0.0867609i
$205$	−5.08027e6	−	5.08027e6i	−0.589692	−	0.589692i
$206$			1.17693e7i			1.34632i
$207$	3.25315e6	−	3.25315e6i	0.366770	−	0.366770i
$208$	2.91987e6	−	2.91987e6i	0.324470	−	0.324470i
$209$	335215.	+	335215.i	0.0367185	+	0.0367185i
$210$		−	1.30708e6i		−	0.141138i
$211$	5.58652e6			0.594695			0.297347	−	0.954769i	$-0.403898\pi$
$211$	5.58652e6			0.594695			0.297347	+	0.954769i	$0.403898\pi$
$212$		−	818674.i		−	0.0859219i
$213$			2.18717e6i			0.226331i
$214$	−2.54533e6	−	2.54533e6i	−0.259719	−	0.259719i
$215$			1.26762e7i			1.27548i
$216$	−855279.	−	855279.i	−0.0848685	−	0.0848685i
$217$	−491136.	−	491136.i	−0.0480643	−	0.0480643i
$218$	−5.65989e6			−0.546310
$219$	−93982.7			−0.00894778
$220$	−890389.	+	890389.i	−0.0836203	+	0.0836203i
$221$		−	2.82179e7i		−	2.61425i
$222$	1.27213e6	+	398069.i	0.116271	+	0.0363831i
$223$	2.11007e6			0.190276			0.0951378	−	0.995464i	$-0.469671\pi$
$223$	2.11007e6			0.190276			0.0951378	+	0.995464i	$0.469671\pi$
$224$	−2.31290e6	−	2.31290e6i	−0.205784	−	0.205784i
$225$			5.57943e6i			0.489827i
$226$			7.68333e6i			0.665617i
$227$	−9.94008e6	+	9.94008e6i	−0.849791	+	0.849791i	−0.990107	−	0.140316i	$-0.955188\pi$
$227$	−9.94008e6	+	9.94008e6i	−0.849791	+	0.849791i	0.140316	+	0.990107i	$0.455188\pi$
$228$	111547.	−	111547.i	0.00941140	−	0.00941140i
$229$	1.89642e7			1.57917			0.789583	−	0.613644i	$-0.210297\pi$
$229$	1.89642e7			1.57917			0.789583	+	0.613644i	$0.210297\pi$
$230$	−2.28841e6	+	2.28841e6i	−0.188084	+	0.188084i
$231$	1.17512e6			0.0953334
$232$	−3.66691e6			−0.293654
$233$		−	1.40728e7i		−	1.11254i	−0.831003	−	0.556268i	$-0.812233\pi$
$233$		−	1.40728e7i		−	1.11254i	0.831003	−	0.556268i	$-0.187767\pi$
$234$	−1.61359e7			−1.25935
$235$	3.27339e6	−	3.27339e6i	0.252228	−	0.252228i
$236$	−869188.	−	869188.i	−0.0661269	−	0.0661269i
$237$	739846.	+	739846.i	0.0555771	+	0.0555771i
$238$	−2.23520e7			−1.65800
$239$	−6.59523e6	+	6.59523e6i	−0.483099	+	0.483099i	−0.906120	−	0.423021i	$-0.860970\pi$
$239$	−6.59523e6	+	6.59523e6i	−0.483099	+	0.483099i	0.423021	+	0.906120i	$0.360970\pi$
$240$	296288.	+	296288.i	0.0214329	+	0.0214329i
$241$	−1.24712e7	+	1.24712e7i	−0.890955	+	0.890955i	−0.994613	−	0.103658i	$-0.966945\pi$
$241$	−1.24712e7	+	1.24712e7i	−0.890955	+	0.890955i	0.103658	+	0.994613i	$0.466945\pi$
$242$	6.28575e6	+	6.28575e6i	0.443518	+	0.443518i
$243$			7.12533e6i			0.496576i
$244$	−5.08132e6	+	5.08132e6i	−0.349790	+	0.349790i
$245$	−1.25147e7	+	1.25147e7i	−0.850986	+	0.850986i
$246$	−1.51985e6	−	1.51985e6i	−0.102093	−	0.102093i
$247$		−	4.27335e6i		−	0.283581i
$248$	222662.			0.0145979
$249$			538046.i			0.0348515i
$250$		−	1.16996e7i		−	0.748777i
$251$	−3.07516e6	−	3.07516e6i	−0.194467	−	0.194467i	0.603156	−	0.797623i	$-0.293910\pi$
$251$	−3.07516e6	−	3.07516e6i	−0.194467	−	0.194467i	−0.797623	+	0.603156i	$0.793910\pi$
$252$			1.27816e7i			0.798703i
$253$	−2.05738e6	−	2.05738e6i	−0.127044	−	0.127044i
$254$	6.55227e6	+	6.55227e6i	0.399844	+	0.399844i
$255$	2.86335e6			0.172685
$256$	1.04858e6			0.0625000
$257$	4.61967e6	−	4.61967e6i	0.272152	−	0.272152i	−0.557814	−	0.829966i	$-0.688360\pi$
$257$	4.61967e6	−	4.61967e6i	0.272152	−	0.272152i	0.829966	+	0.557814i	$0.188360\pi$
$258$			3.79231e6i			0.220823i
$259$	−1.32621e7	−	2.53419e7i	−0.763330	−	1.45861i
$260$	1.13507e7			0.645809
$261$	1.01321e7	+	1.01321e7i	0.569874	+	0.569874i
$262$		−	1.97382e7i		−	1.09750i
$263$			1.06190e7i			0.583736i	0.956459	+	0.291868i	$0.0942768\pi$
$263$			1.06190e7i			0.583736i	−0.956459	+	0.291868i	$0.905723\pi$
$264$	−266376.	+	266376.i	−0.0144771	+	0.0144771i
$265$	1.59126e6	−	1.59126e6i	0.0855074	−	0.0855074i
$266$	−3.38501e6			−0.179852
$267$	3.57277e6	−	3.57277e6i	0.187703	−	0.187703i
$268$	1.34255e7			0.697470
$269$	1.77872e7			0.913798			0.456899	−	0.889519i	$-0.348960\pi$
$269$	1.77872e7			0.913798			0.456899	+	0.889519i	$0.348960\pi$
$270$		−	3.32482e6i		−	0.168918i
$271$	3.14639e7			1.58090			0.790451	−	0.612526i	$-0.209846\pi$
$271$	3.14639e7			1.58090			0.790451	+	0.612526i	$0.209846\pi$
$272$	5.06676e6	−	5.06676e6i	0.251781	−	0.251781i
$273$	−7.49024e6	−	7.49024e6i	−0.368135	−	0.368135i
$274$	7.40489e6	+	7.40489e6i	0.359970	+	0.359970i
$275$	3.52858e6			0.169669
$276$	−684619.	+	684619.i	−0.0325628	+	0.0325628i
$277$	−1.77649e6	−	1.77649e6i	−0.0835841	−	0.0835841i	0.664079	−	0.747663i	$-0.268824\pi$
$277$	−1.77649e6	−	1.77649e6i	−0.0835841	−	0.0835841i	−0.747663	+	0.664079i	$0.768824\pi$
$278$	589876.	−	589876.i	0.0274553	−	0.0274553i
$279$	−615242.	−	615242.i	−0.0283291	−	0.0283291i
$280$		−	8.99118e6i		−	0.409583i
$281$	−2.20419e7	+	2.20419e7i	−0.993411	+	0.993411i	−0.999978	−	0.00656705i	$-0.997910\pi$
$281$	−2.20419e7	+	2.20419e7i	−0.993411	+	0.993411i	0.00656705	+	0.999978i	$0.497910\pi$
$282$	979291.	−	979291.i	0.0436681	−	0.0436681i
$283$	−1.19827e7	−	1.19827e7i	−0.528682	−	0.528682i	0.391497	−	0.920179i	$-0.371957\pi$
$283$	−1.19827e7	−	1.19827e7i	−0.528682	−	0.528682i	−0.920179	+	0.391497i	$0.871957\pi$
$284$			1.50452e7i			0.656814i
$285$	433629.			0.0187320
$286$			1.02048e7i			0.436221i
$287$			4.61215e7i			1.95100i
$288$	−2.89734e6	−	2.89734e6i	−0.121289	−	0.121289i
$289$		−	2.48279e7i		−	1.02860i
$290$	−7.12738e6	−	7.12738e6i	−0.292238	−	0.292238i
$291$	2.70247e6	+	2.70247e6i	0.109668	+	0.109668i
$292$	−646492.			−0.0259666
$293$	1.05846e7			0.420797			0.210399	−	0.977616i	$-0.432524\pi$
$293$	1.05846e7			0.420797			0.210399	+	0.977616i	$0.432524\pi$
$294$	−3.74400e6	+	3.74400e6i	−0.147331	+	0.147331i
$295$		−	3.37889e6i		−	0.131616i
$296$	8.75075e6	+	2.73825e6i	0.337420	+	0.105584i
$297$	2.98915e6			0.114098
$298$	−1.62040e7	−	1.62040e7i	−0.612312	−	0.612312i
$299$			2.62276e7i			0.981172i
$300$		−	1.17418e6i		−	0.0434881i
$301$	5.75408e7	−	5.75408e7i	2.10997	−	2.10997i
$302$	1.80119e7	−	1.80119e7i	0.653941	−	0.653941i
$303$	534758.			0.0192234
$304$	767315.	−	767315.i	0.0273120	−	0.0273120i
$305$	−1.97532e7			−0.696205
$306$	−2.80001e7			−0.977228
$307$		−	1.92323e7i		−	0.664684i	−0.943159	−	0.332342i	$-0.892161\pi$
$307$		−	1.92323e7i		−	0.664684i	0.943159	−	0.332342i	$-0.107839\pi$
$308$	8.08345e6			0.276659
$309$	−6.84377e6	+	6.84377e6i	−0.231964	+	0.231964i
$310$	432788.	+	432788.i	0.0145275	+	0.0145275i
$311$	−1.52351e7	−	1.52351e7i	−0.506483	−	0.506483i	0.406962	−	0.913445i	$-0.366588\pi$
$311$	−1.52351e7	−	1.52351e7i	−0.506483	−	0.506483i	−0.913445	+	0.406962i	$0.866588\pi$
$312$	3.39577e6			0.111809
$313$	1.55419e7	−	1.55419e7i	0.506840	−	0.506840i	−0.406715	−	0.913555i	$-0.633326\pi$
$313$	1.55419e7	−	1.55419e7i	0.506840	−	0.506840i	0.913555	+	0.406715i	$0.133326\pi$
$314$	6.82935e6	+	6.82935e6i	0.220592	+	0.220592i
$315$	−2.48437e7	+	2.48437e7i	−0.794850	+	0.794850i
$316$	5.08928e6	+	5.08928e6i	0.161285	+	0.161285i
$317$			4.24209e6i			0.133169i	0.997781	+	0.0665843i	$0.0212101\pi$
$317$			4.24209e6i			0.133169i	−0.997781	+	0.0665843i	$0.978790\pi$
$318$	476054.	−	476054.i	0.0148038	−	0.0148038i
$319$	6.40782e6	−	6.40782e6i	0.197396	−	0.197396i
$320$	2.03812e6	+	2.03812e6i	0.0621985	+	0.0621985i
$321$		−	2.96019e6i		−	0.0894961i
$322$	2.07755e7			0.622277
$323$		−	7.41539e6i		−	0.220053i
$324$			1.55066e7i			0.455913i
$325$	−2.24913e7	−	2.24913e7i	−0.655185	−	0.655185i
$326$		−	1.50822e7i		−	0.435324i
$327$	−3.29119e6	−	3.29119e6i	−0.0941260	−	0.0941260i
$328$	−1.04548e7	−	1.04548e7i	−0.296275	−	0.296275i
$329$	−2.97176e7			−0.834500
$330$	−1.03551e6			−0.0288146
$331$	−2.14024e7	+	2.14024e7i	−0.590171	+	0.590171i	−0.937678	−	0.347507i	$-0.887028\pi$
$331$	−2.14024e7	+	2.14024e7i	−0.590171	+	0.590171i	0.347507	+	0.937678i	$0.387028\pi$
$332$			3.70114e6i			0.101140i
$333$	−1.66133e7	−	3.17455e7i	−0.449907	−	0.859706i
$334$	4.56918e7			1.22631
$335$	2.60951e7	+	2.60951e7i	0.694105	+	0.694105i
$336$		−	2.68987e6i		−	0.0709110i
$337$		−	5.02488e7i		−	1.31291i	−0.754364	−	0.656456i	$-0.772055\pi$
$337$		−	5.02488e7i		−	1.31291i	0.754364	−	0.656456i	$-0.227945\pi$
$338$	4.57385e7	−	4.57385e7i	1.18449	−	1.18449i
$339$	−4.46780e6	+	4.46780e6i	−0.114682	+	0.114682i
$340$	1.96965e7			0.501133
$341$	−389095.	+	389095.i	−0.00981279	+	0.00981279i
$342$	−4.24037e6			−0.106005
$343$	4.71823e7			1.16922
$344$			2.60867e7i			0.640831i
$345$	−2.66139e6			−0.0648115
$346$	3.22937e7	−	3.22937e7i	0.779632	−	0.779632i
$347$	2.40332e7	+	2.40332e7i	0.575206	+	0.575206i	0.933579	−	0.358373i	$-0.116668\pi$
$347$	2.40332e7	+	2.40332e7i	0.575206	+	0.575206i	−0.358373	+	0.933579i	$0.616668\pi$
$348$	−2.13228e6	−	2.13228e6i	−0.0505949	−	0.0505949i
$349$	−2.15497e7			−0.506950			−0.253475	−	0.967342i	$-0.581574\pi$
$349$	−2.15497e7			−0.506950			−0.253475	+	0.967342i	$0.581574\pi$
$350$	−1.78158e7	+	1.78158e7i	−0.415530	+	0.415530i
$351$	−1.90529e7	−	1.90529e7i	−0.440596	−	0.440596i
$352$	−1.83236e6	+	1.83236e6i	−0.0420128	+	0.0420128i
$353$	−5.13793e6	−	5.13793e6i	−0.116806	−	0.116806i	0.646288	−	0.763094i	$-0.276321\pi$
$353$	−5.13793e6	−	5.13793e6i	−0.116806	−	0.116806i	−0.763094	+	0.646288i	$0.776321\pi$
$354$		−	1.01085e6i		−	0.0227866i
$355$	−2.92434e7	+	2.92434e7i	−0.653646	+	0.653646i
$356$	2.45765e7	−	2.45765e7i	0.544717	−	0.544717i
$357$	−1.29975e7	−	1.29975e7i	−0.285665	−	0.285665i
$358$			5.62515e7i			1.22599i
$359$	−4.76138e7			−1.02908			−0.514540	−	0.857466i	$-0.672037\pi$
$359$	−4.76138e7			−1.02908			−0.514540	+	0.857466i	$0.672037\pi$
$360$		−	1.12632e7i		−	0.241409i
$361$			4.59229e7i			0.976130i
$362$	9.98335e6	+	9.98335e6i	0.210451	+	0.210451i
$363$			7.31024e6i			0.152831i
$364$	−5.15242e7	−	5.15242e7i	−1.06833	−	1.06833i
$365$	−1.25659e6	−	1.25659e6i	−0.0258413	−	0.0258413i
$366$	−5.90951e6			−0.120534
$367$	3.34092e7			0.675877			0.337939	−	0.941168i	$-0.390270\pi$
$367$	3.34092e7			0.675877			0.337939	+	0.941168i	$0.390270\pi$
$368$	−4.70939e6	+	4.70939e6i	−0.0944977	+	0.0944977i
$369$			5.77759e7i			1.14992i
$370$	1.16865e7	+	2.23312e7i	0.230717	+	0.440867i
$371$	−1.44463e7			−0.282902
$372$	129476.	+	129476.i	0.00251514	+	0.00251514i
$373$			6.45549e7i			1.24395i	0.783037	+	0.621975i	$0.213669\pi$
$373$			6.45549e7i			1.24395i	−0.783037	+	0.621975i	$0.786331\pi$
$374$			1.77080e7i			0.338497i
$375$	6.80326e6	−	6.80326e6i	0.129010	−	0.129010i
$376$	6.73639e6	−	6.73639e6i	0.126725	−	0.126725i
$377$	−8.16872e7			−1.52451
$378$	−1.50923e7	+	1.50923e7i	−0.279434	+	0.279434i
$379$	−5.21159e7			−0.957310			−0.478655	−	0.878003i	$-0.658875\pi$
$379$	−5.21159e7			−0.957310			−0.478655	+	0.878003i	$0.658875\pi$
$380$	2.98287e6			0.0543605
$381$			7.62020e6i			0.137782i
$382$	−7.11097e7			−1.27567
$383$	1.81165e7	−	1.81165e7i	0.322462	−	0.322462i	−0.527249	−	0.849711i	$-0.676777\pi$
$383$	1.81165e7	−	1.81165e7i	0.322462	−	0.322462i	0.849711	+	0.527249i	$0.176777\pi$
$384$	609740.	+	609740.i	0.0107684	+	0.0107684i
$385$	1.57118e7	+	1.57118e7i	0.275324	+	0.275324i
$386$	1.44224e7			0.250769
$387$	7.20807e7	−	7.20807e7i	1.24362	−	1.24362i
$388$	1.85898e7	+	1.85898e7i	0.318259	+	0.318259i
$389$	−6.35528e6	+	6.35528e6i	−0.107966	+	0.107966i	−0.759026	−	0.651060i	$-0.774324\pi$
$389$	−6.35528e6	+	6.35528e6i	−0.107966	+	0.107966i	0.651060	+	0.759026i	$0.274324\pi$
$390$	6.60038e6	+	6.60038e6i	0.111269	+	0.111269i
$391$			4.55119e7i			0.761368i
$392$	−2.57544e7	+	2.57544e7i	−0.427556	+	0.427556i
$393$	1.14776e7	−	1.14776e7i	0.189092	−	0.189092i
$394$	−5.10493e7	−	5.10493e7i	−0.834643	−	0.834643i
$395$			1.97841e7i			0.321015i
$396$	1.01261e7			0.163063
$397$		−	3.62833e7i		−	0.579876i	−0.957046	−	0.289938i	$-0.906365\pi$
$397$		−	3.62833e7i		−	0.579876i	0.957046	−	0.289938i	$-0.0936346\pi$
$398$			1.29135e7i			0.204831i
$399$	−1.96836e6	−	1.96836e6i	−0.0309875	−	0.0309875i
$400$		−	8.07700e6i		−	0.126203i
$401$	3.88483e7	+	3.88483e7i	0.602476	+	0.602476i	0.940969	−	0.338493i	$-0.109917\pi$
$401$	3.88483e7	+	3.88483e7i	0.602476	+	0.602476i	−0.338493	+	0.940969i	$0.609917\pi$
$402$	7.80682e6	+	7.80682e6i	0.120170	+	0.120170i
$403$	4.96021e6			0.0757852
$404$	3.67852e6			0.0557865
$405$	−3.01402e7	+	3.01402e7i	−0.453713	+	0.453713i
$406$			6.47063e7i			0.966871i
$407$	−2.00767e7	+	1.05067e7i	−0.297789	+	0.155841i
$408$	5.89257e6			0.0867609
$409$	−1.58858e7	−	1.58858e7i	−0.232188	−	0.232188i	0.581417	−	0.813605i	$-0.302498\pi$
$409$	−1.58858e7	−	1.58858e7i	−0.232188	−	0.232188i	−0.813605	+	0.581417i	$0.802498\pi$
$410$		−	4.06422e7i		−	0.589692i
$411$			8.61178e6i			0.124042i
$412$	−4.70772e7	+	4.70772e7i	−0.673161	+	0.673161i
$413$	−1.53377e7	+	1.53377e7i	−0.217726	+	0.217726i
$414$	2.60252e7			0.366770
$415$	−7.19391e6	+	7.19391e6i	−0.100652	+	0.100652i
$416$	2.33590e7			0.324470
$417$	686018.			0.00946079
$418$			2.68172e6i			0.0367185i
$419$	−2.15441e7			−0.292878			−0.146439	−	0.989220i	$-0.546781\pi$
$419$	−2.15441e7			−0.292878			−0.146439	+	0.989220i	$0.546781\pi$
$420$	5.22831e6	−	5.22831e6i	0.0705689	−	0.0705689i
$421$	1.03580e8	+	1.03580e8i	1.38812	+	1.38812i	0.829258	+	0.558865i	$0.188763\pi$
$421$	1.03580e8	+	1.03580e8i	1.38812	+	1.38812i	0.558865	+	0.829258i	$0.311237\pi$
$422$	2.23461e7	+	2.23461e7i	0.297347	+	0.297347i
$423$	−3.72270e7			−0.491854
$424$	3.27470e6	−	3.27470e6i	0.0429609	−	0.0429609i
$425$	−3.90283e7	−	3.90283e7i	−0.508409	−	0.508409i
$426$	−8.74867e6	+	8.74867e6i	−0.113165	+	0.113165i
$427$	8.96651e7	+	8.96651e7i	1.15170	+	1.15170i
$428$		−	2.03627e7i		−	0.259719i
$429$	−5.93402e6	+	5.93402e6i	−0.0751583	+	0.0751583i
$430$	−5.07048e7	+	5.07048e7i	−0.637740	+	0.637740i
$431$	−4.17269e7	−	4.17269e7i	−0.521176	−	0.521176i	0.396751	−	0.917926i	$-0.370138\pi$
$431$	−4.17269e7	−	4.17269e7i	−0.521176	−	0.521176i	−0.917926	+	0.396751i	$0.870138\pi$
$432$		−	6.84223e6i		−	0.0848685i
$433$	−6.68121e6			−0.0822984			−0.0411492	−	0.999153i	$-0.513102\pi$
$433$	−6.68121e6			−0.0822984			−0.0411492	+	0.999153i	$0.513102\pi$
$434$		−	3.92909e6i		−	0.0480643i
$435$		−	8.28905e6i		−	0.100702i
$436$	−2.26396e7	−	2.26396e7i	−0.273155	−	0.273155i
$437$			6.89237e6i			0.0825894i
$438$	−375931.	−	375931.i	−0.00447389	−	0.00447389i
$439$	−9.36036e7	−	9.36036e7i	−1.10637	−	1.10637i	−0.993624	−	0.112742i	$-0.964037\pi$
$439$	−9.36036e7	−	9.36036e7i	−1.10637	−	1.10637i	−0.112742	−	0.993624i	$-0.535963\pi$
$440$	−7.12311e6			−0.0836203
$441$	1.42325e8			1.65945
$442$	1.12872e8	−	1.12872e8i	1.30713	−	1.30713i
$443$			816162.i			0.00938783i	0.999989	+	0.00469392i	$0.00149413\pi$
$443$			816162.i			0.00938783i	−0.999989	+	0.00469392i	$0.998506\pi$
$444$	3.49623e6	+	6.68078e6i	0.0399439	+	0.0763270i
$445$	9.55390e7			1.08418
$446$	8.44030e6	+	8.44030e6i	0.0951378	+	0.0951378i
$447$		−	1.88450e7i		−	0.210996i
$448$		−	1.85032e7i		−	0.205784i
$449$	−6.58475e7	+	6.58475e7i	−0.727446	+	0.727446i	−0.970110	−	0.242665i	$-0.921979\pi$
$449$	−6.58475e7	+	6.58475e7i	−0.727446	+	0.727446i	0.242665	+	0.970110i	$0.421979\pi$
$450$	−2.23177e7	+	2.23177e7i	−0.244913	+	0.244913i
$451$	3.65390e7			0.398316
$452$	−3.07333e7	+	3.07333e7i	−0.332808	+	0.332808i
$453$	2.09476e7			0.225341
$454$	−7.95206e7			−0.849791
$455$		−	2.00295e8i		−	2.12636i
$456$	892377.			0.00941140
$457$	−8.37919e6	+	8.37919e6i	−0.0877917	+	0.0877917i	−0.749639	−	0.661847i	$-0.769773\pi$
$457$	−8.37919e6	+	8.37919e6i	−0.0877917	+	0.0877917i	0.661847	+	0.749639i	$0.269773\pi$
$458$	7.58568e7	+	7.58568e7i	0.789583	+	0.789583i
$459$	−3.30619e7	−	3.30619e7i	−0.341893	−	0.341893i
$460$	−1.83073e7			−0.188084
$461$	−2.79962e7	+	2.79962e7i	−0.285756	+	0.285756i	−0.835400	−	0.549643i	$-0.814764\pi$
$461$	−2.79962e7	+	2.79962e7i	−0.285756	+	0.285756i	0.549643	+	0.835400i	$0.314764\pi$
$462$	4.70047e6	+	4.70047e6i	0.0476667	+	0.0476667i
$463$	6.92275e7	−	6.92275e7i	0.697486	−	0.697486i	−0.266382	−	0.963868i	$-0.585828\pi$
$463$	6.92275e7	−	6.92275e7i	0.697486	−	0.697486i	0.963868	+	0.266382i	$0.0858282\pi$
$464$	−1.46676e7	−	1.46676e7i	−0.146827	−	0.146827i
$465$			503327.i			0.00500600i
$466$	5.62913e7	−	5.62913e7i	0.556268	−	0.556268i
$467$	5.23779e7	−	5.23779e7i	0.514277	−	0.514277i	−0.401557	−	0.915834i	$-0.631531\pi$
$467$	5.23779e7	−	5.23779e7i	0.514277	−	0.514277i	0.915834	+	0.401557i	$0.131531\pi$
$468$	−6.45438e7	−	6.45438e7i	−0.629676	−	0.629676i
$469$		−	2.36906e8i		−	2.29645i
$470$	2.61871e7			0.252228
$471$			7.94244e6i			0.0760136i
$472$		−	6.95351e6i		−	0.0661269i
$473$	−4.55857e7	−	4.55857e7i	−0.430770	−	0.430770i
$474$			5.91876e6i			0.0555771i
$475$	−5.91049e6	−	5.91049e6i	−0.0551497	−	0.0551497i
$476$	−8.94081e7	−	8.94081e7i	−0.829002	−	0.829002i
$477$	−1.80968e7			−0.166742
$478$	−5.27619e7			−0.483099
$479$	−1.18221e7	+	1.18221e7i	−0.107570	+	0.107570i	−0.758843	−	0.651274i	$-0.774235\pi$
$479$	−1.18221e7	+	1.18221e7i	−0.107570	+	0.107570i	0.651274	+	0.758843i	$0.274235\pi$
$480$			2.37031e6i			0.0214329i
$481$	1.94939e8	+	6.09998e7i	1.75172	+	0.548142i
$482$	−9.97693e7			−0.890955
$483$	1.20808e7	+	1.20808e7i	0.107215	+	0.107215i
$484$			5.02860e7i			0.443518i
$485$			7.22662e7i			0.633447i
$486$	−2.85013e7	+	2.85013e7i	−0.248288	+	0.248288i
$487$	4.59488e7	−	4.59488e7i	0.397821	−	0.397821i	−0.479643	−	0.877464i	$-0.659234\pi$
$487$	4.59488e7	−	4.59488e7i	0.397821	−	0.397821i	0.877464	+	0.479643i	$0.159234\pi$
$488$	−4.06506e7			−0.349790
$489$	8.77022e6	−	8.77022e6i	0.0750039	−	0.0750039i
$490$	−1.00118e8			−0.850986
$491$	1.34051e8			1.13247			0.566233	−	0.824245i	$-0.308400\pi$
$491$	1.34051e8			1.13247			0.566233	+	0.824245i	$0.308400\pi$
$492$		−	1.21588e7i		−	0.102093i
$493$	−1.41749e8			−1.18299
$494$	1.70934e7	−	1.70934e7i	0.141791	−	0.141791i
$495$	1.96820e7	+	1.96820e7i	0.162276	+	0.162276i
$496$	890647.	+	890647.i	0.00729895	+	0.00729895i
$497$	2.65488e8			2.16259
$498$	−2.15219e6	+	2.15219e6i	−0.0174258	+	0.0174258i
$499$	−2.73371e7	−	2.73371e7i	−0.220014	−	0.220014i	0.588490	−	0.808504i	$-0.299723\pi$
$499$	−2.73371e7	−	2.73371e7i	−0.220014	−	0.220014i	−0.808504	+	0.588490i	$0.799723\pi$
$500$	4.67985e7	−	4.67985e7i	0.374388	−	0.374388i
$501$	2.65695e7	+	2.65695e7i	0.211286	+	0.211286i
$502$		−	2.46013e7i		−	0.194467i
$503$	1.42209e8	−	1.42209e8i	1.11744	−	1.11744i	0.125322	−	0.992116i	$-0.460004\pi$
$503$	1.42209e8	−	1.42209e8i	1.11744	−	1.11744i	0.992116	−	0.125322i	$-0.0399964\pi$
$504$	−5.11266e7	+	5.11266e7i	−0.399351	+	0.399351i
$505$	7.14995e6	+	7.14995e6i	0.0555174	+	0.0555174i
$506$		−	1.64590e7i		−	0.127044i
$507$	5.31932e7			0.408162
$508$			5.24181e7i			0.399844i
$509$			9.38003e7i			0.711297i	0.934620	+	0.355649i	$0.115740\pi$
$509$			9.38003e7i			0.711297i	−0.934620	+	0.355649i	$0.884260\pi$
$510$	1.14534e7	+	1.14534e7i	0.0863424	+	0.0863424i
$511$			1.14080e7i			0.0854962i
$512$	4.19430e6	+	4.19430e6i	0.0312500	+	0.0312500i
$513$	−5.00693e6	−	5.00693e6i	−0.0370868	−	0.0370868i
$514$	3.69574e7			0.272152
$515$	−1.83008e8			−1.33983
$516$	−1.51692e7	+	1.51692e7i	−0.110412	+	0.110412i
$517$			2.35433e7i			0.170371i
$518$	4.83193e7	−	1.54416e8i	0.347641	−	1.11097i
$519$	3.75572e7			0.268652
$520$	4.54030e7	+	4.54030e7i	0.322905	+	0.322905i
$521$		−	1.35717e7i		−	0.0959670i	−0.998848	−	0.0479835i	$-0.984721\pi$
$521$		−	1.35717e7i		−	0.0959670i	0.998848	−	0.0479835i	$-0.0152795\pi$
$522$			8.10569e7i			0.569874i
$523$	−9.71683e7	+	9.71683e7i	−0.679234	+	0.679234i	−0.959827	−	0.280593i	$-0.909469\pi$
$523$	−9.71683e7	+	9.71683e7i	−0.679234	+	0.679234i	0.280593	+	0.959827i	$0.409469\pi$
$524$	7.89526e7	−	7.89526e7i	0.548748	−	0.548748i
$525$	−2.07196e7			−0.143187
$526$	−4.24760e7	+	4.24760e7i	−0.291868	+	0.291868i
$527$	8.60727e6			0.0588076
$528$	−2.13101e6			−0.0144771
$529$			1.05734e8i			0.714246i
$530$	1.27301e7			0.0855074
$531$	−1.92134e7	+	1.92134e7i	−0.128328	+	0.128328i
$532$	−1.35401e7	−	1.35401e7i	−0.0899261	−	0.0899261i
$533$	−2.32901e8	−	2.32901e8i	−1.53812	−	1.53812i
$534$	2.85822e7			0.187703
$535$	3.95790e7	−	3.95790e7i	0.258466	−	0.258466i
$536$	5.37019e7	+	5.37019e7i	0.348735	+	0.348735i
$537$	−3.27099e7	+	3.27099e7i	−0.211230	+	0.211230i
$538$	7.11487e7	+	7.11487e7i	0.456899	+	0.456899i
$539$		−	9.00100e7i		−	0.574810i
$540$	1.32993e7	−	1.32993e7i	0.0844591	−	0.0844591i
$541$	−1.30347e8	+	1.30347e8i	−0.823207	+	0.823207i	−0.986567	−	0.163360i	$-0.947767\pi$
$541$	−1.30347e8	+	1.30347e8i	−0.823207	+	0.823207i	0.163360	+	0.986567i	$0.447767\pi$
$542$	1.25856e8	+	1.25856e8i	0.790451	+	0.790451i
$543$			1.16105e7i			0.0725189i
$544$	4.05341e7			0.251781
$545$		−	8.80092e7i		−	0.543674i
$546$		−	5.99219e7i		−	0.368135i
$547$	−1.51034e8	−	1.51034e8i	−0.922813	−	0.922813i	0.0744148	−	0.997227i	$-0.476291\pi$
$547$	−1.51034e8	−	1.51034e8i	−0.922813	−	0.922813i	−0.997227	+	0.0744148i	$0.976291\pi$
$548$			5.92391e7i			0.359970i
$549$	1.12323e8	+	1.12323e8i	0.678813	+	0.678813i
$550$	1.41143e7	+	1.41143e7i	0.0848344	+	0.0848344i
$551$	−2.14666e7			−0.128324
$552$	−5.47696e6			−0.0325628
$553$	8.98055e7	−	8.98055e7i	0.531041	−	0.531041i
$554$		−	1.42119e7i		−	0.0835841i
$555$	−6.18983e6	+	1.97811e7i	−0.0362076	+	0.115710i
$556$	4.71901e6			0.0274553
$557$	9.43010e7	+	9.43010e7i	0.545696	+	0.545696i	0.925193	−	0.379497i	$-0.123903\pi$
$557$	9.43010e7	+	9.43010e7i	0.545696	+	0.545696i	−0.379497	+	0.925193i	$0.623903\pi$
$558$		−	4.92193e6i		−	0.0283291i
$559$			5.81130e8i			3.32689i
$560$	3.59647e7	−	3.59647e7i	0.204792	−	0.204792i
$561$	−1.02971e7	+	1.02971e7i	−0.0583212	+	0.0583212i
$562$	−1.76335e8			−0.993411
$563$	−2.14467e8	+	2.14467e8i	−1.20181	+	1.20181i	−0.228196	+	0.973615i	$0.573283\pi$
$563$	−2.14467e8	+	2.14467e8i	−1.20181	+	1.20181i	−0.973615	+	0.228196i	$0.926717\pi$
$564$	7.83433e6			0.0436681
$565$	−1.19473e8			−0.662406
$566$		−	9.58614e7i		−	0.528682i
$567$	2.73630e8			1.50112
$568$	−6.01807e7	+	6.01807e7i	−0.328407	+	0.328407i
$569$	1.07458e8	+	1.07458e8i	0.583312	+	0.583312i	0.935812	−	0.352500i	$-0.114668\pi$
$569$	1.07458e8	+	1.07458e8i	0.583312	+	0.583312i	−0.352500	+	0.935812i	$0.614668\pi$
$570$	1.73452e6	+	1.73452e6i	0.00936600	+	0.00936600i
$571$	−3.58986e8			−1.92828			−0.964138	−	0.265403i	$-0.914495\pi$
$571$	−3.58986e8			−1.92828			−0.964138	+	0.265403i	$0.914495\pi$
$572$	−4.08192e7	+	4.08192e7i	−0.218110	+	0.218110i
$573$	−4.13498e7	−	4.13498e7i	−0.219791	−	0.219791i
$574$	−1.84486e8	+	1.84486e8i	−0.975501	+	0.975501i
$575$	3.62756e7	+	3.62756e7i	0.190814	+	0.190814i
$576$		−	2.31788e7i		−	0.121289i
$577$	−2.06129e8	+	2.06129e8i	−1.07303	+	1.07303i	−0.0759143	+	0.997114i	$0.524188\pi$
$577$	−2.06129e8	+	2.06129e8i	−1.07303	+	1.07303i	−0.997114	+	0.0759143i	$0.975812\pi$
$578$	9.93117e7	−	9.93117e7i	0.514301	−	0.514301i
$579$	8.38650e6	+	8.38650e6i	0.0432061	+	0.0432061i
$580$		−	5.70190e7i		−	0.292238i
$581$	6.53103e7			0.333007
$582$			2.16197e7i			0.109668i
$583$			1.14449e7i			0.0577571i
$584$	−2.58597e6	−	2.58597e6i	−0.0129833	−	0.0129833i
$585$		−	2.50908e8i		−	1.25328i
$586$	4.23385e7	+	4.23385e7i	0.210399	+	0.210399i
$587$	−1.18964e6	−	1.18964e6i	−0.00588167	−	0.00588167i	0.704160	−	0.710041i	$-0.251324\pi$
$587$	−1.18964e6	−	1.18964e6i	−0.00588167	−	0.00588167i	−0.710041	+	0.704160i	$0.751324\pi$
$588$	−2.99520e7			−0.147331
$589$	1.30350e6			0.00637916
$590$	1.35156e7	−	1.35156e7i	0.0658079	−	0.0658079i
$591$		−	5.93696e7i		−	0.287609i
$592$	2.40500e7	+	4.59560e7i	0.115918	+	0.221502i
$593$	−2.58098e8			−1.23772			−0.618858	−	0.785503i	$-0.712404\pi$
$593$	−2.58098e8			−1.23772			−0.618858	+	0.785503i	$0.712404\pi$
$594$	1.19566e7	+	1.19566e7i	0.0570490	+	0.0570490i
$595$		−	3.47566e8i		−	1.65001i
$596$		−	1.29632e8i		−	0.612312i
$597$	−7.50914e6	+	7.50914e6i	−0.0352913	+	0.0352913i
$598$	−1.04910e8	+	1.04910e8i	−0.490586	+	0.490586i
$599$	−2.47513e8			−1.15164			−0.575821	−	0.817576i	$-0.695317\pi$
$599$	−2.47513e8			−1.15164			−0.575821	+	0.817576i	$0.695317\pi$
$600$	4.69672e6	−	4.69672e6i	0.0217441	−	0.0217441i
$601$	3.27613e8			1.50917			0.754585	−	0.656202i	$-0.227838\pi$
$601$	3.27613e8			1.50917			0.754585	+	0.656202i	$0.227838\pi$
$602$	4.60326e8			2.10997
$603$		−	2.96770e8i		−	1.35353i
$604$	1.44095e8			0.653941
$605$	−9.77410e7	+	9.77410e7i	−0.441378	+	0.441378i
$606$	2.13903e6	+	2.13903e6i	0.00961169	+	0.00961169i
$607$	2.11040e8	+	2.11040e8i	0.943623	+	0.943623i	0.998493	−	0.0548704i	$-0.0174746\pi$
$607$	2.11040e8	+	2.11040e8i	0.943623	+	0.943623i	−0.0548704	+	0.998493i	$0.517475\pi$
$608$	6.13852e6			0.0273120
$609$	−3.76263e7	+	3.76263e7i	−0.166586	+	0.166586i
$610$	−7.90127e7	−	7.90127e7i	−0.348103	−	0.348103i
$611$	1.50066e8	−	1.50066e8i	0.657897	−	0.657897i
$612$	−1.12001e8	−	1.12001e8i	−0.488614	−	0.488614i
$613$		−	6.47850e7i		−	0.281250i	−0.990063	−	0.140625i	$-0.955089\pi$
$613$		−	6.47850e7i		−	0.281250i	0.990063	−	0.140625i	$-0.0449113\pi$
$614$	7.69291e7	−	7.69291e7i	0.332342	−	0.332342i
$615$	2.36331e7	−	2.36331e7i	0.101601	−	0.101601i
$616$	3.23338e7	+	3.23338e7i	0.138329	+	0.138329i
$617$			3.68167e8i			1.56743i	0.621118	+	0.783717i	$0.286679\pi$
$617$			3.68167e8i			1.56743i	−0.621118	+	0.783717i	$0.713321\pi$
$618$	−5.47501e7			−0.231964
$619$			2.12013e8i			0.893905i	0.894558	+	0.446953i	$0.147491\pi$
$619$			2.12013e8i			0.893905i	−0.894558	+	0.446953i	$0.852509\pi$
$620$			3.46231e6i			0.0145275i
$621$	3.07300e7	+	3.07300e7i	0.128318	+	0.128318i
$622$		−	1.21881e8i		−	0.506483i
$623$	−4.33678e8	−	4.33678e8i	−1.79351	−	1.79351i
$624$	1.35831e7	+	1.35831e7i	0.0559043	+	0.0559043i
$625$	5.86798e7			0.240352
$626$	1.24335e8			0.506840
$627$	−1.55940e6	+	1.55940e6i	−0.00632639	+	0.00632639i
$628$			5.46348e7i			0.220592i
$629$	3.38272e8	+	1.05851e8i	1.35929	+	0.425346i
$630$	−1.98750e8			−0.794850
$631$	−6.06974e7	−	6.06974e7i	−0.241592	−	0.241592i	0.575917	−	0.817508i	$-0.304645\pi$
$631$	−6.06974e7	−	6.06974e7i	−0.241592	−	0.241592i	−0.817508	+	0.575917i	$0.804645\pi$
$632$			4.07143e7i			0.161285i
$633$			2.59882e7i			0.102463i
$634$	−1.69684e7	+	1.69684e7i	−0.0665843	+	0.0665843i
$635$	−1.01885e8	+	1.01885e8i	−0.397915	+	0.397915i
$636$	3.80843e6			0.0148038
$637$	−5.73727e8	+	5.73727e8i	−2.21966	+	2.21966i
$638$	5.12625e7			0.197396
$639$	3.32574e8			1.27463
$640$			1.63050e7i			0.0621985i
$641$	−3.13151e8			−1.18899			−0.594496	−	0.804098i	$-0.702649\pi$
$641$	−3.13151e8			−1.18899			−0.594496	+	0.804098i	$0.702649\pi$
$642$	1.18407e7	−	1.18407e7i	0.0447480	−	0.0447480i
$643$	−2.91728e8	−	2.91728e8i	−1.09735	−	1.09735i	−0.994720	−	0.102630i	$-0.967274\pi$
$643$	−2.91728e8	−	2.91728e8i	−1.09735	−	1.09735i	−0.102630	−	0.994720i	$-0.532726\pi$
$644$	8.31019e7	+	8.31019e7i	0.311138	+	0.311138i
$645$	−5.89690e7			−0.219758
$646$	2.96616e7	−	2.96616e7i	0.110026	−	0.110026i
$647$	−2.72642e8	−	2.72642e8i	−1.00665	−	1.00665i	−0.999978	−	0.00667447i	$-0.997875\pi$
$647$	−2.72642e8	−	2.72642e8i	−1.00665	−	1.00665i	−0.00667447	−	0.999978i	$-0.502125\pi$
$648$	−6.20264e7	+	6.20264e7i	−0.227956	+	0.227956i
$649$	1.21511e7	+	1.21511e7i	0.0444508	+	0.0444508i
$650$		−	1.79930e8i		−	0.655185i
$651$	2.28474e6	−	2.28474e6i	0.00828121	−	0.00828121i
$652$	6.03289e7	−	6.03289e7i	0.217662	−	0.217662i
$653$	2.69430e8	+	2.69430e8i	0.967622	+	0.967622i	0.999492	−	0.0318702i	$-0.0101463\pi$
$653$	2.69430e8	+	2.69430e8i	0.967622	+	0.967622i	−0.0318702	+	0.999492i	$0.510146\pi$
$654$		−	2.63295e7i		−	0.0941260i
$655$	3.06921e8			1.09220
$656$		−	8.36386e7i		−	0.296275i
$657$			1.42907e7i			0.0503915i
$658$	−1.18870e8	−	1.18870e8i	−0.417250	−	0.417250i
$659$		−	3.81340e8i		−	1.33247i	−0.745743	−	0.666233i	$-0.767905\pi$
$659$		−	3.81340e8i		−	1.33247i	0.745743	−	0.666233i	$-0.232095\pi$
$660$	−4.14204e6	−	4.14204e6i	−0.0144073	−	0.0144073i
$661$	3.32314e8	+	3.32314e8i	1.15065	+	1.15065i	0.986422	+	0.164231i	$0.0525144\pi$
$661$	3.32314e8	+	3.32314e8i	1.15065	+	1.15065i	0.164231	+	0.986422i	$0.447486\pi$
$662$	−1.71219e8			−0.590171
$663$	1.31268e8			0.450421
$664$	−1.48045e7	+	1.48045e7i	−0.0505698	+	0.0505698i
$665$		−	5.26357e7i		−	0.178985i
$666$	6.05291e7	−	1.93435e8i	0.204900	−	0.654806i
$667$	1.31751e8			0.443994
$668$	1.82767e8	+	1.82767e8i	0.613153	+	0.613153i
$669$			9.81595e6i			0.0327834i
$670$			2.08761e8i			0.694105i
$671$	7.10357e7	−	7.10357e7i	0.235131	−	0.235131i
$672$	1.07595e7	−	1.07595e7i	0.0354555	−	0.0354555i
$673$	−1.69976e8			−0.557626			−0.278813	−	0.960345i	$-0.589941\pi$
$673$	−1.69976e8			−0.557626			−0.278813	+	0.960345i	$0.589941\pi$
$674$	2.00995e8	−	2.00995e8i	0.656456	−	0.656456i
$675$	−5.27045e7			−0.171371
$676$	3.65908e8			1.18449
$677$		−	4.09547e8i		−	1.31989i	−0.751315	−	0.659944i	$-0.770580\pi$
$677$		−	4.09547e8i		−	1.31989i	0.751315	−	0.659944i	$-0.229420\pi$
$678$	−3.57424e7			−0.114682
$679$	3.28036e8	−	3.28036e8i	1.04788	−	1.04788i
$680$	7.87862e7	+	7.87862e7i	0.250567	+	0.250567i
$681$	−4.62407e7	−	4.62407e7i	−0.146414	−	0.146414i
$682$	−3.11276e6			−0.00981279
$683$	−1.83633e8	+	1.83633e8i	−0.576353	+	0.576353i	−0.933896	−	0.357544i	$-0.883614\pi$
$683$	−1.83633e8	+	1.83633e8i	−0.576353	+	0.576353i	0.357544	+	0.933896i	$0.383614\pi$
$684$	−1.69615e7	−	1.69615e7i	−0.0530024	−	0.0530024i
$685$	−1.15143e8	+	1.15143e8i	−0.358234	+	0.358234i
$686$	1.88729e8	+	1.88729e8i	0.584611	+	0.584611i
$687$			8.82204e7i			0.272081i
$688$	−1.04347e8	+	1.04347e8i	−0.320416	+	0.320416i
$689$	7.29500e7	−	7.29500e7i	0.223032	−	0.223032i
$690$	−1.06456e7	−	1.06456e7i	−0.0324057	−	0.0324057i
$691$			1.02763e8i			0.311462i	0.987800	+	0.155731i	$0.0497733\pi$
$691$			1.02763e8i			0.311462i	−0.987800	+	0.155731i	$0.950227\pi$
$692$	2.58350e8			0.779632
$693$		−	1.78684e8i		−	0.536892i
$694$			1.92266e8i			0.575206i
$695$	9.17236e6	+	9.17236e6i	0.0273229	+	0.0273229i
$696$		−	1.70583e7i		−	0.0505949i
$697$	−4.04145e8	−	4.04145e8i	−1.19354	−	1.19354i
$698$	−8.61989e7	−	8.61989e7i	−0.253475	−	0.253475i
$699$	6.54661e7			0.191684
$700$	−1.42527e8			−0.415530
$701$	1.73047e8	−	1.73047e8i	0.502354	−	0.502354i	−0.409815	−	0.912169i	$-0.634407\pi$
$701$	1.73047e8	−	1.73047e8i	0.502354	−	0.502354i	0.912169	+	0.409815i	$0.134407\pi$
$702$		−	1.52424e8i		−	0.440596i
$703$	5.12282e7	+	1.60302e7i	0.147450	+	0.0461394i
$704$	−1.46589e7			−0.0420128
$705$	1.52276e7	+	1.52276e7i	0.0434575	+	0.0434575i
$706$		−	4.11034e7i		−	0.116806i
$707$		−	6.49112e7i		−	0.183680i
$708$	4.04342e6	−	4.04342e6i	0.0113933	−	0.0113933i
$709$	4.64822e8	−	4.64822e8i	1.30421	−	1.30421i	0.378684	−	0.925526i	$-0.376377\pi$
$709$	4.64822e8	−	4.64822e8i	1.30421	−	1.30421i	0.925526	−	0.378684i	$-0.123623\pi$
$710$	−2.33947e8			−0.653646
$711$	1.12498e8	−	1.12498e8i	0.312995	−	0.312995i
$712$	1.96612e8			0.544717
$713$	−8.00019e6			−0.0220715
$714$		−	1.03980e8i		−	0.285665i
$715$	−1.58681e8			−0.434116
$716$	−2.25006e8	+	2.25006e8i	−0.612993	+	0.612993i
$717$	−3.06807e7	−	3.06807e7i	−0.0832352	−	0.0832352i
$718$	−1.90455e8	−	1.90455e8i	−0.514540	−	0.514540i
$719$	9.21702e7			0.247973			0.123986	−	0.992284i	$-0.460432\pi$
$719$	9.21702e7			0.247973			0.123986	+	0.992284i	$0.460432\pi$
$720$	4.50526e7	−	4.50526e7i	0.120704	−	0.120704i
$721$	8.30725e8	+	8.30725e8i	2.21642	+	2.21642i
$722$	−1.83692e8	+	1.83692e8i	−0.488065	+	0.488065i
$723$	−5.80151e7	−	5.80151e7i	−0.153506	−	0.153506i
$724$			7.98668e7i			0.210451i
$725$	−1.12982e8	+	1.12982e8i	−0.296480	+	0.296480i
$726$	−2.92410e7	+	2.92410e7i	−0.0764155	+	0.0764155i
$727$	−3.63916e7	−	3.63916e7i	−0.0947104	−	0.0947104i	0.658164	−	0.752875i	$-0.271333\pi$
$727$	−3.63916e7	−	3.63916e7i	−0.0947104	−	0.0947104i	−0.752875	+	0.658164i	$0.771333\pi$
$728$		−	4.12193e8i		−	1.06833i
$729$	3.20113e8			0.826268
$730$		−	1.00527e7i		−	0.0258413i
$731$			1.00841e9i			2.58159i
$732$	−2.36380e7	−	2.36380e7i	−0.0602668	−	0.0602668i
$733$		−	4.82858e8i		−	1.22605i	−0.790064	−	0.613024i	$-0.789953\pi$
$733$		−	4.82858e8i		−	1.22605i	0.790064	−	0.613024i	$-0.210047\pi$
$734$	1.33637e8	+	1.33637e8i	0.337939	+	0.337939i
$735$	−5.82178e7	−	5.82178e7i	−0.146620	−	0.146620i
$736$	−3.76751e7			−0.0944977
$737$	−1.87685e8			−0.468843
$738$	−2.31104e8	+	2.31104e8i	−0.574960	+	0.574960i
$739$		−	5.23013e7i		−	0.129592i	−0.997899	−	0.0647961i	$-0.979360\pi$
$739$		−	5.23013e7i		−	0.129592i	0.997899	−	0.0647961i	$-0.0206397\pi$
$740$	−4.25788e7	+	1.36071e8i	−0.105075	+	0.335792i
$741$	1.98794e7			0.0488594
$742$	−5.77854e7	−	5.77854e7i	−0.141451	−	0.141451i
$743$		−	8.32627e7i		−	0.202994i	−0.994836	−	0.101497i	$-0.967637\pi$
$743$		−	8.32627e7i		−	0.202994i	0.994836	−	0.101497i	$-0.0323633\pi$
$744$			1.03581e6i			0.00251514i
$745$	2.51966e8	−	2.51966e8i	0.609359	−	0.609359i
$746$	−2.58220e8	+	2.58220e8i	−0.621975	+	0.621975i
$747$	8.18135e7			0.196274
$748$	−7.08321e7	+	7.08321e7i	−0.169249	+	0.169249i
$749$	−3.59320e8			−0.855137
$750$	5.44261e7			0.129010
$751$			4.38765e8i			1.03589i	0.855415	+	0.517944i	$0.173302\pi$
$751$			4.38765e8i			1.03589i	−0.855415	+	0.517944i	$0.826698\pi$
$752$	5.38911e7			0.126725
$753$	1.43055e7	−	1.43055e7i	0.0335056	−	0.0335056i
$754$	−3.26749e8	−	3.26749e8i	−0.762255	−	0.762255i
$755$	2.80078e8	+	2.80078e8i	0.650787	+	0.650787i
$756$	−1.20738e8			−0.279434
$757$	1.46317e8	−	1.46317e8i	0.337293	−	0.337293i	−0.518055	−	0.855348i	$-0.673344\pi$
$757$	1.46317e8	−	1.46317e8i	0.337293	−	0.337293i	0.855348	+	0.518055i	$0.173344\pi$
$758$	−2.08464e8	−	2.08464e8i	−0.478655	−	0.478655i
$759$	9.57082e6	−	9.57082e6i	0.0218889	−	0.0218889i
$760$	1.19315e7	+	1.19315e7i	0.0271802	+	0.0271802i
$761$		−	5.43738e8i		−	1.23377i	−0.787052	−	0.616887i	$-0.788394\pi$
$761$		−	5.43738e8i		−	1.23377i	0.787052	−	0.616887i	$-0.211606\pi$
$762$	−3.04808e7	+	3.04808e7i	−0.0688908	+	0.0688908i
$763$	−3.99498e8	+	3.99498e8i	−0.899376	+	0.899376i
$764$	−2.84439e8	−	2.84439e8i	−0.637835	−	0.637835i
$765$		−	4.35392e8i		−	0.972514i
$766$	1.44932e8			0.322462
$767$		−	1.54902e8i		−	0.343299i
$768$			4.87792e6i			0.0107684i
$769$	−6.06989e8	−	6.06989e8i	−1.33476	−	1.33476i	−0.901058	−	0.433699i	$-0.857208\pi$
$769$	−6.06989e8	−	6.06989e8i	−1.33476	−	1.33476i	−0.433699	−	0.901058i	$-0.642792\pi$
$770$			1.25695e8i			0.275324i
$771$	2.14905e7	+	2.14905e7i	0.0468903	+	0.0468903i
$772$	5.76894e7	+	5.76894e7i	0.125385	+	0.125385i
$773$	6.07034e8			1.31424			0.657120	−	0.753786i	$-0.271775\pi$
$773$	6.07034e8			1.31424			0.657120	+	0.753786i	$0.271775\pi$
$774$	5.76646e8			1.24362
$775$	6.86049e6	−	6.86049e6i	0.0147384	−	0.0147384i
$776$			1.48719e8i			0.318259i
$777$	1.17889e8	−	6.16945e7i	0.251311	−	0.131517i
$778$	−5.08422e7			−0.107966
$779$	−6.12041e7	−	6.12041e7i	−0.129470	−	0.129470i
$780$			5.28030e7i			0.111269i
$781$		−	2.10328e8i		−	0.441514i
$782$	−1.82047e8	+	1.82047e8i	−0.380684	+	0.380684i
$783$	−9.57101e7	+	9.57101e7i	−0.199376	+	0.199376i
$784$	−2.06035e8			−0.427556
$785$	−1.06194e8	+	1.06194e8i	−0.219528	+	0.219528i
$786$	9.18208e7			0.189092
$787$	9.02274e7			0.185103			0.0925517	−	0.995708i	$-0.470498\pi$
$787$	9.02274e7			0.185103			0.0925517	+	0.995708i	$0.470498\pi$
$788$		−	4.08394e8i		−	0.834643i
$789$	−4.93990e7			−0.100574
$790$	−7.91364e7	+	7.91364e7i	−0.160507	+	0.160507i
$791$	5.42321e8	+	5.42321e8i	1.09579	+	1.09579i
$792$	4.05042e7	+	4.05042e7i	0.0815313	+	0.0815313i
$793$	−9.05568e8			−1.81594
$794$	1.45133e8	−	1.45133e8i	0.289938	−	0.289938i
$795$	7.40246e6	+	7.40246e6i	0.0147324	+	0.0147324i
$796$	−5.16542e7	+	5.16542e7i	−0.102416	+	0.102416i
$797$	6.32067e8	+	6.32067e8i	1.24850	+	1.24850i	0.956383	+	0.292115i	$0.0943591\pi$
$797$	6.32067e8	+	6.32067e8i	1.24850	+	1.24850i	0.292115	+	0.956383i	$0.405641\pi$
$798$		−	1.57469e7i		−	0.0309875i
$799$	2.60404e8	−	2.60404e8i	0.510513	−	0.510513i
$800$	3.23080e7	−	3.23080e7i	0.0631015	−	0.0631015i
$801$	−5.43264e8	−	5.43264e8i	−1.05709	−	1.05709i
$802$			3.10787e8i			0.602476i
$803$	9.03781e6			0.0174549
$804$			6.24546e7i			0.120170i
$805$			3.23051e8i			0.619275i
$806$	1.98408e7	+	1.98408e7i	0.0378926	+	0.0378926i
$807$			8.27450e7i			0.157442i
$808$	1.47141e7	+	1.47141e7i	0.0278932	+	0.0278932i
$809$	1.03089e8	+	1.03089e8i	0.194701	+	0.194701i	0.797724	−	0.603023i	$-0.206037\pi$
$809$	1.03089e8	+	1.03089e8i	0.194701	+	0.194701i	−0.603023	+	0.797724i	$0.706037\pi$
$810$	−2.41122e8			−0.453713
$811$	−2.99249e8			−0.561009			−0.280504	−	0.959853i	$-0.590502\pi$
$811$	−2.99249e8			−0.561009			−0.280504	+	0.959853i	$0.590502\pi$
$812$	−2.58825e8	+	2.58825e8i	−0.483435	+	0.483435i
$813$			1.46368e8i			0.272380i
$814$	−1.22334e8	−	3.82802e7i	−0.226815	−	0.0709742i
$815$	2.34523e8			0.433224
$816$	2.35703e7	+	2.35703e7i	0.0433805	+	0.0433805i
$817$			1.52715e8i			0.280038i
$818$		−	1.27087e8i		−	0.232188i
$819$	−1.13894e9	+	1.13894e9i	−2.07324	+	2.07324i
$820$	1.62569e8	−	1.62569e8i	0.294846	−	0.294846i
$821$	−7.74937e6			−0.0140035			−0.00700175	−	0.999975i	$-0.502229\pi$
$821$	−7.74937e6			−0.0140035			−0.00700175	+	0.999975i	$0.502229\pi$
$822$	−3.44471e7	+	3.44471e7i	−0.0620208	+	0.0620208i
$823$	4.19229e8			0.752058			0.376029	−	0.926608i	$-0.377289\pi$
$823$	4.19229e8			0.752058			0.376029	+	0.926608i	$0.377289\pi$
$824$	−3.76618e8			−0.673161
$825$			1.64148e7i			0.0292330i
$826$	−1.22702e8			−0.217726
$827$	6.29822e8	−	6.29822e8i	1.11353	−	1.11353i	0.120858	−	0.992670i	$-0.461435\pi$
$827$	6.29822e8	−	6.29822e8i	1.11353	−	1.11353i	0.992670	−	0.120858i	$-0.0385646\pi$
$828$	1.04101e8	+	1.04101e8i	0.183385	+	0.183385i
$829$	−2.06988e8	−	2.06988e8i	−0.363314	−	0.363314i	0.501718	−	0.865031i	$-0.332702\pi$
$829$	−2.06988e8	−	2.06988e8i	−0.363314	−	0.363314i	−0.865031	+	0.501718i	$0.832702\pi$
$830$	−5.75513e7			−0.100652
$831$	8.26414e6	−	8.26414e6i	0.0144011	−	0.0144011i
$832$	9.34360e7	+	9.34360e7i	0.162235	+	0.162235i
$833$	−9.95568e8	+	9.95568e8i	−1.72241	+	1.72241i
$834$	2.74407e6	+	2.74407e6i	0.00473040	+	0.00473040i
$835$			7.10491e8i			1.22039i
$836$	−1.07269e7	+	1.07269e7i	−0.0183593	+	0.0183593i
$837$	5.81170e6	−	5.81170e6i	0.00991121	−	0.00991121i
$838$	−8.61764e7	−	8.61764e7i	−0.146439	−	0.146439i
$839$		−	2.85697e8i		−	0.483749i	−0.970308	−	0.241875i	$-0.922238\pi$
$839$		−	2.85697e8i		−	0.483749i	0.970308	−	0.241875i	$-0.0777623\pi$
$840$	4.18265e7			0.0705689
$841$		−	1.84478e8i		−	0.310138i
$842$			8.28637e8i			1.38812i
$843$	−1.02537e8	−	1.02537e8i	−0.171159	−	0.171159i
$844$			1.78769e8i			0.297347i
$845$	7.11216e8	+	7.11216e8i	1.17878	+	1.17878i
$846$	−1.48908e8	−	1.48908e8i	−0.245927	−	0.245927i
$847$	8.87347e8			1.46030
$848$	2.61976e7			0.0429609
$849$	5.57427e7	−	5.57427e7i	0.0910889	−	0.0910889i
$850$		−	3.12227e8i		−	0.508409i
$851$	−3.14413e8	−	9.83849e7i	−0.510166	−	0.159639i
$852$	−6.99894e7			−0.113165
$853$	−6.46168e8	−	6.46168e8i	−1.04111	−	1.04111i	−0.999118	−	0.0419961i	$-0.986628\pi$
$853$	−6.46168e8	−	6.46168e8i	−1.04111	−	1.04111i	−0.0419961	−	0.999118i	$-0.513372\pi$
$854$			7.17321e8i			1.15170i
$855$		−	6.59362e7i		−	0.105493i
$856$	8.14506e7	−	8.14506e7i	0.129859	−	0.129859i
$857$	1.96760e8	−	1.96760e8i	0.312604	−	0.312604i	−0.533313	−	0.845918i	$-0.679053\pi$
$857$	1.96760e8	−	1.96760e8i	0.312604	−	0.312604i	0.845918	+	0.533313i	$0.179053\pi$
$858$	−4.74721e7			−0.0751583
$859$	−6.42288e7	+	6.42288e7i	−0.101333	+	0.101333i	−0.755956	−	0.654623i	$-0.772827\pi$
$859$	−6.42288e7	+	6.42288e7i	−0.101333	+	0.101333i	0.654623	+	0.755956i	$0.272827\pi$
$860$	−4.05638e8			−0.637740
$861$	−2.14555e8			−0.336147
$862$		−	3.33815e8i		−	0.521176i
$863$	1.14737e8			0.178514			0.0892568	−	0.996009i	$-0.471551\pi$
$863$	1.14737e8			0.178514			0.0892568	+	0.996009i	$0.471551\pi$
$864$	2.73689e7	−	2.73689e7i	0.0424342	−	0.0424342i
$865$	5.02155e8	+	5.02155e8i	0.775872	+	0.775872i
$866$	−2.67248e7	−	2.67248e7i	−0.0411492	−	0.0411492i
$867$	1.15498e8			0.177222
$868$	1.57164e7	−	1.57164e7i	0.0240322	−	0.0240322i
$869$	−7.11470e7	−	7.11470e7i	−0.108417	−	0.108417i
$870$	3.31562e7	−	3.31562e7i	0.0503509	−	0.0503509i
$871$	1.19631e9	+	1.19631e9i	1.81046	+	1.81046i
$872$		−	1.81117e8i		−	0.273155i
$873$	4.10928e8	−	4.10928e8i	0.617622	−	0.617622i
$874$	−2.75695e7	+	2.75695e7i	−0.0412947	+	0.0412947i
$875$	−8.25808e8	−	8.25808e8i	−1.23269	−	1.23269i
$876$		−	3.00745e6i		−	0.00447389i
$877$	5.99142e7			0.0888241			0.0444121	−	0.999013i	$-0.485859\pi$
$877$	5.99142e7			0.0888241			0.0444121	+	0.999013i	$0.485859\pi$
$878$		−	7.48829e8i		−	1.10637i
$879$			4.92391e7i			0.0725010i
$880$	−2.84925e7	−	2.84925e7i	−0.0418102	−	0.0418102i
$881$			3.00403e8i			0.439316i	0.975577	+	0.219658i	$0.0704941\pi$
$881$			3.00403e8i			0.439316i	−0.975577	+	0.219658i	$0.929506\pi$
$882$	5.69300e8	+	5.69300e8i	0.829727	+	0.829727i
$883$	−7.28935e8	−	7.28935e8i	−1.05878	−	1.05878i	−0.998161	−	0.0606219i	$-0.980692\pi$
$883$	−7.28935e8	−	7.28935e8i	−1.05878	−	1.05878i	−0.0606219	−	0.998161i	$-0.519308\pi$
$884$	9.02972e8			1.30713
$885$	1.57184e7			0.0226766
$886$	−3.26465e6	+	3.26465e6i	−0.00469392	+	0.00469392i
$887$			2.27806e8i			0.326434i	0.986590	+	0.163217i	$0.0521870\pi$
$887$			2.27806e8i			0.326434i	−0.986590	+	0.163217i	$0.947813\pi$
$888$	−1.27382e7	+	4.07080e7i	−0.0181915	+	0.0581355i
$889$	9.24971e8			1.31651
$890$	3.82156e8	+	3.82156e8i	0.542089	+	0.542089i
$891$		−	2.16779e8i		−	0.306467i
$892$			6.75224e7i			0.0951378i
$893$	3.94359e7	−	3.94359e7i	0.0553780	−	0.0553780i
$894$	7.53801e7	−	7.53801e7i	0.105498	−	0.105498i
$895$	−8.74690e8			−1.22007
$896$	7.40127e7	−	7.40127e7i	0.102892	−	0.102892i
$897$	−1.22009e8			−0.169050
$898$	−5.26780e8			−0.727446
$899$		−	2.49170e7i		−	0.0342939i
$900$	−1.78542e8			−0.244913
$901$	1.26588e8	−	1.26588e8i	0.173068	−	0.173068i
$902$	1.46156e8	+	1.46156e8i	0.199158	+	0.199158i
$903$	2.67677e8	+	2.67677e8i	0.363536	+	0.363536i
$904$	−2.45867e8			−0.332808
$905$	−1.55237e8	+	1.55237e8i	−0.209436	+	0.209436i
$906$	8.37904e7	+	8.37904e7i	0.112670	+	0.112670i
$907$	−2.01517e8	+	2.01517e8i	−0.270079	+	0.270079i	−0.829132	−	0.559053i	$-0.811165\pi$
$907$	−2.01517e8	+	2.01517e8i	−0.270079	+	0.270079i	0.559053	+	0.829132i	$0.311165\pi$
$908$	−3.18083e8	−	3.18083e8i	−0.424896	−	0.424896i
$909$		−	8.13136e7i		−	0.108261i
$910$	8.01181e8	−	8.01181e8i	1.06318	−	1.06318i
$911$	9.91925e8	−	9.91925e8i	1.31197	−	1.31197i	0.392007	−	0.919962i	$-0.371781\pi$
$911$	9.91925e8	−	9.91925e8i	1.31197	−	1.31197i	0.919962	−	0.392007i	$-0.128219\pi$
$912$	3.56951e6	+	3.56951e6i	0.00470570	+	0.00470570i
$913$		−	5.17410e7i		−	0.0679865i
$914$	−6.70336e7			−0.0877917
$915$		−	9.18907e7i		−	0.119952i
$916$			6.06854e8i			0.789583i
$917$	−1.39320e9	−	1.39320e9i	−1.80678	−	1.80678i
$918$		−	2.64495e8i		−	0.341893i
$919$	−5.79876e8	−	5.79876e8i	−0.747117	−	0.747117i	0.226819	−	0.973937i	$-0.427167\pi$
$919$	−5.79876e8	−	5.79876e8i	−0.747117	−	0.747117i	−0.973937	+	0.226819i	$0.927167\pi$
$920$	−7.32292e7	−	7.32292e7i	−0.0940418	−	0.0940418i
$921$	8.94674e7			0.114521
$922$	−2.23969e8			−0.285756
$923$	−1.34064e9	+	1.34064e9i	−1.70493	+	1.70493i
$924$			3.76038e7i			0.0476667i
$925$	3.53991e8	−	1.85253e8i	0.447267	−	0.234067i
$926$	5.53820e8			0.697486
$927$	1.04064e9	+	1.04064e9i	1.30636	+	1.30636i
$928$		−	1.17341e8i		−	0.146827i
$929$		−	8.81650e8i		−	1.09964i	−0.835285	−	0.549818i	$-0.814697\pi$
$929$		−	8.81650e8i		−	1.09964i	0.835285	−	0.549818i	$-0.185303\pi$
$930$	−2.01331e6	+	2.01331e6i	−0.00250300	+	0.00250300i
$931$	−1.50770e8	+	1.50770e8i	−0.186838	+	0.186838i
$932$	4.50331e8			0.556268
$933$	7.08730e7	−	7.08730e7i	0.0872641	−	0.0872641i
$934$	4.19023e8			0.514277
$935$	−2.75353e8			−0.336865
$936$		−	5.16350e8i		−	0.629676i
$937$	−1.24092e9			−1.50843			−0.754215	−	0.656627i	$-0.771983\pi$
$937$	−1.24092e9			−1.50843			−0.754215	+	0.656627i	$0.771983\pi$
$938$	9.47625e8	−	9.47625e8i	1.14823	−	1.14823i
$939$	7.23000e7	+	7.23000e7i	0.0873256	+	0.0873256i
$940$	1.04748e8	+	1.04748e8i	0.126114	+	0.126114i
$941$	3.40137e8			0.408211			0.204106	−	0.978949i	$-0.434571\pi$
$941$	3.40137e8			0.408211			0.204106	+	0.978949i	$0.434571\pi$
$942$	−3.17698e7	+	3.17698e7i	−0.0380068	+	0.0380068i
$943$	3.75640e8	+	3.75640e8i	0.447957	+	0.447957i
$944$	2.78140e7	−	2.78140e7i	0.0330634	−	0.0330634i
$945$	−2.34679e8	−	2.34679e8i	−0.278086	−	0.278086i
$946$		−	3.64686e8i		−	0.430770i
$947$	5.10039e8	−	5.10039e8i	0.600556	−	0.600556i	−0.339904	−	0.940460i	$-0.610394\pi$
$947$	5.10039e8	−	5.10039e8i	0.600556	−	0.600556i	0.940460	+	0.339904i	$0.110394\pi$
$948$	−2.36751e7	+	2.36751e7i	−0.0277886	+	0.0277886i
$949$	−5.76073e7	−	5.76073e7i	−0.0674029	−	0.0674029i
$950$		−	4.72840e7i		−	0.0551497i
$951$	−1.97340e7			−0.0229442
$952$		−	7.15265e8i		−	0.829002i
$953$			2.42837e7i			0.0280566i	0.999902	+	0.0140283i	$0.00446550\pi$
$953$			2.42837e7i			0.0280566i	−0.999902	+	0.0140283i	$0.995535\pi$
$954$	−7.23871e7	−	7.23871e7i	−0.0833712	−	0.0833712i
$955$		−	1.10573e9i		−	1.26952i
$956$	−2.11047e8	−	2.11047e8i	−0.241550	−	0.241550i
$957$	2.98088e7	+	2.98088e7i	0.0340102	+	0.0340102i
$958$	−9.45771e7			−0.107570
$959$	1.04533e9			1.18522
$960$	−9.48123e6	+	9.48123e6i	−0.0107164	+	0.0107164i
$961$		−	8.85991e8i		−	0.998295i
$962$	5.35759e8	+	1.02376e9i	0.601789	+	1.14993i
$963$	−4.50116e8			−0.504018
$964$	−3.99077e8	−	3.99077e8i	−0.445477	−	0.445477i
$965$			2.24262e8i			0.249560i
$966$			9.66464e7i			0.107215i
$967$	9.08688e8	−	9.08688e8i	1.00493	−	1.00493i	0.00494063	−	0.999988i	$-0.498427\pi$
$967$	9.08688e8	−	9.08688e8i	1.00493	−	1.00493i	0.999988	−	0.00494063i	$-0.00157266\pi$
$968$	−2.01144e8	+	2.01144e8i	−0.221759	+	0.221759i
$969$	3.44960e7			0.0379138
$970$	−2.89065e8	+	2.89065e8i	−0.316724	+	0.316724i
$971$	−1.44810e9			−1.58176			−0.790879	−	0.611973i	$-0.790376\pi$
$971$	−1.44810e9			−1.58176			−0.790879	+	0.611973i	$0.790376\pi$
$972$	−2.28010e8			−0.248288
$973$		−	8.32717e7i		−	0.0903980i
$974$	3.67591e8			0.397821
$975$	1.04628e8	−	1.04628e8i	0.112885	−	0.112885i
$976$	−1.62602e8	−	1.62602e8i	−0.174895	−	0.174895i
$977$	1.63465e8	+	1.63465e8i	0.175283	+	0.175283i	0.789296	−	0.614013i	$-0.210446\pi$
$977$	1.63465e8	+	1.63465e8i	0.175283	+	0.175283i	−0.614013	+	0.789296i	$0.710446\pi$
$978$	7.01617e7			0.0750039
$979$	−3.43574e8	+	3.43574e8i	−0.366162	+	0.366162i
$980$	−4.00471e8	−	4.00471e8i	−0.425493	−	0.425493i
$981$	−5.00447e8	+	5.00447e8i	−0.530092	+	0.530092i
$982$	5.36203e8	+	5.36203e8i	0.566233	+	0.566233i
$983$			7.18044e8i			0.755946i	0.925817	+	0.377973i	$0.123379\pi$
$983$			7.18044e8i			0.755946i	−0.925817	+	0.377973i	$0.876621\pi$
$984$	4.86353e7	−	4.86353e7i	0.0510465	−	0.0510465i
$985$	7.93797e8	−	7.93797e8i	0.830617	−	0.830617i
$986$	−5.66996e8	−	5.66996e8i	−0.591493	−	0.591493i
$987$		−	1.38245e8i		−	0.143780i
$988$	1.36747e8			0.141791
$989$		−	9.37289e8i		−	0.968913i
$990$			1.57456e8i			0.162276i
$991$	−5.45227e7	−	5.45227e7i	−0.0560217	−	0.0560217i	0.678541	−	0.734563i	$-0.262613\pi$
$991$	−5.45227e7	−	5.45227e7i	−0.0560217	−	0.0560217i	−0.734563	+	0.678541i	$0.762613\pi$
$992$			7.12517e6i			0.00729895i
$993$	−9.95626e7	−	9.95626e7i	−0.101683	−	0.101683i
$994$	1.06195e9	+	1.06195e9i	1.08130	+	1.08130i
$995$	−2.00801e8			−0.203843
$996$	−1.72175e7			−0.0174258
$997$	−2.73710e8	+	2.73710e8i	−0.276188	+	0.276188i	−0.831585	−	0.555397i	$-0.812566\pi$
$997$	−2.73710e8	+	2.73710e8i	−0.276188	+	0.276188i	0.555397	+	0.831585i	$0.312566\pi$
$998$		−	2.18697e8i		−	0.220014i
$999$	2.99875e8	−	1.56932e8i	0.300776	−	0.157404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.a.31.5	✓	18
37.6	odd	4	inner	74.7.d.a.43.5	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.a.31.5	✓	18	1.1	even	1	trivial
74.7.d.a.43.5	yes	18	37.6	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 4.00000i) q^{2} +4.65195i q^{3} +32.0000i q^{4} +(-62.1985 + 62.1985i) q^{5} +(-18.6078 + 18.6078i) q^{6} +564.672 q^{7} +(-128.000 + 128.000i) q^{8} +707.359 q^{9} +O(q^{10})\)	\(q+(4.00000 + 4.00000i) q^{2} +4.65195i q^{3} +32.0000i q^{4} +(-62.1985 + 62.1985i) q^{5} +(-18.6078 + 18.6078i) q^{6} +564.672 q^{7} +(-128.000 + 128.000i) q^{8} +707.359 q^{9} -497.588 q^{10} -447.353i q^{11} -148.862 q^{12} +(-2851.44 + 2851.44i) q^{13} +(2258.69 + 2258.69i) q^{14} +(-289.344 - 289.344i) q^{15} -1024.00 q^{16} +(-4948.00 + 4948.00i) q^{17} +(2829.44 + 2829.44i) q^{18} +(-749.331 + 749.331i) q^{19} +(-1990.35 - 1990.35i) q^{20} +2626.83i q^{21} +(1789.41 - 1789.41i) q^{22} +(4599.01 - 4599.01i) q^{23} +(-595.449 - 595.449i) q^{24} +7887.69i q^{25} -22811.5 q^{26} +6681.87i q^{27} +18069.5i q^{28} +(14323.9 + 14323.9i) q^{29} -2314.75i q^{30} +(-869.772 - 869.772i) q^{31} +(-4096.00 - 4096.00i) q^{32} +2081.06 q^{33} -39584.0 q^{34} +(-35121.8 + 35121.8i) q^{35} +22635.5i q^{36} +(-23486.3 - 44878.9i) q^{37} -5994.65 q^{38} +(-13264.7 - 13264.7i) q^{39} -15922.8i q^{40} +81678.3i q^{41} +(-10507.3 + 10507.3i) q^{42} +(101901. - 101901. i) q^{43} +14315.3 q^{44} +(-43996.7 + 43996.7i) q^{45} +36792.1 q^{46} -52628.1 q^{47} -4763.59i q^{48} +201206. q^{49} +(-31550.8 + 31550.8i) q^{50} +(-23017.8 - 23017.8i) q^{51} +(-91246.1 - 91246.1i) q^{52} -25583.6 q^{53} +(-26727.5 + 26727.5i) q^{54} +(27824.7 + 27824.7i) q^{55} +(-72278.1 + 72278.1i) q^{56} +(-3485.85 - 3485.85i) q^{57} +114591. i q^{58} +(-27162.1 + 27162.1i) q^{59} +(9259.01 - 9259.01i) q^{60} +(158791. + 158791. i) q^{61} -6958.18i q^{62} +399426. q^{63} -32768.0i q^{64} -354711. i q^{65} +(8324.24 + 8324.24i) q^{66} -419546. i q^{67} +(-158336. - 158336. i) q^{68} +(21394.4 + 21394.4i) q^{69} -280974. q^{70} +470162. q^{71} +(-90542.0 + 90542.0i) q^{72} +20202.9i q^{73} +(85570.5 - 273461. i) q^{74} -36693.1 q^{75} +(-23978.6 - 23978.6i) q^{76} -252608. i q^{77} -106118. i q^{78} +(159040. - 159040. i) q^{79} +(63691.3 - 63691.3i) q^{80} +484581. q^{81} +(-326713. + 326713. i) q^{82} +115661. q^{83} -84058.4 q^{84} -615517. i q^{85} +815209. q^{86} +(-66633.8 + 66633.8i) q^{87} +(57261.1 + 57261.1i) q^{88} +(-768017. - 768017. i) q^{89} -351974. q^{90} +(-1.61013e6 + 1.61013e6i) q^{91} +(147168. + 147168. i) q^{92} +(4046.13 - 4046.13i) q^{93} +(-210512. - 210512. i) q^{94} -93214.6i q^{95} +(19054.4 - 19054.4i) q^{96} +(580932. - 580932. i) q^{97} +(804824. + 804824. i) q^{98} -316439. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9 + 2352 * q^10 - 2048 * q^12 - 6766 * q^13 - 416 * q^14 - 2136 * q^15 - 18432 * q^16 - 9134 * q^17 - 16168 * q^18 + 7578 * q^19 + 9408 * q^20 + 8928 * q^22 - 50578 * q^23 - 8192 * q^24 - 54128 * q^26 - 42950 * q^29 - 17358 * q^31 - 73728 * q^32 - 11056 * q^33 - 73072 * q^34 + 62152 * q^35 - 238242 * q^37 + 60624 * q^38 + 31572 * q^39 + 229024 * q^42 - 65470 * q^43 + 71424 * q^44 - 482358 * q^45 - 404624 * q^46 + 232192 * q^47 + 791686 * q^49 + 93752 * q^50 - 386848 * q^51 - 216512 * q^52 + 49972 * q^53 - 144560 * q^54 + 160168 * q^55 + 13312 * q^56 + 488476 * q^57 - 181570 * q^59 + 68352 * q^60 + 508802 * q^61 + 404788 * q^63 - 44224 * q^66 - 292288 * q^68 + 604532 * q^69 + 497216 * q^70 - 202632 * q^71 + 517376 * q^72 - 1191224 * q^74 + 2476628 * q^75 + 242496 * q^76 + 1752858 * q^79 - 301056 * q^80 + 2760658 * q^81 - 145808 * q^82 + 2371616 * q^83 + 1832192 * q^84 - 523760 * q^86 - 4188080 * q^87 + 285696 * q^88 + 1148346 * q^89 - 3858864 * q^90 + 433120 * q^91 - 1618496 * q^92 + 1589664 * q^93 + 928768 * q^94 + 262144 * q^96 - 1670270 * q^97 + 3166744 * q^98

Introduction

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